FLIGHT CONTROL SYSTEMS practical issues In design and implementation

FLIGHT CONTROL SYSTE,,MS practical"

" issues In

design and implementation Edited by Roger W. Pratt

The Institution of Electrical Engineers

Copublished by: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts. SG1 2AY, United Kingdom and The American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive Suite 500 Reston VA 20191-4344 USA © 2000 Editorial selection and presentation: The Institution of Electrical Engineers For copyright ownership details see final page of each chapter. This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the Institution of Electrical Engineers (lEE) or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency or Copyright Clearance Centre Inc. Inquiries concerning reproduction outside those terms should be sent to the lEE at the address above. While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral right of the authors to be identified as authors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A CIP catalogue record for this book is available from the British Library ISBN 0 85296 766 7

Printed in England by TJ International, Padstow, Cornwall

To Gill, Joanne, Ian and Sara

Contributors

B.D. Caldwell Aerodynamics (W310C) British Aerospace Warton Aerodrome Preston PR4 lAX UK M.V° Cook Flight Test and Dynamics Group College of Aeronautics Cranfield University Cranfield, Bedfordshire MK43 0AL UK L.F. Faleiro Control Design Engineering Institute for Robotics and Mechatronics German Aerospace Center DLR Oberpfaffenhofen Postfach 1116 82234 Wessling Germany R,D. Felton 14 Cromwell Court Eynesbury St Neots, Cambs. PE19 2NZ UK J. Fenton Smiths Industries Aerospace Bishops Cleeve Cheltenham, Glos. GL52 4SF UK

C. Fielding Aerodynamics (W427D) British Aerospace Warton Aerodrome Preston PR4 lAX UK J. Hodgkinson 7022 Starstone Drive Rancho Palos Verdes, CA 90275 USA R.A. Hyde Cambridge Control Ltd Matrix House Cowley Park Cambridge CB4 0HH UK R. Luckner DaimlerChrysler Aerospace Airbus GmbH Flight Mechanics Flight Guidance and Control PO Box 95 01 09 D-21111 Hamburg Germany D.G. Mitchell Hoh Aeronautics Inc. Vista Verde Center 217 2075 Palos Verdes Drive North Lomita, CA 90717 USA

xiv

Contributors

R.W. Pratt Formerly: Department of Aeronautical and Automotive Engineering Loughborough University Loughborough UK Now with: Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK S.P. Ravenscroft

Flight Systems (W354C) British Aerospace Warton Aerodrome Preston PR4 lAX UK

T,D. Smith Flight Test (W27K) British Aerospace Warton Aerodrome Preston PR4 lAX UK R. Taylor Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK

Preface

If you belong to the school of thought that says 'give me a model and I'll give you a controller' then this book is not for you. If, however, you believe that using linear-control design methodologies to develop flight control laws requires a fuller understanding of the dynamics of the plant (aircraft), the problems associated with implementation and the n e e d to satisfy the requirements of a highly trained h u m a n operator (pilot) then the chapters in this b o o k should help you to develop that understanding. In essence, m u c h of this b o o k is a message to the academic researcher which says: ' I f your work is to be useful to practising engineers in industry, then you n e e d to understand, or at least appreciate, the issues dealt with in this book'. Additionally, young engineers who are beginning their careers in the aerospace industry should find it useful to have a coverage of the key aspects of flight control in a single volume T h e authors were chosen because of their depth of experience and mix of backgrounds, which I believe are reflected in their individual contributions. Additionally, in a n u m b e r of cases the chapters were reviewed by senior managers who have spent their entire careers in the aerospace industry. Hopefully, the experience which lies behind the individual contributions will encourage a new generation of engineers, mathematicians and scientists to b e c o m e involved in this exciting branch of e n g i n e e r i n g - - f l i g h t control systems. In the late seventies and eighties very few texts were p r o d u c e d on flight control. T h e n in the nineties a n u m b e r of books appeared. For readers who are new to flight control it might be useful to attempt to assign a place for this text in the total grouping. Fundamentals of the subject with varying degrees o f emphasis on aircraft dynamics and flight control are covered by a n u m b e r of texts [1-7]. All of these texts should be of use to u n d e r g r a d u a t e students in the final year or years of their courses, as well as to postgraduate students who are in the process of strengthening their knowledge of f u n d a m e n t a l concepts before immersing themselves in their specific topic. The texts by McLean [4] and Stevens and Lewis [7] will extend the r e a d e r ' s knowledge into the realms of research work. The contribution edited by Tischler [8] is significantly different from the other texts in that experienced practitioners, some of whom have contributed to this book, give a strong account of the state of the art, for rotorcraft, combat aircraft and fixed-wing transport

xvi

Preface

aircraft. Our text is seen as bridging the gap between the work on fundamental principles and Tischler's excellent collection of research reviews. The aim of this text is to build on the fundamentals of flight dynamics and flight control as described in References [ 1-7] and embellish these principles by assigning their relevance to the development of flight control systems in the aircraft industry. The first seven chapters cover most of the key areas within the discipline of flight control systems with explicit reference to recent development programmes written by engineers who were closely involved in the work. The last two chapters look at just two of the multitude of m o d e r n control methods which have been the subject of research studies. The text is largely restricted to military and civil fixed-wing aircraft. Only the constraint of space has prevented equivalent material for rotorcraft and missiles from being included. The book comprises nine chapters: Chapter 1 'Industrial considerations for flight control', Chris Fielding and Robert Luckner: the authors set the scene for the whole book by explaining the industry's perspective on flight control systems, giving a comprehensive overview of the subject with more detailed discussions of some particular topics being given in later chapters. The authors have carried through their chapter the parallel themes of military combat aircraft and civil aircraft, an interesting feature which strongly reflects their backgrounds. The Chapter begins by examining the general objectives of flight control and the role of the flight control system (FCS). This is followed by the operational requirements for both types of aircraft and a discussion of the benefits of fly-by-wire (FBW) in the pilot-vehicle system. The systems issues are explored, as are reliability and integrity, the twin versus--verification and validation. The Chapter is rounded off by a discussion of the state-of-the-art and a look at some exciting future developments. Chapter 2 'Aircraft modelling', Mike Cook: the author summarises from his own text [3] the main elements of axis systems and the equations of motion for the longitudinal and lateral dynamics of fixed-wing aircraft. Aircraftresponse transfer functions and state-space representations are then developed from the equations of motion. Any reader who requires a fuller treatment than can be given within the confines of this book is strongly r e c o m m e n d e d to refer to Mike's own text. Chapter 3 'Actuation systems', Steven Ravenscroft: since the advent of powered control surfaces without manual reversion, in the era of the Lightning, actuation systems have assumed great importance. The significance of actuation systems has been further enhanced by the drive to develop highly agile combat aircraft in which a safety-critical flight control system is required to stabilise the unstable open-loop dynamics of the aircraft. This comprehensive chapter begins with an overview of primary and secondary control surfaces and their operation and leads on to a discussion of performance criteria and modelling. The latter sections discuss more

Preface

xvii

advanced topics: nonlinear frequency response, saturation analysis, j u m p resonance and failure transients. Chapter 4 'Handling qualities', J o h n Hodgkinson and Dave Mitchell: uses the response transfer functions developed in Chapter 2 and examines the response of the aircraft from the pilot's viewpoint. The subjectivity which is inherent in the assessment of handling qualities has, inevitably, given rise to a n u m b e r of metrics and these are discussed in relation to the dynamic modes for the longitudinal and the lateral motion. This leads on to stability and control augmentation systems and a discussion of some control design concepts. Clearly, a chapter on handling qualities has to include a discussion of pilot-induced oscillations (PIOs). This topic is given a thorough and up-todate treatment which reflects the very recent research carried out in the United States. Chapter 5 'Automatic flight control system design considerations', J o h n Fenton: this chapter gives a clear and practical breakdown of the tasks which are necessary in the management of the development programme for a complex flight control system. The conciseness of the chapter stems from the detailed breakdown of the main areas, the development programme requirements definition and verification, system design considerations and AFCS architecture, into detailed subtasks. Chapter 6 'Ground and flight testing a digital flight control system', Terry Smith: discusses the techniques which have been employed by the UK's major aircraft manufacturer, British Aerospace, as it has progressed with the development of fly-by-wire combat aircraft. The chapter gives an excellent description of the need to progress a test programme in a way which minimises both risk and cost, from the philosophy, tools and techniques of flight testing through the elements of simulator and rig testing, ground testing and, of course, flight testing. Chapter 7 'Aeroservoelasticity', Brian Caldwell, Roger Pratt, Richard Taylor and Richard Felton: discusses how a safety-critical flight control system can be affected by the elastic behaviour of the aircraft structure, namely the p h e n o m e n o n of aeroservoelasticity or structural coupling. As with the previous chapter, the material draws on the experience gained at British Aerospace with a series of aircraft in which the open stability has been reduced to the point of severe instability in order to enhance manoeuvrability. The contributions from Richard Taylor and Richard Felton are based on the results of research programmes which were carried out at the Universities of Loughborough and Lancaster, respectively. Chapter 8 'Eigenstructure assignment', Lester Faleiro and Roger Pratt: represents one contribution to the work done u n d e r the GARTEUR Action Group on robust flight control in which a group of universities, research establishments and aircraft companies contributed u n d e r Jan Terlouw's (NLR) excellent stewardship. Eigenstructure assignment was chosen in this case because it appeared to offer a more visible methodology than other m o d e r n control techniques. The case study (RCAM) was based on a flight

xviii

Prefa~

profile for a civil aircraft which consisted of a base leg and a two-stage final approach. The chapter is intended as an honest assessment of eigenstructure assignment in this type of application. Chapter 9 'An H0~ loop-shaping design for the VAAC Harrier', Rick Hyde: describes one of the most exciting research programmes which has been carried out in the field of m o d e r n control engineering applied to flight control. H0~ designs were evaluated extensively by piloted simulation and on the VAAC Harrier at DERA Bedford where the controller was in competition with designs from British Aerospace and Smiths Industries. The early work benefited enormously from the rapport between Rick and the RAF's test pilot, Bj6rn Singer. A step-by-step guide is given to the linear loop-shaping design process with a clear description of the use of the knowledge of the aircraft's dynamics. This is followed by the work on implementation and flight testing which explains the approach that was taken to gain-schedule controllers, deal with antiwindup as well as describe the impressive results achieved during flight testing. I would like to thank George Irwin, co-editor for the series, for inviting me 'to write or edit a text of flight control': certainly, there have been moments when I have regretted yielding to George's Celtic persuasion. However, over twenty or so years I have benefited greatly from my association with the control community in the UK and, more recently, this has been equally true o f my association with the guidance, navigation and control activities within the AIAA in the United States and GARTEUR in Europe. My contribution to this book can be viewed as a partial repayment of a very large debt. Obviously, an edited text is the product of a team of authors. I have been extremely fortunate to be able to assemble a very strong team, but more than that, they have been great people to work with. Although, inevitably, experienced people have many calls on their time and from time to time this has caused the usual problems, everyone has come through and I have greatly appreciated their support and friendship throughout the preparation of the text. Additionally, I would like to thank the people who have volunteered to review individual chapters. Tony Lambregts (FAA) and Mike Walker (British Aerospace) are two people who are known to me, others have been acknowledged by individual authors. The process of publishing an edited text with several contributors is a demanding task. I have been extremely fortunate to work with Jonathan Simpson, then the IEE's commissioning editor for the project. Jonathan's quietly efficient style impressed me greatly and on many, many occasions I have been extremely grateful for his support and guidance. I would also like to thank Robin Mellors-Bourne, Director of Publishing, who managed the project in addition to his normal duties during a very difficult period and Sarah Daniels, Book Production Editor, who joined the project at a late stage and injected some much needed energy and enthusiasm. Finally, I would like to express my thanks to Penny Pilkington whose support and commitment I have greatly appreciated throughout this project.

Preface

xix

Penny has acted as the focal point for communications and retyped contributions and patiently, well mostly patiently, e n d u r e d the seemingly endless edits.

References [1] BABISTER, A.W.: 'Aircraft-dynamic stability and response' (Pergamon Press, 1980) [2] BLAKELOCK,J.H.: 'Automatic-control of aircraft and missiles' (Wiley, 1991, 2nd edn.) [3] COOK, M.V.: 'Flight dynamics: principles' (Arnold, 1997) [4] ETKINS, B, and REID, L.D.: 'Dynamics of flight: stability and control' (Wiley, 1996, 3rd edn.) [5] MCLEAN, D.: 'Automatic-flight control systems' (Prentice-Hall, 1990) [6] NELSON, R.C.: 'Flight stability and automatic control' (McGraw-Hill, 1998, 2nd edn.) [7] STEVENS, B.L., and LEWIS, EL.: 'Aircraft control and simulation' (Wiley, 1992) [8] TISCHLER, M.B. (Ed): 'Advances in aircraft flight control' (Taylor & Francis, 1996)

Nomenclature

A B

cg C

cL D

g G h

i, I

I= kq

k~ kw ko kr L m

M M

N N o

P q 1" $

t

state matrix input matrix centre of gravity output matrix drag coefficient lift coefficient direction cosine matrix; direct matrix acceleration due to gravity transfer function matrix height m o m e n t of inertia in roll m o m e n t of inertia in pitch m o m e n t of inertia in yaw identity matrix product of inertia about ox or oz axes pitch-rate transfer function gain constant axial-velocity transfer function gain constant normal-velocity transfer function gain constant pitch-attitude transfer function gain constant turbojet engine gain constant rolling m o m e n t mass pitching m o m e n t 'mass' matrix yawing m o m e n t n u m e r a t o r matrix origin of axes roll-rate perturbation pitch-rate perturbation yaw-rate perturbation Laplace operator time; maximum aerofoil section thickness roll-mode time constant

xxviii

U U

U /] V

V

W X X

X Y Y Y Z

Z

Re

%

A

7/ 0

I"

Nomenclature

spiral-mode time constant numerator zero in axial-velocity transfer function numerator zero in normal-velocity transfer function numerator zero in pitch-rate and attitude transfer functions turbojet engine time constant axial-velocity perurbation input vector total axial velocity axial component of steady-equilibrium velocity lateral-velocity perturbation eigenvector perturbed total velocity; total lateral velocity lateral component of steady-equilibrium velocity steady-equilibrium velocity normal-velocity perturbation total normal velocity normal component of steady-equilibrium velocity longitudinal coordinate in axis system state vector axial-force component lateral coordinate in axis system output vector lateral-force component normal coordinate in axis system normal-force component angle-of-attack or incidence perturbation equilibrium incidence sideslip angle perturbation equilibrium flight-path angle roll-control stick angle pitch-control stick angle rudder-pedal control angle transfer function denominator throttle-lever angle rudder-angle perturbation; damping ratio dutch-roll damping ratio phugoid damping ratio short-period pitching-oscillation damping ratio elevator-angle perturbation pitch-angle perturbation equilibrium pitch angle aileron-angle perturbation engine-thrust perturbation roll-angle perturbation

Nomenclature

¢ ~0 d f-On

% Ws

yaw-angle perturbation dutch-roll u n d a m p e d natural frequency d a m p e d natural frequency phugoid u n d a m p e d natural frequency short-period pitching-oscillation u n d a m p e d natural frequency

SUBSCRIPTS

0 b d e E p q r s u v w

free-stream flow conditions aeroplane body axes dutch roll equilibrium, steady or initial condition datum-path earth axes roll rate; phugoid pitch rate yaw rate; roll mode short-period pitching oscillation; spiral mode axial velocity lateral velocity aeroplane wind or stability axes; normal velocity

(

rudder elevator pitch ailerons thrust

0 ~-

EXAMPLES OF O T H E R SYMBOLS AND NOTATION xu

a shorthand notation to denote a concise derivative, a dimensional derivative divided by the appropriate mass or inertia parameters

.~

a shorthand notation to denote the dimensional Ou

N { (s)

a shorthand notation to denote a transfer function numerator polynomial relating the output response y to the input u

OX

xxix

Glossary of terms

Accident (aircraft): an unintended event that causes death, injury, environ-

mental or material damage Active control technology: the use of feedback control to enhance the performance or controllability and handling of a vehicle Actuator: physical device for producing motion and/or force Adaptive control: real-time parameter identification and controller update Aerodynamic derivative: partial derivative defining changes in vehicle force or moment due to changes in control or motion parameters Air data system: provides flight-condition and velocity vector information from external aircraft measurements Airworthiness: an all-embracing term to describe an aircraft's ability to fulfil its role safely Aliasing: phenomenon in digital systems in which input signal frequencies above half the sampling frequency appear at lower frequencies on the output signal, owing to the sampling process Analogue (computer): using electrical signals that are directly proportional (i.e. analogous) to a continuous physical parameter Angle of attack (AoA): the angle formed by the vector addition of the aircraft body-axis normal and longitudinal velocity components Anti-aliasing filter: function for reducing aliasing by restricting the bandwidth of the signal to be sampled--usually an analogue filter with a natural frequency set to less than half the sampling frequency Authority limit" permissible maximum amplitude of a signal or physical parameter Autopilot- outer-loop automatic control system for reducing pilot workload and/or augmenting weapon-system performance Autostabiliser: simple stability-augmentation system, usually to provide increased damping and often with limited authority Averaging (rolling average): digital process used to provide a smoothing and anti-aliasing function Backlash: a form of hysteresis found in mechanical systems Bandstop filter: see notch filter Bandwidth: range of frequencies over which the amplitude of the frequency response of a device remains essentially constant (numerical definitions vary)

Glossary of terms

xxi

Bode diagram: frequency-response plots covering gain (usually in decibels, dB) against frequency and phase against frequency Break point: frequency at which attenuation (or amplification) appears to occur, for the frequency response of a real pole or zero term Built-in test: checks that are carried out automatically on the system or part of the system by failure-detection algorithms within the flight control system. These checks may be carried out continuously or at specific instances, for example, on start-up Carefree handling: protection of aircraft from both departure and exceedance of loading limits, regardless of pilot-input demands, through the functionality of the flight control system Certification: process for demonstrating that system safety is satisfactory for flight operation Characteristic equation: polynomial defining the linear-stability characteristics of the system (defined by setting the denominator of a transfer function equal to zero) Classical control: range of design and analysis techniques developed early in the 20th century, principally the methods referred to as Bode, Nyquist, Nichols, R o o t - L o c u s . . . Clearance: see certification Closed-loop control: outputs from the aircraft (or system) are measured and fed back to provide corrective action Command path: part of control system between physical input (e.g. pilot's stick) and the point where feedback is applied Conditionally stable: a system that is stable only for a range of values of a particular gain; the system can be made unstable by either increasing or decreasing the nominal gain value by a sufficient amount Control-configured vehicle (CCV): one which incorporates the control system capabilities and limitations at the onset of the project design Control law: architecture containing controller(s), feedback filtering, nonlinear compensation and scheduling Controller: algorithm or filter to provide desired control behaviour, usually acting on an error signal Cooper-Harper rating: a method for quantifying pilot opinion of an aircraft handling task, in terms of perceived controllability and operational effectiveness Crossover frequency: gain crossover occurs when the gain of a system equals unity (0 dB); phase crossover occurs when the phase equal - 1 8 0 degrees. These are the frequencies at which the stability margins are measured Damping: attribute which determines the nature of a response, in terms of the rate of decay of oscillatory behaviour DC block: see high-pass filter Dead-beat (response): exhibiting no overshoot when tracking a step input signal

xxii

Glossary of terms

Dead-zone: nonlinearity in which no output is achieved until the input exceeds some threshold Decade: frequency interval in which the frequency changes by a factor of ten Decibel (riB): defined at each frequency as 101ogl0(g) where g is ratio of powers, or 201ogl0(g) if g is a ratio of voltages or signal amplitudes Defect: the nonconformance of an item to one or more of its required parameters, within the limits defined in the specification Derivative control/action: a function proportional to the rate of change of the applied signal (i.e. differentiation with respect to time) Describing function: approximation of nonlinear behaviour (amplitude dependence) of a system element, by modelling the gain and phase characteristics of the fundamental components of its Fourier transform Digital: described by a function of regularly sampled values Dissimilar redundancy: multiplex arrangement where different lanes use different software a n d / o r hardware to perform the same function Disturbance: an unwanted signal or force which can impair the quality of control Drop back: a reduction in attained angle, following the removal of an angular rate demand Duplex: having two hardware lanes operating in parallel, with crossmonitoring for detection of a single failure Error: a state, resulting from a fault or human mistake, which is liable to lead to incorrect operation Error signal: a control system signal equal to the calculated value between the parameter value commanded and that achieved Failure: an occurrence in which a previously acceptable item is no longer able to perform its required function within the limits defined in the specification Fault: see defect Feedback: signal generated by sensor and applied with the aim of corrective action Feedforward: signal from the command path which bypasses the controller to boost the downstream command to an actuator--improving transient response without affecting stability Flight control laws: control laws (or algorithms) within the flight control system which have broarder capabilities, for example, the monitoring of independent signal channels for possible failures Flight envelope: boundaries which define the limitations imposed on the operation of the aircraft defined in terms of altitude, airspeed/Mach number and load factor Flight management systems: system designed to assist the flight crew in managing the aircraft's systems, for example, fuel and navigational Fly-by-wire (light): connection between pilot's control column, yoke or inceptor made electrically (or by fibre optics) rather than by mechanical

Glossary of terms

xxiii

system consisting of rods, cables and levers Hying qualities: see handling qualities Frequency response: variation of an output signal magnitude and phase characteristics, relative to a sinusoidal input signal, as frequency varies Full authority: allowing the maximum useable range Full-state feedback: all the system states are used as feedback signals Functional requirements document: specification of function requirements (e.g. control laws) Gain: control law parameter for providing a signal-scaling capability Gain margin: the factor by which the gain may be increased or decreased before system instability results Gain schedule: variation of a gain or gains within a control law with respect to some measured scheduling variable (s) Governor: a mechanical system for regulating a controlled parameter Handling (or flying) qualities: piloting characteristics with respect to how easy or safe the aircraft is to fly (for a particular task) Hang-off (also hang-on): transient response characteristics whereby the commanded response fails to achieve its steady-state value within an acceptable time; is associated with undershoot, and with overshoot Hard-over: a failure that causes a control surface to rapidly drive its output to the authority limit Hazard: a state of the system, often following some initiating event, that can lead to an accident High-pass filter: attenuates low frequency signals, allowing high frequencies to pass Hysteresis: nonlinear function in which the i n p u t / o u t p u t relationship for increasing an input is different from that for decreasing the input Inceptor: physical device with variable force a n d / o r motion, for enabling pilot input to the flight control system. Examples might be a centre-stick control column, a side stick or a throttle lever Incidence: see angle-of-attack Incident: an event which results in equipment or property sustaining damage or any person receiving any injury, or which might have resulted in an accident Integrating filter: function for performing integral action on a signal Integrity: freedom from flaw or corruption (within acceptable limits) J u m p resonance: undesirable nonlinear saturation p h e n o m e n o n with a sudden j u m p in its frequency-response characteristics l a n e : a signal path containing all the hardware and functional elements of the control system within a multiplex arrangement Limited authority: having access to only part of the full range available Limit cycle: bounded amplitude and fixed-frequency oscillation of a system, involving nonlinear beahviour Line-replaceable unit or item: equipment fitted into an aircraft Linear system: having no nonlinearities; scaling any input signal scales all the

xxiv

Glossary of terms

outputs by the same factor; the principle of superposition applies Linear quadratic Gaussian (LQG): linear design method which uses a quadratic cost performance and Gaussian noise to determine optimum feedback gains Low-pass filter: function which attenuates high frequency signals but allows low frequency signals to pass Minimum phase: a system which has no zeros in the right half of the complex plane Mission-critical: loss of capability leading to possible reduction in mission effectiveness; compare with safety-critical Mode (FCS): a selectable function of the FCS, e.g. terrain following Modern control: a range of design and analysis techniques developed, generally considered as post 1960 Multi-input multi-output (MIMO) system: a system which has at least two inputs and at least two outputs. Often it is understood that the system possessses significant interaction or cross-coupling Multiplex: having several hardware lanes to enable detection and isolation of equipment failures Multivariable control: theory and techniques for addressing multi-input multi-output systems Natural frequency (damped): the frequency at which a system will tend to respond when excited by a sudden input Nichols chart: frequency response rectangular plot with gain in decibels (dB) plotted against phase in degrees and with frequency varying as a parameter. The chart contains contours of closed-loop gain and phase characteristics superimposed, assuming unity negative feedback Noise: usually, an unwanted signal corrupting the desired signal Nonlinearity: characteristic which introduces amplitude dependency into a system; linear behaviour is not preserved, in that the output magnitude no longer scales with the input Nouminimum phase: having zeros in the right-half complex plane Notch filter: function which produces attenuation over a specified frequency range, normally with minimal attenuation either below or above that range Nyquist diagram: a polar plot of a system's frequency response in the complex plane, with frequency varying as a parameter Open-loop: without the use of any feedback Order: the number of poles in the characteristic polynomial, remembering that a complex pair consists of two poles Overgearing: where the control system gains have been increased beyond the point of optimum performance Overshoot: transient response characteristic whereby the commanded response exceeds its steady-state; usually measured as a percentage Pad6 approximation: a transfer function technique for establishing a loworder approximation to exponential functions (e.g. to model pure time delays)

Glossary of terms

xxv

Phase: the relative angle between a sinusoidal input signal and the corresponding output signal Phase advance filter: function for providing a low frequency phase lead, at the expense of increasing high frequency gain Phase margin: the amount of phase lag (or advance) a system can tolerate before instability is reached Phase-plane analysis: rectangular plot of two system states, usually position and velocity, for analysing system behaviour, particularly when nonlinear characteristics are present Phase-retard filter: function for providing high frequency attenuation, with the associated phase loss being recovered at higher frequencies Pilot-induced oscillation (PIO): p h e n o m e n o n whereby the pilot inadvertently triggers and sustains an oscillation of the aircraft through a control input, owing to adverse coupling with the system dynamics Plant: a device which is to be controlled, for example, an aircraft Pole: real or complex root of transfer function denominator polynomial, sometimes referred to as an eigenvalue of the system Power spectrum: plot of power against frequency where power is defined as the square of the signal magnitude Primary controls: those controls which are fundamental for the safe operation of the system, for example, elevators, ailerons and rudder Proportional, integral and derivative: three-term controller with inherent phase advance and tracking capability Quadruplex: having four hardware lanes for detection and isolation of up to two identical failures Qualification: process for demonstrating that the system meets the customer's requirements Random failure: a failure which results from a variety of degradation mechanisms in the hardware Rate limit: physical or functional limit on rate of change of a parameter, of particular significance in actuation systems Reconfigurable control: redistribution of system functions or hardware following a failure, to maintain satisfactory operation Redundancy: duplication of components or software, to improve system integrity Regulator: a control system in which the design driver is satisfactory disturbance rejection, in order to hold some desired parameter value constant; command tracking is usually of secondary importance Reliability: the probability that a system will be free from faults Resonant frequency: frequency at which the ratio of the magnitudes of a system's output to input is a maximum Rise time: the time taken for the system response to a step input to change from ten per cent to ninety per cent of its steady-state value Risk: the combination of the frequency, or probability, and the consequence of an accident

xxvi

Glossaryof terms

Robustness: the ability of a system to tolerate variations in system parameters

without u n d u e degradation in performance Roll-off: rate of gain reduction at extremes of frequency (usually specified as d B / d e c a d e or dB/octave) Root locus: parametric plot showing variation of closed-loop poles, as a function of a particular system parameter, almost invariably but not essentially, to the controller gain Safe: the state in which the perceived risk is lower than the maximum acceptable risk Safety: the expectation that a system does not, under defined conditions, lead to a state in which human life is endangered Safety-critical: failure or design error could cause a risk to h u m a n life Sample and hold: device for producing an analogue signal from a series of discrete digital pulses Saturation: a state where authority limits, rate limits or acceleration limits are reached Secondary controls: those controls which are not essential for safe operation of the system, but are likely to result in degraded performance if they are not available (for example, flaps) Self-monitoring: capability of a lane of computing to detect its own failures Sensor: physical device for detection of inceptor positions, feedback measurements or scheduling information Servomechanism: control system, literally slave mechanism, in which the design driver is accurate tracking of a varying input signal and where disturbance rejection is usually of secondary importance Servovalve: a hydraulic device applied to a control valve or ram for switching the pressure and controlling the direction and magnitude of flow of hydraulic fluid Settling time: time taken for the c o m m a n d e d response to remain within a specified percentage, often five per cent, of its steady-state value Sideslip: the angle formed by the vector addition of the aircraft body-axis lateral and longitudinal plane velocity components Similar redundancy: multiplex arrangement where different lanes have identical software and hardware to perform the same function Single-input single-output (SISO): system which has only one input with one associated controlled output Stability margin: a measure of system stability--see gain margin and phase margin Validation: process of determining that the requirements are correct and complete Verification): evaluation of results of a process to ensure correctness and consistency with respect to the inputs and standards provided to that process C. Fielding and R. W. Pratt

Contents

Contributors Preface Glossary of terms Nomenclature 1 Industrial considerations for flight control C. Fielding and R. Luckner 1.1 Introduction 1.2 The general objectives of flight control 1.2.1 Military aircraft 1.2.2 Civil aircraft 1.3 The role of the flight control system 1.3.1 History 1.3.2 Military aircraft developments 1.3.3 Civil aircraft developments 1.4 Aircraft in-service requirements 1.4.1 Military aircraft operations 1.4.2 Civil aircraft operations 1.5 The benefits of fly-by-wire 1.5.1 Military aircraft benefits 1.5.2 Civil aircraft benefits 1.6 Flight control systems implementation 1.6.1 Military aircraft--design considerations and systems overview 1.6.2 Civil aircraft--design considerations and systems overview 1.7 Military aircraft--state-of-the-art and future challenges 1.7.1 Eurofighter Typhoon 1.7.2 Future challenges for military aircraft 1.8 Civil aircraft--state-of-the-art and future challenges 1.8.1 The Airbus fly-by-wire family 1.8.2 Boeing 777 1.8.3 Future challenges for civil aircraft 1.9 The flight control system development process 1.9.1 The current situation 1.9.2 The system development process 1.9.3 The flight control laws development process 1.9.4 Cost considerations--recurring and nonrecurring costs 1.10 Closing discussion 1.11 Acknowledgements 1.12 References 2 Aircraft modelling M. V. Cook 2.1 Introduction

xiii xxvfi

1 2 6 6 7 7 9 12 13 13 15 17 18 19 20 20 27 30 30 33 34 34 42 42 43 43 44 46 5O 51 53 53 56 56

Contents

viii 2.2 2.3

2.4

2.5

2.6

2.7

2.8 2.9 2.10

2.11

2.12 2.13

A mathematical framework Axes systems and notation 2.3.1 Earth axes 2.3.2 Aeroplane-body fixed axes 2.3.3 Perturbation variables 2.3.4 Angular relationships in symmetric flight 2.3.5 Choice of axes Euler angles and aeroplane attitude 2.4.1 Linear-quantities transformation 2.4.2 Angular velocities transformation Controls notation 2.5.1 Aerodynamic controls 2.5.2 Engine control The decoupled small-perturbation equations of motion 2.6.t The equations of longitudinal symmetric motion 2.6.2 The equations of lateral-directional asymmetric motion The equations of motion in state-space form 2.7.1 The equations of longitudinal motion 2.7.2 The equations of lateral-directional motion Aircraft-response transfer functions The transfer function matrix Longitudinal response to controls 2.10.1 The longitudinal transfer function matrix 2.10.2 The longitudinal characteristic equation 2.10.3 The short-period pitching oscillation 2.10.4 The phugoid Lateral-directional response to controls 2.11.1 The lateral transfer function matrix 2.11.2 The lateral-directional characteristic equation 2.11.3 The roll-subsidence mode 2.11.4 The spiral mode 2.11.5 The dutch-roll mode Conclusions Reference

3 Actuation systems

57 59 59 60 61 63 64 65 66 66 67 67 67 68 68 69 69 7O 72 72 73 74 74 76 76 79 81 81 84 85 86 87 89 89 9O

S. Ravenscroft 3.1 3.2 3.3

3.4 3.5 3.6 3.7 3.8 3.9 3.10

Introduction Actuation system technology--an overview 3.2.1 Control-surface types 3.2.2 Actuator operation Actuation system-performance criteria 3.3.1 Stall load 3.3.2 Maximum rate capability 3.3.3 Frequency response 3.3.4 Dynamic stiffness 3.3.5 Failure transients Actuation system modelling Nonlinear frequency response Saturation analysis J u m p resonance Failure transients Conclusions Acknowledgements

90 90 90 91 96 98 99 100 104 105 107 109 110 112 112 116 118

Contents 4 Handling qualities

ix

119

J. Hodgkinson and D. Mitchell 4.1 4.2

Introduction Longitudinal flying qualities 4.2.1 Control-input transfer functions 4.2.2 Modal criteria 4.2.3 Phugoid flying qualities 4.2.4 Short-period flying qualities 4.2.5 Criteria for the longitudinal short-period dynamics 4.2.6 Model criteria for the short period 4.2.7 Other short-period criteria 4.2.8 Equivalent systems 4.2.9 Equivalent time delay 4.2.10 The bandwidth method 4.2.11 The Neal-Smith method 4.2.12 Gibson's dropback criterion 4.2.13 Time-history criteria 4.2.14 Flight-path stability 4.3 Lateral-directional flying qualities 4.3.1 Roll mode 4.3.2 Spiral mode 4.3.3 Coupled-roll spiral 4.3.4 Dutch-roll mode 4.3.5 The parameter t%/~a 4.3.6 Phi-to-beta ratio, ~b//3 4.4 Stability and control-augmentation systems 4.4.1 The influence of feedback 4.4.2 The influence of actuators, sensors and processors 4.4.3 Multiple-input, multiple-output flying quality possibilities 4.4.4 Response types 4.5 Notes on some control design concepts 4.5.1 Integration in the forward path 4.5.2 Notch filters 4.5.3 Stick prefilters 4.5.4 Model prefilters 4.6 Pilot-induced oscillations ( P i t s ) 4.6.1 P I t categories 4.6.2 P I t and APC 4.6.3 Criteria for category I P i t s 4.7 Modal P I t criteria 4.7.1 STI high-gain asymptote parameter 4.7.2 A'Harrah-Siewert criteria 4.7.3 Dynamic stick force per g 4.8 Non-modal P I t criteria 4.8.1 Some current criteria 4.8.2 Effectiveness of the criteria 4.9 Effects of rate limiting on P I t 4.9.1 Criteria for category II P i t s 4.9.2 The consequences of rate limiting 4.10 Concluding remarks 4.11 References

119 121 121 121 122 123 124 126 126 127 131 132 132 134 134 136 136 136 139 139 139 140 141 142 142 144 146 147 147 147 149 150 150 150 150 151 151 152 152 155 155 155 156 161 164 164 165 167 167

x

Contents

5 Automatic flight control system design considerations

170

J. Fenton

5.1 AFCS development programme 5.1.1 Study phase/vendor selection 5.1.2 Interface definition 5.1.3 System definition 5.1.4 Software design and code 5.1.5 Hardware design and development 5.1.6 System integration and test 5.1.7 Qualification testing 5.1.8 Preliminary (final) declaration of design and performance (PDDP/FDDP) 5.1.9 Flight testing 5.1.10 Certification 5.1.11 Design reviews 5.2 Requirements definition and verification 5.2.1 Introduction 5.2.2 Design and test methodology 5.2.3 Safety considerations 5.3 System design considerations 5.3.1 Primary considerations 5.4 AFCS architecture 5.4.1 Introduction 5.4.2 AFCS flying control interfaces 5.4.3 AFCS system interfaces 5.4.4 AFCS configurations 5.4.5 Flight control computer data processing 6 Ground and flight testing of digital flight control systems

170 170 172 172 172 172 172 173 173 173 173 173 174 174 175 176 178 178 184 184 184 184 188 189

197

7: Smith

6.1 Introduction 6.2 Philosophy of flight testing 6.2.1 Ground testing 6.2.2 Simulator and rig testing 6.3 Aircraft ground testing 6.3.1 FCS build tests 6.3.2 Ground-resonance tests 6.3.3 Structural-coupling tests 6.3.4 Electromagnetic-compatibility testing 6.3.5 Engine-running tests 6.4 Flight test tools and techniques 6.5 Flight testing 6.5.1 FBWJaguar demonstrator flight test programme 6.5.2 The EAP demonstrator flight test programme 6.6 Conclusion 6.7 Acknowledgements 6.8 References

7 Aeroservoelasticity

197 2O0 201 202 209 210 210 210 211 213 213 214 214 217 223 223 223

225

B.D. CaldweU, R. W. Pratt, tL Taylor and R.D. Felton

7.1 Introduction 7.2 Elements of structural coupling 7.2.1 Flexible-aircraft modal dynamics

225 226 226

Contents

7.3

7.4

7.5 7.6

7.2.2 Inertial excitation of the flexible-aircraft control surface 7.2.3 Actuators, flight control computers and the aircraft-motion sensor unit 7.2.4 Aerodynamic excitation of the flexible-aircraft's control surface 7.2.5 Flexible-aircraft modal aerodynamics 7.2.6 Formulation for solution and design trade-offs FCS-SC structural coupling: design examples 7.3.1 Jaguar-first flight 1968 7.3.2 Tornado-first flight 1974 7.3.3 Experimental aircraft programme (EAP)--first flight 1986 7.3.4 Eurofighter 2000 (EF2000)--first flight 1994 Future developments 7.4.1 Limit-cycle prediction and specification of alternative clearance requirements 7.4.2 Active control for rigid body and structural-mode stabilisation 7.4.3 Flexible aircraft modelling Conclusions References

8 Eigens~ucture assignment applied to the design of an autopilot function for a civil aircraft L.F. Faleiro and R. W. Pratt

8.1 Introduction 8.2 The RCAM control problem 8.2.1 A landing-approach simulation 8.2.2 Performance specifications 8.2.3 Robustness specifications 8.2.4 Ride-quality specifications 8.2.5 Safety specifications 8.2.6 Control-activity specifications 8.3 Eigenstructure analysis and assignment 8.3.1 Eigenstructure analysis 8.3.2 Eigenstructure assignment 8.4 The eigenstructure assignment design cycle 8.4.1 Controller structure 8.4.2 Construction of a desired eigenstructure 8.4.3 Initial synthesis 8.4.4 Methods of controller analysis 8.4.5 Analysis of the longitudinal controller 8.4.6 Analysis of the lateral controller 8.4.70ptimisation of the controllers 8.5 Nonlinear simulation of the controlled aircraft 8.5.1 Performance specifications 8.5.2 Robustness specifications 8.5.3 Ride-quality specifications 8.5.4 Safety specifications 8.5.5 Control-activity specifications 8.5.6 Evaluation using a landing-approach simulation 8.6 Conclusions 8.7 References 9 An H ® loop-shaping design for the VAAC Harrier R.A. Hyde

9.1 Introduction

xi 226 228 230 230 230 234 235 236 237 248 260 260 284 297 298 299 301

301 302 304 305 306 306 306 307 307 307 310 316 316 320 324 324 327 329 330 331 333 337 337 338 338 339 343 346 348

348

xii

Contents

9.2 9.3 9.4 9.5

The VAAC Harrier Ha Loop shaping Linear design for the VAC Implementation and flight testing 9.5.1 Gain scheduling 9.5.2 Anti-windup 9.5.3 Flight modes 9.5.4 Flight testing 9.6 Flight clearance 9.7 The way ahead 9.8 References

350 350 354 359 359 360 362 364 366 371 372

Index

375

Chapter 3

Actuation systems S. Ravenscroft

3.1 Introduction Actuation systems are a vital link in the flight control system, providing the motive force necessary to move flight control surfaces. Whether it is a primary flight control, such as an elevator, rudder, taileron, spoiler or foreplane, or a secondary flight control, such as a leading edge slat, trailing edge flap, air intake or airbrake, some means of moving the surface is necessary. Performance of the actuator can have a significant influence on overall aircraft performance and the implications of actuator performance on aircraft control at all operating conditions must be considered during flightcontrol system design and development programmes. Overall aircraft p e r f o r m a n c e requirements will dictate actuator performance requirements, which can lead to difficult design, control and manufacturing problems in their own right. In this chapter an overview of current actuation system technologies as applied to m o d e r n combat aircraft is presented, and their performance and control requirements are discussed. The implications for aircraft control are considered and an overview of selected modelling and analysis methods is presented.

3.2 Actuation system technologyman overview

3.2.1 Control-surface types Aircraft have a n u m b e r of different flying control surfaces. Some are for primary flight control (control of roll, pitch and yaw manoeuvring and stabilisation) and others are secondary controls (high-lift or lift-dump devices, for example). The type and use of a control surface has a significant impact on the requirements for the actuation system for that surface, in particular the actuator post-failure operation. Primary flight control capability is critical to safety and loss of control in one or more of the primary flight control axes will, in most cases, hazard the © 1999 British Aerospace PLC. Reproduced with permission.

Actuation systems 91 aircraft. The advent of concepts such as active control technology, controlconfigured vehicles and relaxed static stability, resulting in highly unstable combat aircraft to improve performance and agility, have led to an even greater reliance on primary flight control surface availability to the extent that many m o d e r n combat aircraft could not be controlled without the continued operation of the primary flight control surfaces. Accepting that failures within an actuator are inevitable at some time in the life of a fleet of aircraft, the actuation systems for primary flight control of such aircraft are designed to comply with a fail-op-fail-op philosophy; that is the actuator will continue to operate at, or very close to, full performance following one or two failures to meet the safety and integrity requirements. For many secondary control surfaces, it is not necessary to ensure full operation following failures. Although the loss of operation of a secondary surface may introduce flight restrictions, such as requiring a flapless landing or limiting the maximum incidence angle the aircraft can achieve, these will not directly lead to the loss of an aircraft. However, the nature of the failure may, in itself, produce a hazardous situation, such as possible engine flameout if air-intake cowls fail in a closed position, or handling and speed restrictions if an airbrake fails in the open position. In such cases a fail-op-failsafe or simply fail-safe philosophy is used, where one design feature is to ensure that the secondary control surface can be moved to a safe position or simply frozen following a failure. In the examples given above, the actuators may be required to open the intake cowl or close the airbrake following a failure, albeit at a lower rate than would normally be achieved. A similar philosophy exists for landing gear, where the safe state is gear down; the actuators have an extend only capability following loss of normal extend and retract functions. Although secondary flight controls are, of course, very important components of an aircraft and the provision of emergency operation modes can produce interesting engineering challenges, it is the primary flight control actuators that have most influence on basic aircraft stabilisation and handling qualities. T h r o u g h o u t the remainder of this chapter we will concentrate primarily on actuators for primary flight control surfaces.

3.2.2 Actuator operation Most flight control actuation systems on current aircraft are electrically or mechanically signalled and hydraulically powered. Until the early 1970s most actuators were mechanically signalled, but the advent of fly-by-wire technology has led to many actuators now having electrical signalling as the primary, if not only, form of demand. The d e m a n d signal is used to drive a spool valve, opening ports through which high-pressure hydraulic fluid flows. The fluid is metered to the actuator ram, causing the piston rod to extend or retract and providing the force to move the control surface. Movement of the spool valve could be achieved by mechanical input, using mechanical feedback of

92

Flight control systems

actuator r a m position to close the valve when the actuator reaches the d e m a n d e d position; by hydraulic means, using an electrohydraulic servo valve, in effect a mini actuator, to drive the spool; or, as is b e c o m i n g m o r e c o m m o n , by a direct m o t o r drive. These concepts are shown diagramatically in Figure :3.1. Redundancy features such as the n u m b e r of servo valves or m o t o r coils and bypass valves are not shown in this figure. A typical actuator with servo valves providing the motive force for a t a n d e m main control spool valve is shown in Figure 3.2. This particular actuator configuration uses four servo valves to drive the main control (spool) valve, each signalled by one of four flight control computers, four linear variable differential transformers (LVDTs) to measure main-ram displacement and four LVDTs to measure main-control-valve displacement, producing a q u a d r u p l e x r e d u n d a n t actuator. By comparing each of the four signals up to two failed lanes may be isolated, one lane at a time, by a majority vote, to m e e t system safety requirements. Post-failure operation requirements have a significant effect on actuator design philosophy. Redundancy is necessary in primary actuators to ensure continued operation following a failure to m e e t the fail-op-fail-op requirement. This often takes the f o r m of multiplexing, or the addition of a n u m b e r o f identical lanes of control. For example, in the Eurofighter 2000 primary flight control actuators, all feedback sensors are quadruplexed, each o f the four sensors feeding their signal back to one of four flight control c o m p u t e r s (FCCs). T h e four FCCs c o m p a r e signals across a cross-channel data link, to identify whether any of the signals differ significantly from the others. A consolidated or average signal is p r o d u c e d for use in control and m o n i t o r i n g algorithms and each FCC produces an actuator drive signal to one of the four coils in the direct drive valve m o t o r which moves the main control valve to control the t a n d e m actuator. A typical actuator with a direct m o t o r drive for first stage actuation is shown in Figure 3.3. Whereas the Eurofighter 9000 actuators use a linear m o t o r to displace the main control valve, this actuator uses a rotary, brushless DC motor, rotary motion being converted to linear motion through a crank mechanism. A further difference from the Eurofighter 2000 q u a d r u p l e x actuator is the use o f a triplex architecture, with only three coils in the direct drive m o t o r and three feedback sensors (LVDTs) for each main control valve and main ram. For a triplex actuator to survive two similar but i n d e p e n d e n t electrical failures to achieve fail-op-fail-op some element of in-lane fault detection, rather than simply a majority vote between lanes, is needed, for example comparison with a model. T h e level of redundancy refers to the n u m b e r of electrical lanes used and not the n u m b e r of hydraulic supplies. The actuators depicted in Figures 3.2 and 3.3 b o t h use two i n d e p e n d e n t hydraulic supplies with an actuator r a m of t a n d e m construction. In order to maintain separation of the two hydraulic systems the actuator design must minimise, if not eliminate, leakage of fluid between systems and a rip-stop ram design is used to ensure that fatigue

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damage in one side of the cylinder will not cause a crack which will also damage the other side of the cylinder, leading to the potential loss of both hydraulic systems. Following a failure in one of the hydraulic supplies, the remaining hydraulic system will continue to provide enough power to move the actuator against air loads. However, the movement of the ram will cause hydraulic fluid to be pushed into and out of the cylinders on the side o f the failed hydraulic supply, which could cause a drag force to restrict movement of the ram. In order to overcome this drag force, bypass valves are fitted to the actuator in Figure 3.3, to connect each side of the piston in the affected cylinder together in the event of loss of hydraulic pressure. Control of actuator position is achieved with a closed-loop, feedback control system. Ram position is measured, often using an LVDT, although potentiometers or other devices could also be used. Main-control-valve position, which is roughly proportional to ram velocity (excluding the effects o f external loads on the ram, or the effects of nonlinear valve port shapes), is also measured to give improved damping characteristics. Loop closure could be p e r f o r m e d in analogue circuitry, but is more often implemented, at least in part, in digital computers. Typical control loops, for an actuator with servo valves for main valve actuation, are depicted in block diagram form in Figure 3.4. The inner (spool position) loop is analogue, as the high bandwidth of this loop would necessitate a very high sampling rate. In this case outer-loop closure is p e r f o r m e d digitally, with feedback signals sampled at 80 Hz. In analysing the performance characteristics of the actuator it is important not to neglect the effects of digital control, including sample and computational delays, which have an effect on loop stability and actuator frequency response, and nonlinear effects caused by sampling, which can cause such effects as dither.

3.3 Actuation system-performance

criteria

An essential part of a specification for an actuation system is the definition of the system-performance requirements as these requirements will be a primary consideration for the supplier throughout the design phase. Before the airframe manufacturer accepts an actuation system the supplier must demonstrate that the specified performance requirements have been met. With long-lead-time items such as actuation systems and considering the expense involved in the testing of hardware or of modifications late in the design cycle, modelling is an important part of performance assessment both for the supplier and the airframe manufacturer. A primary flight control actuation system has to provide the necessary speed and power of control-surface response to give the aircraft the required stability and manoeuvrability. The basic performance requirements are: • the actuation system should be able to move the control surfaces with a following or opposing load, while maintaining a rate of movement

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adequate for control purposes; • the actuation system should be able to hold the control surface at a required position with a load applied in either direction up to a defined maximum-load magnitude; • the effect of the actuation-system frequency-response characteristics (gain and phase lag) on low frequency (rigid aircraft) FCS loop stability margins should be minimised; • interaction with high frequency (flexible aircraft) vibration modes should be minimised. In addition, requirements for system reliability and integrity, size, weight and installation details and the appropriate technology level have to be considered, in as far as these will have an impact on the actuation system performance. Particular performance requirements that will be considered now in more detail are: • • • • •

stall load; maximum rate capability; frequency response; dynamic stiffness; failure transients.

3. 3.1 Stall load The stall load of an actuator is the maximum force applied directly onto the main ram that can be supported by the available hydraulic supply pressure before the ram will begin to sink. The load can be in either direction (extend or retract) and the criteria will apply equally for both. The stall load is a basic design parameter for the actuator ram and determines the required piston area for a given hydraulic supply pressure available at the actuator. Requirements on the actuator's load capability are usually defined as: • minimum required output thrust (two systems operating with a defined pressure drop across each piston); • minimum single-system thrust (with a defined pressure drop across the pressurised piston, the other being bypassed); • maximum static-output thrust (two systems operating with a defined pressure drop across each piston). These requirements are used by the supplier to determine the size of the actuators within the limitations set by the available standard hydraulic seal sizes. The first two will determine the minimum size (and in particular piston area) to meet load and performance requirements, and the third sets an u p p e r limit on the size to prevent damage to aircraft structure. The magnitude of the design stall load will be based on the maximum aerodynamic hinge m o m e n t predicted at any point in the flight envelope.

Actuation systems 99 This maximum estimated value may be factored upwards to provide the required design stall load. This additional factor is required to ensure that there is sufficient excess capability in the actuator to provide manoeuvring forces in the most severe flight conditions. For unstable aircraft, the loadcarrying capability will be defined such that the maximum load experienced in flight will be no greater than 70 per cent of the single-system stall load, in order to ensure that there is always adequate rate capability for control purposes (following a hydraulic system failure), to maintain control o f the aircraft u n d e r the most adverse conditions. If the aircraft is stable then the maximum flight load may only be slightly less than the single-system stall load on the basis that recovery can be made to a flight condition where thrust capability is adequate. The primary factors affecting the stall load are: • piston area; • hydraulic supply pressure; • n u m b e r of hydraulic systems operating. Secondary factors are: • unequal piston areas on each side of the piston; • force fight in a tandem ram configuration; • cross-piston leakage. When a force is applied that exceeds the stall load the pressure required to support the load is greater than that which is available from the hydraulic supply, the ram stalls and tends to sink and the outer-loop feedback will try to compensate. The dynamic behaviour at this point can potentially be predicted by an actuator model, although post-stall behaviour is not normally regarded as being of significance for performance assessment. When the ram sinks u n d e r the applied stall load a hydraulic flow back through the valve ports against the supply is implied. Because of the main-ram position feedback control the main valve will move hard over to its maximum travel when the ram sinks, so the ports will be fully open for this reverse flow. Some actuation systems are provisioned with non-return valves which prevent reverse flow through the valve ports. If reverse flow is allowed then the sinkage of the ram reduces the static stiffness effectively to zero beyond the stall, causes the normal hydraulic pressure maxima to be exceeded and may even r e n d e r the aircraft uncontrollable.

3.3.2 Maximum rate capability Rate requirements are defined as a required rate, extending and retracting, for a given load and pressure differential across the piston. The required rates are usually defined at no-load conditions and about 60 to 70 per cent of the stall load, for two-system and single-system operation. The supplier uses the rate requirements, along with size information derived from consideration of

100

Flightcontrolsystems

the loading requirements, to d e t e r m i n e the fluid flow needed, and h e n c e the necessary valve size. T h e m a x i m u m rate at which the actuator main ram can be driven corresponds to the m a x i m u m opening of the valve ports. T h e m a x i m u m rate is reduced when the actuator is required to move against the load and increased when required to move with the load. A steady load will be present in practice when a control surface has to be deflected against the airflow, either for a steady manoeuvre or a trim requirement. T h e factors affecting the m a x i m u m rate capability are: • • • • • •

steady load; supply and return pressures; n u m b e r of operating hydraulic systems; piston areas; main-valve p o r t geometry; m a x i m u m main-valve displacement; • cross-piston leakage; • valve-block pressure losses.

From a p e r f o r m a n c e point of view the m a x i m u m rate capability must be sufficient to move the aerodynamic control surface at a speed which is required to give satisfactory pilot-handling qualities. Also, the requirements of automatic flight control systems, including any active control feedback functions where control rate is a factor, must be taken into account, since stability of the aircraft control loops u n d e r large-amplitude motions may be affected by the rate limit. T h e hydraulic supply pressure at the actuator must be maintained close to the nominal design level in order to maintain the m a x i m u m rate capability, as well as other actuation system p e r f o r m a n c e parameters. This must be taken into account when specifying the aircraft hydraulic system supply, including the pumps, accumulators and hydraulic pipe pressure losses at m a x i m u m flow. Figure 3.5 shows a typical plot of m a x i m u m rate capability as a function of steady external load, up to stall conditions for each direction of main-valve opening. The effect on m a x i m u m rate of a cross-piston leak is also given on the plot. With a cross-piston leak there are areas of operation with high steady load for which the main ram will sink against the d e m a n d e d direction as fluid drains across the piston. This should be avoided in an actuation system design by ensuring that valve port size and piston areas are adequate to prevent sink for all operating conditions, taking cross-piston leakage into consideration.

3.3.3 Frequency response Requirements for the actuation-system frequency response u n d e r particular test conditions, e.g. load, amplitude, m e t h o d of loop closure, are defined in the specification d o c u m e n t as boundaries within which the frequency

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response must lie. The gain and phase-lag boundaries are applied to the response of the ram-to-body displacement to an input d e m a n d with representative control-surface inertia loading. An example of typical gain and phase boundaries applied to a fly-by-wire actuation system is shown in Figure 3.6. Bounds are placed on the maximum and minimum gain and on the maximum allowable phase lag, and a particular range of d e m a n d amplitudes is defined to encompass the linear range of operation of the actuation system. The frequency-response boundaries are used by actuator suppliers to assist in determining the distribution of gain around the control loop along with other criteria such as hysteresis, failure transients and valve port size and shape. Frequency-response boundaries are defined to ensure that the effects of the actuator on low frequency (rigid aircraft) modes are minimised with the ram movement to demanded-movement gain of approximately 0 dB and the phase lag at a minimum, while providing sufficient gain roll-off at high frequencies to reduce interaction with aircraft and control-surface structural vibration (flexible aircraft) modes. It should be noted that the gain and phase boundaries are to be respected when control-surface structural modes are included, so it is usually the case that output inertia loading will have to be modelled. T h e frequency response of the actuation system is a very important consideration, since this is a significant measure of the actuation system performance. The total actuation system is normally a fairly high-order system with as many as 12 state variables for a well-specified model (based on current experience), depending on the degree of detail required for analysis. Nevertheless the basic response is a first-order lag resulting from the integration of valve flow (proportional to main-ram velocity), coupled with ram-position feedback. All other states correspond to higher frequency effects such as servo valve or direct-drive valve and inner-loop dynamics, filters, sensors and inertial loads. The basic design and build quality of the actuator is aimed at achieving the required performance for the specified range of frequencies and amplitudes. It is invariably intended that the characteristics are as close to linear as possible. The basic first-order response is the primary factor in determining the actuation-system response bandwidth. The higher-order terms cause variations from the basic response, and can result in undesirable resonances which amplify response at some frequencies. Such linear properties will be evident t h r o u g h o u t the broad mid-range of amplitudes. In specifying the required performance it is necessary to set frequencyresponse gain and phase-lag boundaries which must not be violated and meeting these criteria will determine the feedback control gain, whether electrical or mechanical. Variations from linearity occur t h r o u g h o u t the working range, but these are normally small enough to be acceptable; it is at extremes of input amplitude that significant deviations from linearity become evident on the frequency response.

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The upper-gain boundary is aimed primarily at the linear-system characteristics, to avoid the presence in the system of any excessive resonances. It applies to all amplitudes. The lower gain boundaries apply for very small levels of input excitation and different boundaries are specified for different amplitudes. These levels are taken to correspond with the amplitudes to be applied in the actuation-system tests. The factors affecting low amplitude response are ram and valve friction, valve laps and leakage, hysteresis, electrical tolerances and bearing backlash. Meeting these boundaries will determine the degree of refinement required in manufacturing accuracy of valve ports, ram friction, bearings, components etc. Phase boundaries apply only to maximum allowable phase lag, whether at low or high amplitude. The high-amplitude boundary is intended to define the performance required for the main linear range of operation. Satisfying the phase-lag criterion is important for the flight control system, which is designed assuming a specified standard of actuation-system performance. The usual single number quoted for the actuation system in this regard for comparison purposes is the phase lag at 1 Hz, this being a typical frequency associated with aircraft-handling qualities for pilot control. The large amplitude gain and phase boundaries discussed above can be assumed to apply for the stated amplitudes up to the amplitudes that will result in main-ram rate limiting. No frequency response criteria are specified for very large amplitude inputs that will cause the valve to open to its full extent. The frequency-response boundaries of Figure 3.6 assume that the input is applied directly as an analogue demand. If the input is digital, as when the d e m a n d is injected into a digital computer, then an additional phase lag is incurred in the input path, so the boundaries as shown are no longer applicable and a modified set of boundaries is required. Although it is necessary to meet the gain and phase requirements when the actuator is controlled by the digital flight control computer, it may not be possible for the actuator supplier to test the equipment in this configuration, particularly during the early development stages of an aircraft programme. In practice, a set of frequency-response boundaries is specified covering digital loop-closure methods (the requirement for aircraft control) and analogue loop-closure methods (to allow the supplier to test the actuator before a flight control computer becomes available). Failure cases and external loading conditions are also considered.

3.3. 4 Dynamic stiffness Dynamic stiffness, or impedance, is the ability of the actuator to resist an external oscillatory load, that is, to act as an effective spring and damper. Impedance characteristics are measured by installing the actuator in a suitable test rig, applying a steady load to the ram if required, then applying an incremental oscillatory load at a range of frequencies and measuring

Actuation systems 105 incremental ram displacement relative to jack body. Results are presented as dynamic stiffness, in real and imaginary form representing stiffness and damping respectively, with the units force/displacement ( N / m or lb/in). Impedance requirements are defined in the actuation-system specification as boundaries within which the measured impedance must lie. Typical impedance boundaries, based on those used for a previous fly-by-wire aircraft project, are shown in Figure 3.7. Test conditions are defined, including requirements on steady-load and oscillatory-force amplitude. Impedance considerations will influence actuator sizing and possibly the reversion modes following failures. The criteria usually specified for impedance are based on the need to avoid control-surface flutter. There are no specific criteria set out for the lower frequency range associated with flight control system design, as the impedance which is present in the basic design is generally sufficient and no design constraints need be imposed. At the higher frequencies associated with flutter it may be critical that the actuation system contributes enough stiffness, in conjunction with the stiffness of the back up structure, to the control-surface rotation mode so that the flutter-speed margins are met. The margins with a fully operational actuation system will be greater than when failures are present. When a hydraulic system fails the r a m / b o d y impedance is more or less halved and the impedance boundaries are relaxed. The overall impedance includes the effects of attachment and o u t p u t structural stiffness and so will not be halved when a hydraulic system fails. If the structural stiffnesses are very high relative to the actuator r a m / b o d y impedance, then the overall impedance will be almost halved. If they are relatively very low, halving the r a m / b o d y impedance will have little effect on overall impedance.

3.3.5 Failure transients Requirements for failure transients are usually defined as boundaries on the ram-to-body displacement following the occurrence of the failure. Different classes of failure must be considered, including electrical-lane failures, hardover failures (for example, one lane of a multilane electric m o t o r demands full current, requiring the other lanes to compensate, until the failure is confirmed and isolated, as well as to control the actuator) and hydraulic-supply failures. Figure 3.8 shows typical failure transient boundaries. The actuation system is assumed to be in a state of steady equilibrium prior to the failure, with or without a steady applied force. The class 1 boundaries apply to a first failure or a second failure if the first failed lane has been switched out. The class 2 boundaries apply to a first hydraulic failure and subsequent electrical failures. Failure transients are particularly affected by intersystem force fight and main-valve pressure-gain characteristics, requiring a high-fidelity actuator model to predict results accurately.

106


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3.4 Actuation system modelling During the design phase of an actuator development programme both the equipment supplier and the airframe company purchasing the equipment will use mathematical models to represent actuation-system dynamics. Models are produced for a variety of purposes from simple representation of the actuator dynamics for use in the overall flight control-system analyses to more detailed representation of the actuator itself for use in control and failure monitor system design or performance prediction. The complexity of the model used will be determined by the type and depth of analysis to be performed and can vary from a first- or second-order transfer function through to highly detailed representations of digital computing effects, magnetic characteristics in direct-drive valve motors and the nonlinear flow and pressure characteristics of hydraulic fluid through a valve block. In the following descriptions, a relatively simple model of an actuator is discussed, referring to the block diagram of Figure 3.4. Sampling effects are repre-

108


sented, as are nonlinearities in the f o r m of servo valve and main control-valve displacement limits. Nonlinear orifice flow and fluid compressibility effects are neglected, however, with flow rate, and hence actuator rate, being represented in the model as a linear function of spool displacement using flow gains. Such a model could not be used to assess pressure transients in stopping or starting an actuator, and does not include any representation of loading on the actuator, but will allow an assessment of basic frequency response and failure transient characteristics, including the effects of saturation limits. Servo-valve dynamics are represented in the model as a first-order lag with a time constant of 1.3 ms. A gain defining servo valve spool displacement per milliAmp of current d e m a n d and a displacement limit (e.g. + 0.3 m m ) complete the representation of the servo valve. Fluid flows through the servovalve to move the main control valve. The complete dynamics of the servo-valve flow and resultant force on the main valve, including the effects of friction or backlash, could be included in the model if the effects have a significant effect on the analysis to be p e r f o r m e d . H e r e a simple flow gain and integrator links main valve rate (and position) to servo-valve displacement. Again a travel limit is included (e.g. +3.0 m m ) which may be c o m b i n e d with the integrator to f o r m a limited integrator, setting main valve rate to zero when the travel limit is reached. Inner-loop closure is p e r f o r m e d with a differential amplifier, feeding back main-control-valve position measured using an LVDT, the representation of which is a gain ( V / m m ) and a second-order filter associated with the d e m o d u l a t i o n of the raw a.c. LVDT signal into a d.c. voltage. T h e representation of the main ram could take a n u m b e r of forms, f r o m a simple flow gain and integrator to detailed orifice-flow and fluid-compressibility equations, including representations of external loads and mass-springd a m p e r equations to represent the control-surface structure. T h e level of detail depends on the intended use of the model. In the example shown a flow gain and the integrator effect of the main ram are c o m b i n e d to p r o d u c e an overall gain of 60 ( m / s ) / m . No main-ram position limits are included, as it is m o r e usual to provide a d e m a n d limit in the flight control laws, preventing the actuator from being driven onto the r a m e n d stops. Outer-loop closure is p e r f o r m e d digitally. Ram position feedback is measured by LVDTs and sampled at a rate of 80 Hz. It is i m p o r t a n t that the delays due to sampling and computation are included in the model, in addition to the demodulation, anti-alias filter and loop-closure control-filter dynamics, to give an accurate representation of loop stability and overall frequency response. A model of this type would be used for simulation analyses, to evaluate the response to step, ramp, sinusoidal or other input demands. Transfer function analysis could also be p e r f o r m e d , to d e t e r m i n e gain and phase relationships between input and output for a range of frequencies and amplitudes. T h e m o d e l could also be linearised, to allow linear frequency-response calcula-

Actuation systems 109 tions. In the following sections examples of the results obtained from such analyses are presented to give an indication of the type of work carried out with such a model. 3.5 Nonlinear

frequency response

O n e of the main uses of mathematical models of actuators is to d e t e r m i n e the frequency-response characteristics (the response amplitude and phase lag when responding to a sinusoidal input d e m a n d ) . Linear models can be created and the frequency-response characteristics calculated using traditional, linear-analysis techniques. In this way the ability of the actuator design to m e e t specified frequency response characteristics can be proven. This is particularly i m p o r t a n t in flight control system design, as the aircraft control laws are designed with an assumed gain and phase characteristic for the actuators (usually in the f o r m of a second- or third-order transfer function), and any significant deviation from these ideal characteristics can lead to a reduction of aircraft gain and phase stability margins. However, the linear m o d e l only shows actuator frequency response u n d e r m o d e r a t e amplitude conditions, but in reality response characteristics would vary with d e m a n d amplitude. Nonlinear models are used to assess amplitude effects on frequency response, with a transfer function-analysis m e t h o d for analysis of the response to sinusoidal input demands. T h e m e t h o d is very similar to test methods, when a transfer function analyser or spectrum analyser is used to inject sinusoidal d e m a n d s to the actuator, and to analyse the gain and phase relationship between d e m a n d signals and the resulting actuator response. At larger d e m a n d amplitudes the actuator will start to reach internal limits, such as c u r r e n t or voltage limits in motors and spool displacement limits in servo valves and main control valves. The relationship between the limits reached in terms of amplitude and the frequency of the d e m a n d signal at which each occurs has a significant impact on the nonlinear frequency response of the actuator, and can lead to stability problems (see the c o m m e n t s on j u m p resonance, Section 3.7). In the actuator example presented in Figure 3.4, the position limit of the main control valve represents a limit on the rate of m o v e m e n t of the actuator ram, and the servo-valve position limit forms a rate limit on the main control valve and, hence, an acceleration limit on the main ram. If the combination o f input d e m a n d amplitude and frequency is such that one of these limits is reached, the response of the ram will be affected with a consequent effect on frequency-response characteristics. This effect is illustrated in Figure 3.9. These results, p r o d u c e d using a nonlinear model based on the block diagram of Figure 3.4, show that gain reduces and phase lag increases as d e m a n d amplitude increases. A d e m a n d amplitude of 0.5 m m represents a linear response, in this case, as neither the spool n o r the main control-valve position limits are reached. Even at d e m a n d amplitudes up to 2 m m across the

110

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Figure 3. 9 Effect of demand amplitude on frequency response (simulation results) frequency range considered (up to 40 Hz) the internal limits are not reached, and so the actuator responds in a linear fashion. At higher amplitudes, however, the limits are reached and frequency response is affected. It should be noted, however, that the d e m a n d amplitudes to reach saturation are quite high for the d e m a n d frequency at which the saturation occurs. For example at a d e m a n d of 4 m m the limits are not reached until a b o u t 10 Hz, and at 6 m m the d e m a n d signal must be at 6 Hz for the saturation to occur. T h e actuator would not be expected to operate at these combinations o f d e m a n d amplitude and frequency and can be proven to m e e t the specified frequencyresponse characteristics for all valid operating conditions. In practice, the actuator would be designed for higher rates than necessary for aircraft control and stability, to provide some growth potential. Limits on position d e m a n d and rate would be applied in the control law d e m a n d s on the actuator.

3.6

Saturation

analysis

An analysis technique closely allied with the production of nonlinear frequency-response data is that of saturation analysis. A linear model of the

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actuator is used to calculate the frequency response from i n p u t - d e m a n d signals to the locations of the various limits, such as servo-valve posidon or main-control-valve position. T h e gain information from this analysis can then be used to d e t e r m i n e the d e m a n d amplitude which will cause the limit to be reached across a range of frequencies. Figure 3.10 shows the results of such an analysis, based on the actuator model of Figure 3.4. From this figure it can be seen that saturation will not occur for sinusoidal d e m a n d s of up to 2 m m in amplitude. For d e m a n d s between 2 and 4 m m the servo-valve position limit will be reached if the frequency of the d e m a n d signal is above 12 Hz, but the main valve limit will not be reached for any d e m a n d signal. For d e m a n d s with a frequency below 12 Hz, the main-control-valve position limit will be reached before the servo-valve position limit, if the amplitude o f the d e m a n d signal is higher than 4 m m . A d e m a n d signal o f 6 m m amplitude will cause the main control-valve limit to be reached if the frequency is above 6 Hz. These results support the findings from the nonlinear frequency response discussed above, giving confidence that no untoward nonlinear effects are likely to affect actuator response. However, it is possible to have combinations

112


o f gains and limits around the control loop which can cause a j u m p resonance effect, with serious performance implications for the actuator, as discussed below.

3.7 Jump resonance U n d e r conditions of large amplitude d e m a n d when servo-valve travel limits are e n c o u n t e r e d an actuation system can display sudden large increases in phase lag. This p h e n o m e n o n is described by the term j u m p resonance, although there is no gain peak associated with the sharp phase variation, and is caused by an effective acceleration limit. In practice, if in some extreme manoeuvres it is possible to reach such limits, the additional phase lag caused by the j u m p resonance can lead to severe temporary reduction of aircraft stability margins, with consequent potential handling difficulties. To avoid this problem at the design stage it is important to ensure that the valve ports (for both the main control valve and the servo valve) and travel limits are sized adequately. Increased valve-port width can be compensated for by a reduction of electrical gain, maintaining the overall loop gain required for actuator stability and response. Jump-resonance is characterised by a very rapid increase in phase lag over a narrow frequency band, as shown in Figure 3.11. This figure shows nonlinear frequency response results obtained from a model configured to exhibit jump-resonance effects. As d e m a n d amplitude increases the frequency at which saturation occurs reduces and a reduction in gain is seen, along with an even more dramatic increase in phase lag. The presence of any potential for j u m p resonance can be predicted from saturation-analysis results. Figure 3.12 shows the saturation characteristics for the actuator with j u m p resonance. Saturation of the servo-valve position limit will occur before saturation of main-control-valve position leading to an effective actuator acceleration limit, for the majority of d e m a n d amplitude and frequency combinations. The crossover frequency, where the two saturation loci intersect, is at a relatively low frequency (2.5 Hz), within the bandwidth of aircraft control. An actuator such as this is likely to cause severe handling deficiencies in an aircraft, and the valve ports and control gains would need to be redesigned to give a better balance, and to produce the sorts o f characteristic exhibited in Figures 3.9 and 3.10.

3.8 Failure transients C o m p u t e r models of an actuation system are used to predict the transients which occur following a failure within the system. Although redundancy features are included in the actuator design to ensure continued operation following failures, it is also important that the actuator does not produce an

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excessive transient when transitioning from one level of redundancy to another. Boundaries, within which the transient must lie, are defined in an actuator specification, and failure to comply with this r e q u i r e m e n t will lead to excessive actuator transient m o v e m e n t immediately following a failure, which could p r o d u c e structural damage in the area of the actuator mountings or a high transient acceleration at the crew's stations or at sensitive equipment, owing to aircraft response to control-surface movement. T h e effect of the failure can be countered either by a failure-absorption m e t h o d , where the presence of the failure is countered by the rest of the system with no special action being taken, or by failure rejection, where the failure is detected and an appropriate action removes the effects of the failure, leaving the remaining parts of the system to continue operating. For either a p p r o a c h the transient response induced following a failure must be assessed, and a design be p r o d u c e d which will m e e t the specified requirements. For the failure-rejection approach, the failure detection and isolation

Actuation systems 115 lane 1 v

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algorithms must also be designed. Failure-detection algorithms are often referred to as built-in-test, or BIT. A n u m b e r of levels of BIT will exist on an aircraft actuation system, ranging from start-up checks and preflight checks carried out automatically by the flight control system, through to the continuous monitoring of actuator operation, referred to as continuous built-in test, or CBIT. The level and m e t h o d of CBIT depends largely on the actuator design, but the following typical example will illustrate the principles. Ram-position measurement for feedback control is often p e r f o r m e d using linear variable differential transformers (LVDTs), with three or four used to provide the necessary levels of redundancy. The individual LVDT signals are consolidated in each computer, to produce an average signal which is used for actuator control-loop closure. In this way slight build tolerances, temperature effects etc. on each LVDT can be averaged out, minimising the difference in drive signals between lanes which would produce a force fight on mechanical components. However, this m e t h o d also means that any fault in one of the LVDTs will be propagated to the consolidated ram-position signal in all of the flight control computers. In order to reduce this effect averaging algorithms are used, weighted towards the median to reduce the influence of extreme signals and failed sensors. A typical voter algorithm for a triplex system is shown in Figure 3.13. The incoming signal samples are first sorted to determine the highest, median and lowest values. The voter algorithm then produces a consolidated or averaged value based on the three input values. A n u m b e r of alternative algorithms could be used, including simple averaging of the three values or selection of the median. To minimise the influence of faults on the consolidated value the algorithm will limit the authority of the highest or

116


lowest signals, weighting the average towards the median. Having produced algorithms that limit the influence of faulty sensors on control-loop closure, it is also necessary to determine which lane is faulty and to reconfigure the voter monitor to ignore that lane. This is the purpose of the CBIT algorithms. In the case of the LVDT monitor u n d e r consideration here, the faulty lane could be identified by comparing each lane's signal with the consolidated value. As we have already established that the influence of the faulty lane on the consolidated signal is limited, any lane which shows a significant difference to the consolidated value (more than a certain tolerance value) can be considered faulty. In order to minimise the n u m b e r of nuisance failure warnings the tolerance value is selected to allow for a difference in build standard of the LVDTs and, to remove the effects of glitches causing spurious failure warnings, a fault must be present for a certain period o f time, such as five consecutive computer iterations, before it is confirmed as a failure and the appropriate action taken. In this case the appropriate action would be to change the voter algorithm to simple duplex averaging, using the two healthy signals only. Simulation is used in defining the voter algorithms to minimise the influence of the faulty signals, and to design CBIT algorithms. An actuator model is produced including various redundancy features and signalconsolidation algorithms. Typical faults can then be simulated and the effects on actuator response predicted, as shown in Figure 3.14. In this Figure a transient response for the actuator model shown in Figure 3.4 is given, as the outer-loop (ram-position) consolidation changes from triplex to duplex.

3.9 Conclusions Actuation systems for m o d e r n combat aircraft flight control are, in general, highly complex devices relying on state-of-the art technology. They are often required to operate at, or very close to, full performance following multiple failures, requiring sophisticated control and monitor algorithms. Closed-loop control systems, often implemented in digital computers, are designed to give actuator performance in accordance with specified requirements, which are driven by the need for high performance and failure tolerance to provide high agility and control basically unstable airframes. Two control loops are usually used, the inner loop with main-control-valve position feedback (similar to main ram rate feedback) and the outer loop with mainram-position feedback. Monitor algorithms, again usually implemented in digital computers, detect c o m p o n e n t failures so that the overall actuatorcontrol system can take the appropriate action to remove the effects o f the failure. This may involve isolation of a servo valve or direct-drive motor coil, or reconfiguration of voter algorithms to exclude signals from faulty feedback sensors.

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Dynamic mathematical models play an important role in the design and analysis of control and monitor algorithms. Both linear and nonlinear models and a wide range of analysis techniques are used to design the control systems, and prove that performance requirements defined in the e q u i p m e n t specification can be met. The complexity of the model will reflect the analysis to be performed, and it is vital that consideration is given to this point to ensure that any model produced is appropriate to the task. In this chapter an overview of typical performance requirements, modelling methods and analysis techniques has been given. For future aircraft projects, flight control actuation may use electro hydrostatic actuators, electro-mechanical actuators or further developments of the more conventional hydraulic actuator. Whichever technology is used, control and monitor systems will be designed using methods based on those defined here.

118


3.10 Acknowledgments The author wishes to thank Dr. Robert Stirling of Stirling Dynamics Limited for his assistance in the preparation of this chapter. Thanks are also due to Dowty Aerospace Wolverhampton, for permission to use Figure 3.2, and to John Tucker, Dave Allison, Mike Walker and Peter Chambers of British Aerospace Military Aircraft and Aerostructures for their comments.

© British Aerospace plc, 2000. Published with permission of the copyright owner.

Chapter 4

Handling qualities J. Hodgkinson and D. Mitchell

4.1 Introduction In this Chapter, we first introduce in simple terms what we mean by handling qualities, how we specify them, and how we achieve them. Then we introduce pilot-induced oscillations (PIOs) because they are one of the more serious consequences of failure to design for good handling qualities, and because current PIO studies offer an interesting example of state-of-the-art research in handling qualities. Handling qualities have been variously defined. For our purposes they are those characteristics of the dynamic behaviour of the aircraft that allow precise control with low pilot workload. A major objective of flight control system design is to bestow good handling (or flying) qualities on the aircraft. Engineers, oblivious to the philosophical fact that measuring a quality transforms it into a quantity, define metrics for handling qualities. Precision of flight can be quantified in terms of rounds on target for gun tracking, circular error probability for bombing or sink rate for landing, for example. Workload is more difficult to quantify, and for the time being we simply ask the pilot how easy or difficult his job is. Much of the achievement of handling-qualities practitioners has been in acquiring reliable information on pilot workload from pilots. Goodness is generally with reference to the pilot's comments in flight or in the flight simulator, and as summarised by Cooper-Harper ratings (Figure 4.1). The scale has ten points, where one is excellent and ten represents the worst qualities possible. Coarser gradations, levels 1, 2 and 3, are also defined. The scale is dichotomous. This feature improves repeatability by leading the evaluation pilot through a series of decisions regarding the task performance and the pilot workload. Among the factors affecting pilot opinion are piloting task, what failures are present and atmospheric environment. US specifications have distinguished between different task difficulties by defining flight-phase categories A, B and C [1]. Category A consists of demanding tasks like air-to air combat and refueling, category B includes less demanding tasks like cruise and climbs and descents and category C includes terminal tasks such as landing and take-off. The idea behind incorporating failure probabilities into flying-quality specifications is simply that the more

120


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Handling qualities 121 likely a failure, the better the consequent and subsequent flying qualities should be. Gusts make an airplane m o r e difficult to fly, so we sometimes p e r m i t worse flying qualities in turbulence. This does not m e a n that the aircraft itself is worse. O u r a p p r o a c h is to use classical control to identify those p a r a m e t e r s in the aircraft response which the pilot uses in p e r f o r m i n g his task. We will then define values of those parameters of the response which c o r r e s p o n d to good through to bad characteristics or, in our language, level 1, 2 or 3. T h e notation in this Chapter largely conforms to the n o m e n c l a t u r e defined at the beginning of this book. The occasional differences are due to the variations in accepted practice between the notations in use in the UK and the United States.

4.2 Longitudinal flying qualities

4.2.1 Control-input transfer functions T h e relevant transfer functions which describe the longitudinal notion were covered in Chapter 2. They are repeated here for completeness. For pitch attitude O(s) to elevator ~/(s) O (s) -

n

N°(s)

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A(s)

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where the subscripts p and s refer to the phugoid and short-period modes, respectively. If 77 is used as the input, this refers to the stick deflection. Notice that when the polynomials in the transfer functions are factored, the factors are given names, like 1/T, that are reminders of the response from which they 0 come. Notice too, for example, that the notation N n is the n u m e r a t o r of the transfer function for response of 0 to r/. These transfer functions are for aircraft either without feedback control systems or for aircraft with control laws which do not a u g m e n t the order of the aircraft response. For these, the concept of a u g m e n t e d stability derivatives is applicable.

4.2.2 Modal criteria T h e coefficients in eqns 4.6 and 4.7 describe i n p u t / o u t p u t relationships along with the c o m m o n notation for the modes of motion. These equations also show some useful relationships between the response quantities (these apply to conventional aircraft). T h e two modes are the short period, generally with frequencies f r o m one to ten rad/s, and the phugoid, with frequencies below that. If a m o d e of the

122


response does not appear in the time response of a particular variable to an input, it will be manifest in the transfer function as a numerator term which cancels or nearly cancels the modal term in the denominator. For example, there is usually very little angle-of-attack variation in the phugoid oscillations, therefore the second-order numerator in N~ is closely equal to the secondorder phugoid in the denominator. Recall that from Chapter 2:

w(s) -_ N~(s) kw(s + 1/T~) (s2 + 2(~w,~s + w 2) 71(s) A(s) = (s2+2(pwps+w~)(s2+2(,w,s+w~)

(2.36)

4. 2.3 Phugoid f l y i n g qualities The phugoid is a long-period (low frequency) mode in which forward speed (kinetic energy) and altitude (potential energy) are interchanged. The resulting oscillations are in pitch, speed, altitude and flight path, but as mentioned already the angle-of-attack remains roughly constant. The denominator of the transfer function for speed and pitch motion is:

+

(4.1)

where U0 is the steady-state velocity, Ue in Chapter 2. Here the constant term, - g Z J U o, is the undamped natural frequency squared, ¢02n,for the phugoid. The derivative: ,

P

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(4.2)

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g

(4.4)

and the period of the phugoid in seconds, as McRuer et aL [2] point out, is about a fifth of the true airspeed in miles per hour. The above analysis is obtained from a two-degree-of-freedom model of the phugoid. In the three-degree-of-freedom model, the derivative M u appears. Aeroelastic and thrust effects that are highly configuration dependent introduce this parameter. The total damping of the phugoid mode is Xu, which is a measure of the drag of the aircraft. In high-speed flight, altitude can change significantly in phugoid motions and this can affect the phugoid damping because air density changes with altitude. The phugoid period will also be decreased as a consequence of the density gradient. The requirements for the phugoid are in terms of damping ratio for stable phugoids and time-to-double-amplitude for unstable phugoids. For level 1, (p should be at least 0.04 and at least zero for level 2. Time-to-double-amplitude, T2 should be at least 55 seconds for level 3. No distinction is made between classes of aircraft. Time-to-double-amplitude is -0.693/(pWnp and (p is negative if the phugoid is unstable. Pilots can control phugoid oscillations quite readily by closing a low-gain pitch loop. Nevertheless, this does require the pilot's attention and side tasks are difficult if poor phugoid characteristics are present. 4.2.4

Short-period f l y i n g qualities

The short period is a relatively rapid mode which governs the transient changes in angle-of-attack, pitch, flight path and normal load factor that occur at relatively constant speed following rapid control (generally elevator) or gust inputs. The mode is usually a stable underdamped second-order oscillation. For small angles, the angle-of-attack ot~- w~ Uo and L , ~ - Z,0 so we can use: Z. = UoZ~,-~ - UoL,~~ - Uo / To2

(4.5)

Define the parameter n / a in g per radian, as the steady-state normal load factor per steady-state angle of attack, so: n/ a = UoLJ g

This gives us a number of useful relationships which govern the short-period motions and the response variables to elevator input as follows:


124

For pitch-rate:

sO Ms(s+ L`,) 6 A for angle-of-attack:

8

A

for normal acceleration at the c.g. or 1x ahead of it:

(4.6)

n~ M~n/ a S /X n~p= n~cx+s2OlJg for flight-path:

Y_~. MsL`, 6 sA where It is helpful to look at response ratios, for example to imagine what the response of angle-of-attack is to pitch angle, of flight-path angle to pitch angle, and of normal load factor to pitch angle: a 0

1 s+ L`,

y 0

L`, s+ L`,

(4.7)

• z . •n/OL 0

s+L`,

This is a convenient way of viewing the responses because pitch is the fastest initial response. The other response variables, including flight path, lag it with a time constant of 1/L,,, which is consequently sometimes called the flightpath time constant.

4.2.5 Criteria for the longitudinal short-period dynamics The stick force required to develop unit steady-state normal load factor, stick force per g is the short-period steady-state gain.

Handling qualities 125

stick force per g

short period resonancei /

/

3 pounds/ g

frequency of pilot's stick excitation Figure 4.2 Floor stick force/g specified to prevent sensitivity in dynamic manoeuvres around the short-period resonance

The stick forces in a steady manoeuvre must not be so great that the pilot cannot comfortably attain the maximum g load on the aircraft, and not so light that he inadvertently overstresses the aircraft. Fighters require light forces to avoid fatigue in prolonged manoeuvring up to 9 g for example. Transport aircraft, with their gradual manoeuvring and low maximum g capability, typically have higher stick forces. At flight conditions with low dynamic pressure, i.e. at high altitudes a n d / o r low speeds, the acceleration generation capability of the aircraft is low, so higher overall stick force per g is allowed at these conditions. Similarly, at higher dynamic pressures, we could allow lower stick force per g, Fin, so that the pilot can attain the maximum load factor that the airframe allows without excessive effort. F,/n is therefore specified to be a function of acceleration sensitivity, n/a, the steady-state normal load factor per unit angle-of-attack, n/a is a measure of flight condition, corresponding to high or low dynamic pressure. A floor minimum value of Fs/n is specified to prevent sensitivity problems. Classical airplane dynamics produce a constant Fs/n with flight condition so the variation with n/a is really a concession to aircraft with artificial feel systems and real flexibility effects. Classical airplane dynamics do not produce a constant stick deflection per g. Larger deflections are required for a given g at lower n/a. A dynamic value of Fs/n is also specified by requiring that the floor value be maintained during a sinewave sweep of the pilot's longitudinal controller for a frequency range spanning the effective short period (see Figure 4.2). To understand both the steady and the dynamic Fin, consider the transfer function for nz/F~:

126


n~

KM~UoL~

~, = g( ;Z + 2(spW,~ s + o92~t,)

(4.8)

where the numerator is just a multiplier depending o n / ~ a measure of the effectiveness of the stick-force-to-elevator system, M n, the surface effectiveness, U0, the true speed and L,~, the dimensional lift-curve slope. The denominator consists only of the gravitational constant and the second-order short-period mode. From this transfer function and the final value theorem, the steady-state for a step input is:

gf.O2p

'

or equivalently:

KM n / a

(4.9)

The minimum stick force per g is determined by plotting the amplitude ratio of the nz/F s transfer function, which will have a maximum at the resonant frequency.

4.2. 6 M o d a l criteria for the short period Short-period natural frequency is specified via the control-anticipation parameter (CAP): O92 nsp

n/a

(4.10)

again, where n / a ~- UoL~/g. CAP boundaries are specified in the form of Figure 4.3. The short-period damping ratio is specified alone as a parameter according to Figure 4.4. The step-time histories and frequency responses of the various damping ratios are shown along with this Figure.

4.2. 7 Other short-period criteria A number of criteria have emerged that attempt to deal with longitudinal dynamics in the presence of feedback control systems. Sometimes these systems have introduced phase lags and delays from various mechanisation features like actuators, sensors, filters etc. The consequent mathematical model of the system becomes far higher than the fourth-order dynamics we

Handling qualities 127 100

I

I

I

I

II I II II I I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

,

,

, ,,~,I0.0

-

i

i llll

v

:iiL .,,l'7~.._u. 0.28 o.~s

short period natural frequency, COnsp,rad/s 10 •-~l ; lineal I ~dl il~.~l

f

, ,, :

1.0

11,, :

~

~ lli

jf 0.1

:

i

it" ~ :

. . . . . .! ! ! ! !

!!!!!

v~,li

~,,ii

:

i

,

1.0

controlanticipation parameter,

. . . .

,

10

:

• "

:

::

(.0 2nsp nAz

ioo

acceleration sensitivity, n/m, g's/rad

Figure 4.3 Boundaries of control-anticipation parameter have mostly considered so far. As an example, the longitudinal dynamics of the F-18 were commonly modelled as a 75th-order system.

4.2. 8

Equivalent systems

The equivalent system concept [3] is simply to match the augmented, highorder dynamics with a low-order equivalent which has the same form as an unaugmented aircraft, plus a time delay to approximate the phase lag of system components. Equivalent systems form the basis of all current modal criteria (longitudinal, lateral and directional) in the military specifications in the United States. The process works best if frequency responses are matched in the range 0.1-10 rad/s for estimating short-period parameters. For the phugoid, extension down to 0.01 generally works. With the gain in decibels, the phase in degrees and a weighting on the phase match around 0.02, a sumof-squares mismatch function is minimised. The approach is a vast improvement on picking one, dominant mode from the s-plane array (see Figure 4.5).

128

,..o

,.o O


C

e~

01

0

0

]

O

O

~0

¢-

0 t~o

)loelle Io al6Ue

O

O

__tD

O O,I

O

0~

E

.

phase, deg .

p 'apnl!u6em

.

.

.

~

.

~

.

~

~

~

oN

0

N~ =9

~

.-,9,

0

Handling qualities

~

~

•

",~ ~

~

~

"~.~ .~..~~ ~. ~

-~

129

130


,..i

\_

"0

e-

II II ~

I I

~uency,ra~,s ~

~[ u ~ eequsinp~acedc ~i on e logsscale I

4.5a

imaginary usedfordominant-~ rootapproximation~

" ~ X ,~=, ,,,,

~1

4.5b

¢.. e~

ill]

I,H~I~LI J~LI~III 1 II II II1~ _ . H H - - ..._ Illl! I I11~,,I11"1.L IIIII "',@l.IJ. IIIII 1~1 IIIII III1'

I~

frequency,rad/s

4.5c

Handling qualities 131 4.2. 9 Equivalent time delay A key addition to the low-order equivalent is a time delay of T seconds. This parameter T approximates the high frequency phase lag generated by the high-order terms in the response. A useful rule of thumb is to look at the additional phase lag at 10 rad/s, and to r e m e m b e r that 0.1 seconds of delay produces 57.3 degrees of lag at that frequency. For demanding piloting tasks for fighter aircraft, a delay of 0.1 s, i.e. 100 ms, is enough to preclude level 1 flying qualities and 150 ms is excessive even for large transports if they are required for precision landings, in-flight refuelling, formation flying or other tight tasks. For fighters, the level 2 limit is 200 ms, and for level 3 it is 250 ms. Delay worsens the pilot loop closure only when the loop gain is increased by the pilot in an attempt to get tighter control and a faster pilot-in-the-loop response. This p h e n o m e n o n - - t h e aircraft becoming more out of control as the pilot works harder to control i t - - i s very disconcerting to the pilot; R.E. Smith has called the effect the flying-qualities cliff. Large delays in demanding tasks often result in pilotinduced oscillations. The degradation in pilot rating has been summarised by plots like Figure 4.6. Unfortunately, there are insufficient research data available to determine whether the stick force or stick-position characteristics should be used in the equivalent system m e t h o d (or in any other method, for that matter). In an attempt to quantify the acceptable mismatch in determining an equivalent system, Wood and Hodgkinson [4] examined the added dynamics that would cause a noticeable difference in pilot rating. When the dynamics (from the Neal-Smith variable stability experiment [5]) were overlaid, they had the form of hour-glass-shaped envelopes of allowable mismatch against frequency, as shown in Figure 4.7. The envelopes show that differences a r o u n d a centralised frequency are more noticeable than at the frequency extremes. The equivalent system form must be appropriate for the response type. If novel response types are used, whatever the axis of control, the equivalent

Figure 4.5 Definition of equivalent-system mismatch, and comparison of po~-zero arrays and frequency responsesfor high-order system, its dominant root approximation, and its low-orderequivalent system 2O

a Minimise cost (i.e., mismatch) functional: = Z ( G2 + KP~): K= 0.02 i=1 - - high-order-response - equivalent response b x O high-order poles, zero X O low-order equivalent poles, zero c - - high-order system dominant-root approximation . . . . equivalent with delay - - - equivalent, no delay (Note: amplitude ratios for equivalent with/out delay, coincide.) -

-

-


132

Cooper-Harper rating 10

F-8 h~. s" .,u, ,.-stress t" lanoings s"

Navion altitude .... ,.,n~ t,=~,~,, u

~s" /s

(Lateral)\

NT-33

NT--33(lateral)landing

.,t"

s

.~o~-

,oo

i

. ' ",.-"

. • . .

t's"

..s/\/ ,/ _., "'7"'" landings , ; . . ~ _ ~ . . . . t % : ~ ,.............. field-carrier \ - "" ~"" - 7 " ' " " s S _.."" ~ .......... xe ~ ho~,, landing ~ ....~.~,~" ~.'""..~.....:..........~ NT-33 landing (lateral)"'x-" . . ' " ' " s" / . " " . ' 2 " ' . . ......... ~ ..... \ \

Navion

-

•

t" t~...

/ /."

.

.

.

.

.......

.

I

0

Figure 4.6

.°.

.

-" L - ' ; . " , . . . . . ' S .0s~..~

.

.

.......

7>"-""=---=~""

.

~ . . ~ - ~ ~-'; . . . . .

I

0.1

I

/

---1

~'-

I

........

\

| " Navion approach and landing, 75 kts I

I

~

...... F-8 I o w s t r e s s

Y

I~ndinn ......

=

aavion approachand landing in turbulence

I

0.2 0.3 equivalent time delay, s

I

I

0.4

I

0.5

Rate of degraduation of Cooper-Harper pilot ratings increases with difficulty of task

form must comply with the physics of the dynamics. For example, a pitchangle command system can generally be matched with a zero-over-second-order equivalent plus a time delay, yielding a damping ratio, natural frequency and time delay which are useful for specifying flying qualities and for comparing the qualities of design changes. The damping and frequency here are not strictly the classical short-period values, and would not strictly be compared with classical criteria since the response is not classical, but we would expect them to be in the same general range of values.

4.2.10 The bandwidth method From the frequency response of the pitch attitude to the longitudinal controller, the bandwidth frequency is the frequency where the phase margin is 45 degrees, or where the gain margin is 6 dB (see Figure 4.8). The bandwidth hypothesis [6] is that the pilot can adequately follow input commands with frequencies up to the bandwidth without causing instability. The phase roll-off or slope at high frequency, that causes this characteristic is essentially the same as equivalent time delay and is measured using a parameter called phase delay, ~'p.Figure 4.8 defines bandwidth and ~-p.

4.2.11 The Neal-Smith method Neal and Smith [5] proposed for pitch-angle control a pilot model of the form shown in Figure 4.9. Here the pilot shifts his parameters so as to reduce

Handling qualities 133 20.0 amplitude ratio, dB

0

s 2 + 11.6s + 4.96 -20.0 0.1

i 1.0

180.0 [--L

~

phase, dB

I 10.0

~

68.89s 2 + 1100.12s- 275.22

I 100.0 frequency, rad/s

e

.0059s

0

.

.

.

.

S2 + 11.66S + .0389 -180.0 0.1

-0.0072s

~

I

i

1.0

10.0

I

[ I

I

100.0 frequency, rad/s

Figure 4. 7 Envelopes of allowable mismatchfor longitudinal equivalent systems

steady-state closed-loop errors to reasonable levels (this is the 3 dB droop) and to reproduce rapid closed-loop commands (this is the fixed bandwidth frequency--not the same definition of bandwidth as we used previously). See Figure 4.10 for a Bode plot of the resulting closed-loop dynamics. The Neal-Smith criterion is a two-dimensional plot of pilot compensation against pilot-in-the-loop resonance (see Figure 4.11, which contains some recommended corrections to the boundaries made by Rickard [8]). Compensation is defined as the phase angle of the pilot's compensation measured at the specified bandwidth frequency, and the resonance (a measure of the pilot-in-the-loop oscillatory tendency) is presented in dB. The boundaries reflect the fact that pilots dislike PIOs and they dislike generating lead or lag. Figure 4.11 summarises the pilot comments corresponding to the

134

Flightcontrolsystems 1;p- 180 - (¢#)2~18o 2m18o

amplitude ratio of e

I ,

Flong

gain margin = 6dB

I s

phase angle of e

F,o.g

phase

............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..... .t ....

e';=

Figure 4.8 Definition of bandwidthfrequency and phase delay

different regions on the Neal-Smith plane, and uses a range of bandwidths as a design guide. Figure 4.12 shows that Neal--Smith pilot compensation is strongly correlated to equivalent frequency, as we would expect.

4.2.12 Gibson's dropback criterion Both the equivalent systems and the bandwidth criteria have had problems correlating configurations with excessive lead compensation and Gibson's dropback criterion (Figure 4.13) is a way of screening these configurations. Gibson [9] suggests the ratio of dropback to steady-state pitch rate, dropback/qs s should be less than 0.25 for precision tracking and less than 1.0 for landing.

4.2.13 Time-history criteria A number of workers have proposed measuring features from step-time histories as a generic way of determining flying qualities. Although in a design effort the step history is easily calculated, it is difficult to test and measure. A true step has infinite slope at its leading edge and instantaneously changes that slope to zero following an elapse of zero time. Inputs like this can be approximated electrically, but are quite different from even the most abrupt inputs of pilots.

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to o

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+

ot 5"

(M

÷

v

+

÷

÷

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Handling qualities 135

136


Hr, ax I~ T~ ~ . . . . . . . . . . . . . .

~............. ~ ..................... ~J .....

~.......... ~

N

-/(-6~'c) ' I deg I -901

o

log (.o

( BVlOmin

Figure 4.10 Neal-Smith criterion: pilot-in-the-loop tracking standards 4.2.14 Flight-path stability At speeds well above stall, airspeed is generally controlled with power and the flight path is controlled with the elevator. At very slow speeds, however, pilots are trained to add power to bring the flight path back to the desired value and to control the speed by using the elevator. The two control strategies correspond to operation at speeds above or below the speed for minimum drag, or the speed for minimum thrust required. The criteria for flight-path instability are generally stated as a restriction on the slope of the plot of flightpath angle against speed, using elevator control only.

4.3 L a t e r a l - d i r e c t i o n a l f l y i n g q u a l i t i e s Here we are considering the three equations for rolling moment, yaw rate and side force, as we see in Chapter 2, and the modes of motion which result from solving the equations.

4.3.1 Roll mode For an aircraft rolling about its x axis:

sp- Lps = I%

(4.11)

Handling qualities 20 abrupt response, .&.. ~ .. ~

strong PIO @,,.' tendencies, . have to fly it smoothly t 16 / closed-

--,

~

'

dB

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.,

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-60

-40

-20

~

0

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20

.,

./

•' I level 21 • tendendesto ~ J/". .'F'~ •'~nitialresponse./ o~illate ~ t .~i~tL././~ / abrupt tends / rim ~ •' to bobble on / / / "~ /" ~ O/target, have to • / / ~ ' " ~ lty it smoothly2~ / / J ...... ~ initial = . - . ! ~ __j('_ _ ~ / _ .,==__# _ _~ _ ~ ....... -==-_ forces .,. == v " • • ........ :Z'D--..

-4

11

1/

./." RJckard s. ~ o u n d a r y

8

sluggish response, strong PIO tendencies, have to overdrive it ,..~

strong PIO tendencies

@ i. loop ,.. resonance , 12 Neal and Smith s b o u n d a r y

137

'

J

~"~ Ii I I = I / ~ / kZ,) .~1 A .."

in'~al . response . final response difficultto predict, tendency to overcontrolor dig in, initialforces heavy, lightening up as response develops 40

60

80

100

pilot compensation, deg

key(bandwidth,rad/s)

Figure 4.11

•

1.5

•

2.0

•

2.5

• •

3,0 3.5 4.0

Neal-Smith criterion showing Neal and Smith's boundaries with Rickard's level 1/2 boundary, typical pilot comments for the various criterion regions and the effect of changing Neal-Smith bandwidth on configurations with various pilot ratings Note: Position command, pilot delay = 0.2 s Various LAHOS configurations (Smith, 1978) Pilot rating shown in circles, @

T h e transfer f u n c t i o n for roll-rate response to aileron is then: P_

Le,

~a S--Lp o r in generalised forms: p_ 6~

K T~+I

(4.12)

138


0

80

pilot compensation. deg

0

40

J Zpc=114"2-33"8me(00~

-40 0

Figure 4.12

1.0 2.0 3.0 equivalent short-period frequency, we, rad/s

4.0

Comparison of pilot compensation in Neal-Smith c~terion against equivalent short-period frequency. (Note: line fitted to data with correlation coefficient of 94 %)

pitch attitude I

4, dropback i' overshoot

~/,,,,~_

(negative dropback)

attitude dropback

time control input removed

Figure 4.13

Gibson's dropback criterion

or

----K/ (1/TR)

(4.13)

in the shorthand notion where (s+a) is written simply (a). Typically, the roll-mode time constant is of the order of one second or so for fighters and somewhat longer for larger aircraft. If it is much longer (the

Handling qualities

139

requirements range from 1.0 to 1.4 s for level 1, 1.4 to 3.0 s for level 2, and 10 s for level 3), the initial slope region of the step-time history persists t h r o u g h o u t roll manoeuvres. The pilot's perception is then that he is c o m m a n d i n g roll acceleration, not rate, as he prefers. The Bode plot interpretation would be that, in the likely piloted crossover region (essentially his usual frequency range of interest) around say 3 rad/s, the response in roll rate drops off, so we would have to differentiate the response (multiply it by s) to make it look like a gain-type response,/~ This means that the pilot would see an sp or ~type response, which is not impossible to control but requires full attention, i.e. it leaves little or no reserve for side tasks.

4.3.2 Spiral mode T h e spiral mode is a slow recovery (or divergence) from a bank-angle disturbance. Usually it is very slow and so can be approximated by the ratio of the low-order coefficients of the transfer function denominator. Specifications prevent too rapid divergence. We often treat the spiral mode separately from the shorter-period roll and dutch-roll modes because it is generally at a far lower frequency and is differently handled by the pilot.

4.3.3 Coupled-roll spiral When bank angle is fed back to aileron, a low frequency oscillation can result. Unusual combinations of stability derivatives can also result in a low frequency oscillatory mode, similar to the phugoid, which is sometimes called the lateral phugoid. Although it is not generally associated with good flying qualities, total damping values (i.e., the product (r~OJn) of 0.5, 0.3 and 0.15 are currently used as the levels 1, 2 and 3 boundaries, respectively, based on data from the variable stability aircraft, NT-33.

4.3.4 Dutch-roU mode T h e dutch-roll mode is the lateral-directional short-period oscillatory mode. It generally occurs at frequencies similar to those of the longitudinal shortperiod mode, i.e. of the order of one to five radians per second or so. T h e dutch-roll mode can helpfully be considered very approximately as the m o d e through which the sideslip of the aircraft is controlled with the rudder. More realistically, the dutch roll is a nuisance mode in the basic roll response to lateral control. Along with its frequency and damping characteristics are specified measures of how much it appears in the lateral response (the magnitude of its residue) and its phasing. T h e r e are parallels between this sideslip response to r u d d e r and the response of angle-of-attack to elevator. The damping term is the sum of the rotational damping, N r and the resistance o f the aircraft to the velocity that generates the sideslip, Yr. The frequency or stiffness is mostly the rotational resistance of the aircraft to the


140

Level

1

Flight-phase category

Class

Min srd*

Min ~r~fJd* (rad/s)

Min wd (rad/s)

A (CO and GA)

IV

0.40

0.40

1.0

A

I, IV, II, III

0.19 0.19

0.35 0.35

1.0 0.4

B

All

0.08

0.15

0.4

C

I, II-C, IV

0.08

0.15

1.0

II-L, III

0.08

0.10

0.4

2

all

all

0.02

0.05

0.4

3

all

all

0

-

0.4

* The governing requirement is that yielding the large value of (d, except that a (d of 0.7 is the maximum required for Class III. When the product w21 qb/fll is greater than 20 (rad/s) 2, the minimum specified dutch roll total damping ~'dt0,~is increased by A~'dto,,a values as follows; level 1: Asrdto,~= 0.014 (w,,~21¢/fll - 20) level 2:A(dmn=O.OO9(o)na2lqb/[31 20) -

-

level 3: AsrdW.e=0.005 (w.d21¢/fll -- 20)

Figure 4.14

Dutch-roll damping and frequency requirements

velocity w h i c h g e n e r a t e s the sideslip. T h e similarity o f Yv to Zw, Mq to N Ta n d o f N B to M s is q u i t e direct. T h e y can b e c o n s i d e r e d c o n c e p t u a l l y to b e the s a m e derivatives r o t a t e d t h r o u g h 90 d e g r e e s . T h e r a p i d i t y o f t h e d u t c h roll a n d t h e d e g r e e o f its o s c i l l a t o r y d e c a y a r e s p e c i f i e d by t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d t h e d a m p i n g ratio, respectively. T h e s e c r i t e r i a a r e specified in F i g u r e 4.14. N o t e t h a t t h e total d a m p i n g , i.e. the p r o d u c t o f t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d the d a m p i n g ratio, is also specified. T h e r e is c o m m o n l y significant d u t c h - r o l l c o n t e n t in t h e l a t e r a l o r roll r e s p o n s e to lateral c o n t r o l . We n e x t discuss c r i t e r i a w h i c h cover this effect, w h i c h is d e l e t e r i o u s since t h e p i l o t p r e f e r s a relatively p u r e roll r e s p o n s e to control.

4 . 3 . 5 The parameter w 4 J w d T h e l u m p e d p a r a m e t e r r e s p o n s e to lateral c o n t r o l is:

¢ = U ~ , =K¢(s2 + 2~¢wcs+(w2¢) 6a A (TRS+I)(TsS+I)(s2+2(dWnS+W2)

(4.14)

M a t h e m a t i c a l l y , if 56= (d a n d e0¢~ w.,, t h e n the two s e c o n d - o r d e r t e r m s c a n c e l e a c h other.

Handling qualities

141

bank angle, ~)

sideslip angle, -

t

Figure 4.15 Time responsedefinition of 8/,B roll-to-sideslipratio in the dutch roll Physically, the cancellation would mean that the bank-angle response does not contain any dutch-roll oscillations. Often, the parameter e0C/0a,~, which is usually abbreviated to eo¢,/ead,is a measure of the vertical separation of roots in this dipole, and requiring this parameter to be about unity has been used as a crude way of keeping the dutch roll out of the bank-angle response. However, it can be shown that yawing m o m e n t due to roll rate, Np, (the dynamic version of adverse yaw) causes the zero to move in a circular locus a r o u n d the pole, giving lateral root separation. The time-history equation for sideslip following a step aileron input is:

fl---: Co+ Csea't+ CReW"t+CDRe-g~'~t COS ( o a , a ~ + ~a

¢13)

(4.15)

and the criteria (not reproduced here for brevity) restrict the ratio of oscillatory rolling to average rolling as a function of the phase parameter 4'13 [1].

4.3.6 Phi-to-beta ratio, qS/fl The phi-to-beta ratio distinguishes between dutch-roll oscillations which occur in sideslip, with the wings roughly level, and dutch-roll oscillations which occur in bank angle, with roughly zero sideslip. Figure 4.15 defines qS/fl ratio in terms of time responses, which is readily calculated from the modal response ratios in the transfer functions. Current specifications state that when the product wz,dd?/fl is greater than 20 (rad/s) 2, the minimum specified dutch-roll total damping, (d0~,,t, is increased to prevent high roll accelerations due to side gusts. In addition to roll accelerations due to side gusts, pilots object to lateral accelerations due to roll manoeuvres. T h e specified maximum values of the parameter;

n~t'u°t'"x[ Pmax

tepinput,t<~2.5

s

are 0.012, 0.035 and 0.058

g/deg/s

for levels 1, 2 and 3, respectively.

142


[ reversible I

stick deflection

I irreversibleI

stick - ~ deflection

.~ aerodynamic I stickforce forces I [-~ roll rate I '~1~] ~'-

r

"1 -L.I

actuator sy-stem ~ "

roll rate

stickforce

Figure 4.16 Reversibleand irreversiblelateralsystems

These apply to the lateral acceleration at the pilot's station in g during the first 2.5 s of roll manoeuvres during which the maximum roll rate is Pmax degrees per second. The requirements apply to large and small control inputs for all classes of aircraft. For example, both C-5A and F-15 pilots have c o m m e n t e d on these effects.

4.4 Stability and control-augmentation systems Today's handling-qualities engineer is a key m e m b e r of the flight control design team. He or she must have some familiarity with the purpose and content of the systems as well as with the criteria which the design must meet. This section contains some considerations for design for good flying qualities of full-authority systems. For brevity, the following notes are confined to linear design concepts. T h e r e are some nonlinear aspects of control systems which have serious effects on handling qualities. We will discuss one of these, rate limiting, in the later section (4.6) on PIO.

4.4.1 The influence of feedback Consider as an example the roll-rate dynamics described by the first-order transfer function: p _ KL~,

(4.16)

8p, , s- Lp Here, the Kis a constant that accounts for the conversion from the pilot-input deflection o f ~pilot to the aileron command, with the associated units. For a simple light aircraft this will consist of the gearing ratio of the cables, rods, bellcranks etc. which convert stick deflection to aileron deflection. For a heavy or high-performance aircraft, the gearing will include an actuator which, like power steering in a car, also converts the pilot's inputs into aileron deflection (see Figure 4.16). Suppose we implement a feedback system in which roll rate is measured,

Handling qualities

143

1

stick

~

+

~'

ro, rate

which is equivalently stick ~ F ' ~ I . ~ _ ~ t ' ~ , . J ' ~ - ' L deflection~ L I ~ I . ~ I ~ ~

~ ~'-

rollrate

Figure 4.17 Lateral system with roll-rate feedback, ignoring the actuator and sensor models fed back and compared with the pilot's command, and the difference is used to command the aileron. We will neglect the actuators which move the ailerons and the sensor which senses roll rate. More correctly, we will model them as unity, i.e. devices which pass all signals perfectly (Figure 4.17). Inserting a gain /(9 that converts the roll-rate command error into the actuator command, we get a transfer function for roll-rate response to the pilot's command of:

KK~8o p _ s-Lp 8pil°' 1 ÷ KpLSa s - Lp

(4.17)

which is easily rearranged to get: p =

KK~,

(4.18)

~pilot S-- ( Lp- KpLsa) Comparing eqns 4.16 and 4.18, and the block diagram in Figure 4.17, we see that the roll-mode root has simply been augmented by the quantity KpLa. With the usual signs of these two parameters, the roll-mode root has been moved to a higher frequency, making bank-angle corrections more rapid. Knowing the original value of Lp and LB, a designer could choose a desired value of the augmented root and use a gain Kp to place the root exactly where desired. Since this root is of course a pole of the simple transfer function here, the designer has used a very simple implementation of pole placement to achieve the desired closed-loop, i.e. augmented, dynamics. This simple example illustrates that using the concepts of approximate factors (here, the roll-mode root), a designer can understand how feedbacks will affect flying qualities. In this case, the gain, Kp, could modify the rollmode root from one which is unsatisfactory (e.g. too slow) to one that is fast enough. Many flying quality criteria are specified in terms of the roots of the approximate factors. Many control design methods use multiple feedbacks to place multiple poles in the desired locations. As a general rule, experience

144


stick deflectio~..i"~L.~.P~ ~n ~ I ~1 ~ stick s= Kact deflection~~~] e)a~2+2gaa S+lKsens~actL,

i

~

roll rate

=~'~ r]s-Lp[

rollrate "~

s= +2gs°'~ s+1r (~sens 2

Figure 4.18

(~ser)s

J

Lateral system with roll-ratefeedback and actuator and sensor models

has shown that ensuring that an augmented aircraft flies like an aircraft with the familiar dynamics which the approximate factors describe, is the first step to good flying qualities.

4.4.2 The influence of actuators, sensors and processors Figure 4.18 includes the numerator and denominator dynamics of the actuator and sensor. The closed-loop transfer function becomes: =

~pilot Aac,(S-- tp)Asens + KpNaaL6.Ns~s

(4.19)

Suppose the actuator and sensor are both modeled by, for example, a secondorder system, so that the Naa and Ns~ terms are gains and the Aact and Ase~ terms are second-order transfer functions. Then we no longer have a firstorder system to describe the aircraft's roll-rate response. The denominator product Aact(s-Lp)Asen~ is of fifth order. The Bode analyses in Figure 4.19 show key features of feedback control. The upper plot is of amplitude ratio against frequency of excitation, and the lower is phase angle. The plots reflect increasing attenuation and phase lag at all frequencies. The pair of lines marked A compare the characteristics of a simple first-order lag representation with and without the actuator dynamics included. Notice that the actuator increases attenuation and phase lag at higher frequencies, the lines marked C. The lines marked B are the dynamics with feedback. Notice the improved bandwidth of the response, meaning that the aircraft will respond better to higher frequencies of excitation (in other words, rapid pilot inputs). Notice, too, that the marked falling off in both amplitude ratio and phase is still present. Root-locus analysis shows that the phase lag comes mostly from the actuator

Handling qualities

145

0

rn "o

o5 "0

%

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B

-20

-30

cli

-40

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-60

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i

100

=,,

I

101

i

i

. i , ,

10 2

frequency, rad/s

Figure 4.19 Bode plots of roU response to aileron command A bare roll m o d e B with f e e d b a c k C with a c t u a t o r

146

Flight control systems Mode

Constraints

Equivalent System

Direct lift, or normal acceleration (a=O)

w--* 8,. u---, 8 r

a~_..,NadVu 8,~A.= Z 6L N~r ~l.

Pitch pointing

ac--* 6t, u-'* 8 7-

o ~, = Ms~ 0.... N 8~8,8.~ azu 6, N8,8.,, [~2 _ M q s - m~]

Vertical translation

6--* 8 0 u'-* 6 7,

w

w Olu

N~,A8 ,.

Z81

K'-'W°Z-~ L ~ ",T - Is- z j Direct side force, or wings level turn

fl---* 6~ ~b~ 6,

Yaw pointing

fl-"* 6~ ~b"-*6,

tPSF

qt--~ 6, ¢---* 6,

~ • 6,B n

¢~_ 4) N ~,si,,s 8,.

Lateral translation

N a y tick 6~.,5,Ba

a

~

N s, [~-N'rs+N;]

p ._~, 8~,,sA

Y'~,

~

[s-V~]

*primes denote effective derivatives which account for cross products of inertia.

Figure 4.20 Tableof equivalent systems (limiting responseforms) for unconventional response-types (direct-force-controlmodes) (from Hoh et al. [I0]) in the forward path and the root which originates from A e The root originating from the sensor denominator Ase,, is nearly cancelled by the closed-loop numerator term Ase,s. Therefore the sensor, because it is in the feedback path, contributes comparatively little to the closed-loop dynamics. This is another reason why we frequently neglect sensor dynamics. In summary, feedback control can improve the basic character o f the response, but can introduce excessive phase lag due to, for example, excessively slow (i.e. low frequency) actuators.

4.4.3 Multiple-input, multiple-output flying quality possibilities The advent of digital flight control has raised the possibility of aircraft which have relatively pure, or decoupled, responses. Thus with a pitch input, for example, the aircraft could be made to pitch while thrust and active lift controls keep the speed and altitude constant. This mechanisafion involves control laws which decouple the natural dynamics of the aircraft. These modes also usually involve an effector which produces a significant c o m p o n e n t of direct force along the lift or side force axis, and are often known as direct-force modes. The modes are summarised in terms of their limiting response forms in Figure 4.20 [10]. These forms represent the best that can be accomplished

Handling qualities

147

with decoupling in the control laws. They are also very useful as the basis for equivalent system forms for each mode. Well validated criteria for these modes are lacking. H o h et al. [10] suggest using the bandwidth criterion, which does deal simply with piloted-loop closure without regard for the form of the response.

4.4.4 Response types A little less radical than the direct-force modes are the various response types. A pitch attitude response type, which we mentioned earlier, is one in which an aft step c o m m a n d on the stick or column rapidly produces a constant pitch angle. Often this is combined with a throttle c o m m a n d that regulates the speed. Some idea of the flying qualities of these modes can be gained from Figure 4.21, from H o h [ 11 ], which sketches the responses associated with the various response types. Some of the response types produce flying qualities which are very good, even for untrained pilots, but they are artificial modes and they must be integrated with artificial features (like special flare modes) to make them practical for full-envelope flying. Augmenting the elevator's action to produce rapid dynamics in essentially outer-loop responses like flight path can result in high-loop gains and control-surface-actuator limiting. With sufficient attention to detail and training of the pilot to understand the dynamics and their necessarily unfamiliar failure characteristics, successful production versions of various response types have flown for many years. However, there is currently a move back towards more conventional response types which mimic the behaviour of unaugmented aircraft but minimise nuisance coupling and provide rapid, well-damped responses. These systems minimise the pilot training and make dealing with failures much more natural.

4.5 Notes on some control design concepts

4.5.1 Integration in the forward path An example of integration in the forward path is seen in the pitch dynamics of an aircraft which is unstable longitudinally (Figure 4.22). The short period has degenerated to one unstable first-order root and one first-order stable root. Using proportional plus integral (P+I) compensation in the forward loop, we ensure that the steady-state error for pitch-rate commands is zero. More importantly, the integrator stabilises the system by pulling the locus over to the left half plane. Also, if we look at the details of the root locus of Figure 4.22, we observe that for this example there is a closed-loop pole very close to the zero f o r m e d by the P+I numerator. The closed-loop transfer function (which uses the shorthand s+ r ~ (r)) is:

148

A~


7 ~l~ ®1.~_._

~J._~

.~- E

~1~

~

eq

o~o

Handling qualities

149

imaginary axis

augmented (i.e. closed loop) poles

unstable aircraft pole |(

real axis

-2

-4

I -4

I

I -2

I

I 0

I 2

I

I 4

Figure 4.22 Root locus for proportional-plus-integral (P +I) control of longitudinally unstable pitch dynamics Kq(K)(1/To 2) (0)( - a) (b) + Kq(K) (1/7"02)

(4.20)

so this closed-loop pole root near K is essentially cancelled by the n u m e r a t o r root (K). This cancellation is an important design objective. By choosing the P+I zero to be close to the stable aircraft root, we have a closed-loop transfer function which is approximately:

Kq(1/ T°")

r(,p. ,0'.,p]

(4.21)

where the primes denote closed-loop values and the square brackets reflect the shorthand for a second-order term. The flying qualities of this expression can easily be determined by examination or using a short-period equivalent system.

4.5.2 Notch filters Notch filters are designed to cancel a known resonance, particularly those due to structural vibration modes. Ideally, of course, if the notch perfectly cancels the structural resonance we see no net effect. Unfortunately the cancellation is rarely perfect and the phase lag of the notch can fall in the u p p e r end of the flying-quality frequency range and hence contribute to equivalent delay. Placement of these and similar filters in the feedback path helps avoid this problem.

150


4.5.3 Stick prefilters When a force sensor is used to translate the pilot's commands into an electrical signal for the flight control system to process, then a stick (or yoke or wheel) lag filter is a common way of removing the high frequency signals resulting from the pilot's inadvertent high frequency inputs. Experience is mounting, however, to show that force command systems are inadvisable because the attendant stick filter, although usually only a first-order lag, causes too much equivalent time delay for good flying qualities. By using a position command with some stick motion, the dynamic combination of the pilot's limb with the manipulator appears to give the desired filtering effect. If the pilot's force input is used in calculating the equivalent delay, the feelsystem dynamics can contribute significantly to the delay. However, the pilot seems relatively tolerant of the equivalent delay generated by a feel system. The subject of feel-system dynamics is covered elsewhere.

4.5.4 Model prefilters A number of full authority systems have used a transfer function or statespace model of desirable dynamics in a prefilter. Unfortunately, the very high loop gain desired is often unattainable for realistic stability margins. When an attainable gain is selected, the aircraft loop is not high-pass and the model (which is a lag) and the high-gain loop (also a lag), now cascaded together, simply produce too much total high frequency phase lag, i.e. equivalent delay.

4.6 Pilot-induced oscillations (PIOs) Pilot-induced oscillations (PIOs) have plagued piloted aircraft since the beginnings of powered flight. The original 1903 Wright Flyer was susceptible to PIO, and the problem as a whole has not yet been solved. As defined by the 1995 revision to the US flying-qualities interface standard, MIL-STD-1797A [12], PIOs (renamed pilot-in-the-loop oscillations) are sustained or uncontrollable oscillations resulting from the efforts of the pilot to control the aircraft. Implicit in this definition is that these are unintentional oscillations: experience has shown that some pilots naturally apply oscillatory-looking control inputs during normal operations with perfectly good airplanes.

4.6.1 PIO categories Researchers into the unpredictable, and often castastrophic, p h e n o m e n o n of PIO have found it convenient to classify the event into one of three categories, depending upon cause:

Category I: linear pilot-vehicle system oscillations. These PIOs result from identifiable p h e n o m e n a such as excessive time delay, excessive phase loss due

Handling qualities 151 to filters, improper control/response sensitivity etc. They are the simplest to model, understand and prevent. Category II: quasilinear events with some nonlinear contributions, such as rate or position limiting. For the most part, these PIOs can be modeled as linear events, with an identifiable nonlinear contribution which may be treated separately. Category III: nonlinear PIOs with transients. Such events are difficult to recognise and rarely occur, but are always severe. Mode switching which cannot be represented by a quasilinear equivalent, is the c o m m o n culprit.

4.6.2 PIO and APC A new term for PIO (and related events) has recently been introduced: aircraft-pilot coupling (APC). The US National Research Council f o r m e d a Committee on the Effects of Aircraft-Pilot Coupling on Flight Safety to study the larger APC problem; their final report is interesting reading [13]. It is important to note that the correct term is unfavourable APC, since it can be augued that normal piloted control is favourable APC. The NRC committee's report defines APC as either 'oscillatory' - - therefore PIO - - or 'divergent (nonoscillatory)' - - therefore 'APC events or nonoscillatory APC events'. This distinction is rather arbitrary, and for the most part unnecessary: the entire NRC committee report contains only two examples of nonoscillatory APC events - - and one is also referred to as a PIO! It is difficult to pin down exactly what constitutes a nonoscillatory APC, but there are literally hundreds of well defined oscillatory events - - PIOs. Until more evidence can be assembled for the existence of a distinct class of problems u n d e r the definition of nonoscillatory APC, it is r e c o m m e n d e d that the specific terminology for PIO be retained.

4.6.3 Criteria for category I PIOs It is generally recognised that PIO is one of the possible consequences of a deficiency in basic flying qualities. Before the advent of boosted controls and active augmentation, PIOs were due almost entirely to poor design of the airplane. These events were category I in nature; that is, they were due to some deficiency such as low short-period damping or low control sensitivity (stick force per g). As a result, early PIO criteria were mode based: they addressed the p h e n o m e n o n by restricting the attainable values for a few specific modes. Recently, most PIOs on highly-augmented, fly-by-wire airplanes have been category II or III events, usually resulting from rate limiting. These include the YF-22 at Edwards AFB [14,15], two occurrences with the Swedish SAABJAS-39 Gripen [16] and early flight tests of both the C-17 and the Boeing 777 transport aircraft [17,18]. Prevention of PIOs for highlyaugmented airplanes requires more sophisticated criteria, especially when it becomes difficult to determine precisely what the airplane's modes actually are.

152


A common contributer to category II PIO is discussed later in this chapter. Here we will focus on category I events. We will limit ourselves to longitudinal PIOs, because they are the most common though there have been some spectacular roll PIOs, including the M2-F2 lifting body [19] and the YF-16 lightweight fighter prototype [20].

4.7 Modal PIO criteria Beginning in the early 1960s, largely as a result of a now-famous PIO involving a T-38A airplane [21], there was an intense effort to develop criteria for prediction of PIOs primarily in low-altitude, high-speed flight. Several candidate criteria that showed considerable promise were proposed by researchers. For the most part, these criteria were modal - - that is, they placed explicit limits on the short-period mode, or some combination of the short-period and stick force per g o r control system phase lags. The most likely culprit for PIOs in an unaugmented, conventional airplane is short-period damping. Low short-period damping results in an airplane which is oscillatory hands free, so it certainly will promote PIO with the pilot in the loop. Three of the modal criteria are described below. For simple (unaugmented or lightly-augmented) airplanes in low-altitude, high-speed flight, they might still be of some use. As we will see, however, for the more complex modern airplane, a more sophisticated requirement must be applied.

4. 7.1 STI high-gain asymptote parameter Ashkenas and associates [21] at Systems Technology Inc. (STI) observed that pitch control at high speeds and low altitude, using pitch-attitude cues, can be described by the relationship between the total damping of the short-period mode, 2(spoJsp, and the pitch attitude zero 1/7"02. For a pure-gain pilot (as is hypothesised for PIOs), the limiting value of short-period total damping is dictated by the high-gain asymptote parameter o-a (spC.Osp- (1/2 × 1/Ta2). The closer this value is to zero, the more likely a PIO will develop. The STI researchers point out further, however, that this high-gain asymptote parameter will be greater than zero for all but the most unusual airframe configurations. They conclude that 'for airplanes with negligible controlsystem dynamics (including nonlinear elements or bobweight effects), longitudinal PIOs involving only attitude control are essentially impossible'. Obviously, the initial assumption that the pilot is a pure-gain operator with no input shaping or time delay is key to this conclusion. Nonetheless, the high-gain asymptote parameter, although useful for illustration, has never been formally adopted as a criterion for predicting PIO. STI developed a requirement which incorporated a measure of the phase lag of the flightcontrol system at the short-period frequency [22], with a lower limit on ora of 0.5 for most flight tasks. =

Handling qualities

153

16 Fs/n, Ib/g

IX

IX

12

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0

I

I

I

I

1

2

3

4

1

1 )

high-gain asymptote (aa=~Spt%p 2 7-02 • PIO occurrence IX No PIO occurrence

Figure 4.23 PIO prediction using the high-gain asymptote parameter Examination of a single example dataset will illustrate the overall lack of correlation for the high-gain asymptote parameter. A r o u n d the same time that Ashkenas and STI were doing their PIO work, two researchers at N o r t h American Aviation, A'Harrah and Siewert, were pursuing their own criteria. T h e criteria will be discussed below; for now we are interested only in the data collated by A ' H a r r a h and Siewert [23], comprising a list of 43 flight data points for low-altitude, high-speed flight involving fighter and attack aircraft. For 41 of these points the basic dynamics (short-period characteristics plus stick force and position per g) were noted. PIO was observed for 14 of the 41 cases. Figure 4.23 shows the high-gain asymptote for the 41 cases. T h e crossplotted parameter, stick force per g, was selected simply for convenience, not because it is necessarily expected to help to correlate the data. T h e r e is some indication that ~ra is important, since all PIO cases lie below a value of a b o u t 0.9. On the other hand, it is clearly not the only p a r a m e t e r of importance, since there are also many non-PIO points at low ~ra values. T h e second p a r a m e t e r selected by STI for their criteria [22], control system phase lag at the short-period frequency, is unavailable for these cases. As will be seen below, however, there are other parameters - - especially stick force per g which better correlate the Figure 4.23 data, so we may conclude that ~ra is not the answer to the PIO p r o b l e m for traditional airplanes.

154

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control metric, (Fs/n) 3 x (~/n), in Ib3/g4 • elO occurrence z~ No PIO occurrence

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i

i

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manoeuvring ~ 1 > _ - - t ~ t - - l - - I - - ~ force ~ ~ ' , ¢ ~ _ ~ graFdi?n?t' ~ . ~ !

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0.10 short-period damping ratio, ~sp • PIO occurrence z~ No PIO occurrence

1.00

Figure 4.25 PIO criteria using dynamic stickforce per g

Handling qualities

155

4. 7.2 A'Harrah-Siewert criteria A'Harrah and Siewert proposed their own criteria for prevention of PIO, especially for low-altitude, high-speed flight, in the 1960s. The most mature of these recently resurfaced as the US Federal Aviation Administration searched for ways to regulate against PIOs in commercial airliners. Early draft advisory circulars proposed the A'Harrah-Siewert criteria, but later versions have not. A'Harrah-Siewert PIO criteria [23] use an airplane response metric and a control metric. The response metric is defined as the time to one-tenth amplitude of the short-period response, compu ted as T l / 10 In (0.1) / ((spC0sp), and the control metric is a combination of stick force and position per g, (FJ nL)~x (6/nL), in units of in-lbS/g 4. The PIO boundary for their criteria is shown in Figure 4,24, along with their flight data introduced in Figure 4.23. Correlation is very good for the flight data, as there are only two PIO cases clearly on the nonPIO side of the boundary (and both are at least near the boundary), and two nonPIO cases on the PIO side. This makes the A ' H a r r a h Siewert criteria appear to be very effective. (One significant shortcoming, n o t e d by large-airplane manufacturers, has been that the control metric for wheel-and-yoke transports is orders of magnitude larger than the highest value in Figure 4.24, and this has understandably raised some concern.) =

4. 7.3 Dynamic stick force per g T h e developers of the US military specifications in the 1960s were aware of the work of both STI and A'Harrah and Siewert. Based on research at Cornell Aeronautical Laboratory (later Calspan), however, the choice for the military requirements was a dynamic stick force per g parameter that is primarily a function of short-period damping ratio. The requirements on stick force per g from the military standard [12] are shown in Figure 4.25, along with the now-familiar data collected by A'Harrah and Siewert [23]. The requirements of Figure 4.25 are even more effective at correlating the data, better than either the high-gain asymptote or A'Harrah-Siewert criteria. One PIO case lies on the nonPIO side, and one nonPIO case is on the PIO side of the boundary. Thus, we may conclude that, for conventional airplanes where short-period damping and control response are the primary causes of PIO, dynamic stick force per g is a very effective PIO criterion.

4.8 N o n - m o d a l PIO criteria Flying-qualities criteria introduced up to now have been directed towards airplanes responses for controlling inputs look similar to those of unaugm e n t e d aircraft, whether augmentation is used or not. As long as the basic characteristics of the airplane resemble those of the conventional response type in Figure 4.21, the modal criteria may be applied. The modal criteria are applicable even to less conventional-looking responses if the source of the

156


unconventional form is well approximated by a time delay at frequencies below about 10-20 rad/s. T h e n we can apply the equivalent-systems approach and make use of the same criteria, along with a new limit on equivalent time delay. Examples of such high frequency dynamics include the typical noise, structural and anti-aliasing filters applied to the output signals of aircraft motion gyros and accelerometers. T h e r e are cases where this adherence to the traditional criteria breaks down, however. Historically this has been a result of the addition of lag or lead/lag filters in the pilot's command path with break frequencies near the pilot's operating frequency. The dynamics often are not conventional looking on a frequency-response plot, and use of traditional criteria (by applying equivalent-systems techniques to the responses) has resulted in controversy [24]. Another example of the shortcomings of traditional criteria is the unconventional response type, where the basic response form is not even close to that of the conventional airplane. Consider, for instance, the attitude response type where the short-term response to pitch control inputs looks like this: 0

K0e-r~

8e = IS2 + 2~',OS + ,oZl

T h e r e is certainly nothing wrong with fitting an equivalent system to an attitude response type to obtain this transfer function. Note, however, that this equivalent airplane does not have the same form as that for the traditional airplane: it is missing the zero 1~To2 and a free s in the denominator. The second-order lag that dictates the response clearly is not the same as the traditional short-period mode with which we are familiar. Therefore, it would be incorrect to blithely plot this root on the traditional criteria and make judgements about the short-period flying qualities of the airplane. What is needed, then, is a way of judging the flying qualities of aircraft which defy the traditional modal criteria.

4.8.1 Some current criteria Numerous flying-qualities researchers have proposed n o n m o d a l criteria for prediction of category I PIO. Typically these criteria apply well to the database u p o n which they are based, but break down when confronted with data from other experiments. The following is a brief summary of four longitudinal PIO criteria.

Airplane bandwidth~pitch-rate overshoot Pitch-attitude bandwidth criteria were developed for evaluation o f the handling qualities of highly augmented airplanes where more conventional criteria cannot be easily applied [26]. The criteria are included in the

Handling qualities 157 handling-qualities interface standard MIL-STD-1797A[12]. (The limits in MIL-STD-1797A have been found to be much too stringent and have been adjusted significantly, especially with the addition of a requirement on pitchrate overshoot [25].) They have been adapted to the prediction of PIO susceptibility as sketched in Figure 4.26. All of the bandwidth parameters are to be measured with the feel system included at all times (even if force sensing is used for aircraft commands). This differs from the approach taken by most other researchers. The argument is made that the feel system is not transparent to the pilot, and that it will therefore influence both pilot opinion of flying qualities and probability of encountering a PIO [26]. The developers of the bandwidth-based PIO criteria observed that, if a PIO occurs, the likely frequency for the oscillations is well approximated by the pitch-attitude neutral-stability frequency, tol800, with a slight adjustment of an additional 0.5 rad/s [27]. The hypothesis is that, in a PIO, the pilot adds little in the way of dynamics to the pilot-vehicle system (i.e., the pilot displays synchronous tracking behaviour [21]). The added 0.5 is an admitted fudge factor which probably indicates the addition of some small amount of lead as the pilot attempts to cope with the PIO.

Neal-Smith The Neal-Smith criteria [5] were also designed for the evaluation of flying qualities of highly augmented airplanes. The original requirements explicitly referred to handling-qualities levels but only indirectly addressed PIOs (Figure 4.11). Although there is a region (corresponding to handling qualities level 3) where PIO tendencies are mentioned, there is no clear P I O / no PIO dividing line on Figure 4.11. Strong PIO tendencies are indicated throughout the level 3 region, so this is clearly a region where PIO is predicted, but tendencies to oscillate in the middle of level 2 might also signify a milder PIO tendency. As with all the nonmodal criteria considered here, the Neal-Smith criteria are frequency-domain based. Unlike the others, however, application is best performed using transfer function models of the airplane, rather than frequency-response plots (in their original development [5], application was entirely graphical and it was possible to avoid obtaining transfer functions). This is a shortcoming of the criteria, since it raises the issue of the best way to obtain the transfer function, especially from flight test data. A significant complication of the criteria is the requirement to perform closed-loop analysis of the pilot-vehicle system. This requires assumptions about the pilot model to be used. Neal and Smith established several ground rules which they applied to their own flight research data to derive the boundaries. These ground rules have been varied, relaxed, tightened and ignored by other researchers over the years, but there is no real evidence that these variations are significantly more successful than the original version. As

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originally developed by Neal and Smith, the parameters in the criteria are obtained by finding the dynamics of the pilot model given in Figure 4.10, i.e.,

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Yp= I~ (TLS+ I) e-'P for the pitch-attitude dynamics of the airplane described by Y~= O/bes. The pilot time delay, rp, is a fixed value (Neal and Smith assumed 0.3 s) and K p, 7"/ and TL are varied to meet specific performance constraints. In the original Neal-Smith analysis, the performance criteria were a specified closed-loop bandwidth, BW (where the phase of the closed-loop system, / ( 0 / 0 c ) , is - 9 0 degrees), of either 3.0 or 3.5 rad/s and closed-loop droop of exactly - 3 dB. The parameters of the Neal-Smith criteria are the closed-loop resonance, ]0/ 0clm~,, and the phase angle of pilot compensation, /_pc, at the bandwidth frequency. Determination of the best pilot model is not a trivial task when performed manually. Most users of the Neal-Smith criteria have developed software which will perform the loop-closure process automatically.

Smith-Geddes The Smith-Geddes P I t criteria were developed from basic principles of closed-loop piloted control of pitch attitude and normal acceleration [28]. They were initially aimed towards handling qualities, and they owe as their foundation the Neal-Smith database. The criteria have undergone some revisions as well as extension into the roll axis. Smith and Geddes define three types of P I t . These types are not to be confused with the categories of P I t mentioned earlier. The parameters of the Smith-Geddes criteria, as currently applied [29], are as follows: (i)

Slope of the pitch-attitude-to-stick force transfer function, S, defined between 1 and 6 rad/s, in units of dB/octave. (ii) Criterion frequency, too defined as 6+0.24S. If a P I t is predicted this is the expected P I t frequency. (iii) Phase angle of the O/Fe~transfer function measured at toe If the phase angle /-O/Fe~(jtoc) is more negative than - 1 8 0 °, a type III (attitudedominant) P I t is predicted. (iv) Normal acceleration parameter, ~(/'toc). If the phase is between - 160 and - 1 8 0 o, a type I (acceleration-dominant) P I t is predicted if, in addition, the normal acceleration response at the pilot's station is such that ~(Jtoc) = Ln~/Fs(Jtoc) - 14.3toe ---<- 180 deg. In other words, given no phase margin in pitch attitude at the criterion

160


frequency, the aircraft is definitely susceptible to PIOs; if there is 20 ° or less phase margin, PIO will occur if there is no phase margin in adjusted normal acceleration. The Smith-Geddes criteria define a type II PIO whenever any open-loop (airplane) mode has damping ratio of less than 0.2. The Smith-Geddes criteria are known to be in favour by many US researchers [14]. Unfortunately, they have not proven to be very effective at distinguishing between PIO-prone and PIO-resistant airplanes [25] and have been shown to lack some fundamental measures of those characteristics which lead to PIO in the first place. A basic premise of the Smith-Geddes criteria is that the magnitude of the airplane's pitch-attitude response, in the frequency range of typical piloted control (1 to 6 rad/s), may be considered to be a straight line. The more k/s-like this line, the better. This premise is well founded in experimental data and theory [30]. It assumes, however that all of the dynamics typical of a short-period-controlled airplane (i.e., the pitch-attitude zero 1/T~2 and the short-period mode described by (sp and 0Jsp), plus any possible added dynamics in the flight control system can be approximated by a single slope. This is too low order an approximation of the dynamics in that region.

Gibson phase rate Numerous PIO design guides and criteria have been developed by J o h n Gibson. One version is included in MIL-STD-1797A [12] as a short-term pitch requirement. The version considered here [31] consists of a combination of limits on pitch-attitude phase rate and on control/response sensitivity beyond the neutral stability frequency, 0Jl800, as illustrated in Figure 4.27. Gibson's phase-rate parameter is a measure of the slope of the attitude phase curve around Wl8Ooand 2Oils%. If it is defined between to18% like and 2oJ1800, it is identical to the phase-delay parameter used in the bandwidth criteria. One significant difference exists, however, for the bandwidth criteria. All requirements are referenced to control force, and therefore control-feel system dynamics are included as part of the system. For Gibson's criteria, the feel-system dynamics are excluded. Application does require, however, that the gearing resulting from the feel system be included, i.e., the frequency response plotted on the Nichols chart, Figure 4.27, is referenced to control force, even though the force-feel dynamics are excluded. Gibson observes that if a PIO occurs, the likely PIO frequency is 0J1800.It has been demonstrated for a limited set of data [27] that this is indeed the case - - as long as the feel system dynamics are included as a part of the aircraft model. The level limits in Figure 4.27 actually deal explicitly with PIO susceptibility and severity, not handling qualities as is traditionally the case. L1 defines the region where no category I PIO will occur. If a design falls in L2 some PIO tendency might be expected, but it is likely to be dangerous. For a design in L3 PIO susceptibility makes it dangerous.

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162


Second in the evaluations were the Gibson criteria, with an overall success rate o f 80 per cent (166 of the 207 cases). The primary shortcoming was in the application of the gain-sensitivity parameter to a set of transport airplane configurations, indicating a need for the definition of new limits for large, wheel-and-column-controlled airplanes. The Smith-Geddes criteria proved to be too conservative: they correctly predicted PIO for 82 of the 91 PIO cases, but also predicted PIO for 66 of the 117 which did not PIO (overall success rate of 64 per cent). This conservatism is primarily a result of the insistence by the developers that the parameters and criteria are universal; i.e., that they apply to all airplanes in all flight conditions. Almost all transport airplanes fail the criteria, especially in landing configuration, and many smaller airplanes also have trouble in the same configuration. The Smith-Geddes criteria also suffer from the lack o f an explicit measure of phase roll-off as frequency increases. The phase-delay and phase-rate parameters directly define the rapidity with which the phase angle between pitch attitude and cockpit control degrades as frequency is increased. The Gibson criteria take only a snapshot of this phase angle at a single frequency.

Prediction of PIO frequency T h r e e of the four criteria summarised above include estimates of the expected PIO frequency. Certainly we must give some credence to any criterion that can accurately predict both the occurrence and frequency o f a PIO. Estimation of PIO frequency, however, is more difficult than determination of its occurrence in the first place: it requires both time-history information on the event and an accurate analytical model. Sample time-history plots are available from four flight-research studies, and from these we can measure the approximate PIO frequency. The studies are referred to as Neal-Smith [5] (with a total of only three annotated time histories), LAHOS [33] (with six), HAVE PIO [34] (with 12) and TIFS 86 (or TIFS flared landing) [35] (with 19). Neal-Smith was a study of fighter-type responses in up-and-away flight; LAHOS and HAVE PIO were fighter-landing studies; TIFS 86 was a transport-landing study. All but the last were p e r f o r m e d on the USAF variable-stability NT-33A airplane; the TIFS is the USAF total inflight simulation. A total of 40 PIO frequencies can be obtained from the four references. Figure 4.28 is a summary of the effectiveness of each of the three criteria at predicting PIO frequency. This figure shows a crossplot o f measured PIO frequency and prediction error given by (measured frequency) - (predicted frequency). Perfect prediction results in an error of zero; values above zero indicate a prediction which is too low and below zero is a prediction which is too high in frequency. The dashed lines in Figure 4.28 represent ten per cent e r r o r bounds. Part a of Figure 4.28 is for the bandwidth-based definition, WPto(pre-

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164


For part b of Figure 4.28, the Smith-Geddes estimate, criterion frequency, is centred heavily between about 3 and 5 rad/s. If the actual PIO is in this range, the prediction is not bad; outside this range and the prediction gets worse. The obvious skewing of the data points in part b reflects this bias in criterion frequency - - for example, if we said that 'all PIOs occur at 4 rad/s', the data would line up perfectly but with zero error only at 4 r a d / s and increasing e r r o r on either side. The Smith-Geddes prediction effectively does this. Finally, Gibson uses neutral-stability frequency, to18%, but with the feelsystem dynamics excluded and with no adjustment factor. The result (part c of Figure 4.28) is a slightly greater shift upward for most of the data points c o m p a r e d with the bandwidth definition (part a). For the very high frequency points, the prediction is too high by a factor of two, reflecting the lack of feelsystem dynamics. When the feel system was included (part a) these two points were accurately predicted. It must be concluded that n o n e of the parameters used in Figure 4.28 does an outstanding job at predicting PIO frequency. Possible complications include the measurement of frequency in the first place (from time histories, averaged over several cycles of the oscillation), accuracy of the analytical model used for the predictions and ability of the variable-stability airplanes to accurately reproduce the model dynamics during the PIOs.

4.9 Effects o f rate limiting o n P I O Many recent PIOs have exhibited some form of rate limiting. It has not been d e t e r m i n e d if the rate limiting has ever been the direct cause of a PIO, or simply the result of it. Nor has it been demonstrated whether rate limiting exacerbates or attenuates the severity of PIOs. At this time one thing is certain: we do not have hard evidence that a good, solid airplane with no flying-quality deficiencies has ever encountered a PIO owing solely to rate limiting. The most c o m m o n form of rate limiting is rate saturation of the surface drive actuators, caused by excessive demands on the hydraulic system. Interestingly, this is not the most c o m m o n form of rate limiting for PIO. Instead, there has been a c o m m o n practice of implementing a rate-limiter function in the software of the airplane's flight control system, immediately upstream of the surface c o m m a n d signal. Such a software rate limiter is intended to preclude surface rate limiting, usually for reasons other than PIO (alleviation of loads on the tail, for example [17] ), but in reality it has served simply to relocate the source of the rate saturation from hardware to software.

4.9.1 Criteria for category II PIOs Criteria for the prediction and prevention of PIOs due to rate limiting have only recently begun to appear. The added complication of a nonlinear

Handling qualities

165

element means that any usable criteria must account for both frequency and amplitude of pilot inputs, and means an enormous increase in complication for the criteria themselves. The fledgling state of these criteria as of this writing prevents our including them.

4.9.2 The consequences of rate limiting Contrary to popular opnion, reaching a surface rate limiter (whether hardware or software) in flight is not guaranteed to be catastrophic. In fact, evidence from a recent flight research program [36,37] suggests that, if the basic airplane possesses sufficient gain and phase margins, the consequences of hitting the rate limit will be limited to pilot complaints about some sluggishness, but there will not be a tendency to PIO. A ground-based simulation p e r f o r m e d on the US Air Force's large amplitude mulitimode aerospace research simulator (LAMARS) confirmed this observation. Although the results of this simulation are not yet available in published form, a graphical example is shown in Figure 4.29. This is a 30-second segment from a HUD pitch and roll tracking task of over two minutes, flown by one pilot. The dashed lines are for a solid, level 1 airplane with no augmentation but with severe rate limiting at ten degrees per second (configuration 2DR10). The pilot considered the airplane to be a bit sluggish, with bobble tendencies, but no hint of a PIO. By contrast, the solid lines in Figure 4.29 are for an airplane with similar dynamics--achieved via feedbacks (configuration 2DUR20). The bare aircraft is highly unstable, and when the rate limit of 20 degrees per second is reached a rapid pitch divergence develops. As the bottom plot shows, the pilot successfully avoids the rate limits until about 83 seconds into the run, where a push and pull on the stick drives the airplane onto the limits. A PIO o f about one cycle results, and the stimulation was halted at 86 seconds as the airplane was reaching almost 7g normal acceleration. Not surprisingly the pilot considered this to be a highly PIO-prone airplane, although he thought it had good flying qualities up until the rate limit was reached. For the first 83 seconds of the runs in Figure 4.29, the pilot is on the rate limit 21 per cent of the time for the good configuration 2DR10, and only two per cent of the time for configuration 2DUR20. So it is clear that the a m o u n t of time spent on the rate limit is not the final determinant of flying qualities or PIO. Intsead there appear to be two primary factors. (i) How much more does the pilot need out of the airplane; (ii) What are the ramifications on airplane response. In the case o f the two examples, the pilot does not appear to need much more out of the airplane, or the sluggishness of configuration 2DR10 would be more degrading. On the other hand, the very large, sudden and adverse

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change in dynamics that occurs for configuration 2DUR20 makes it susceptible to catastrophic PIO and loss of control.

4.10 Concluding remarks The language of handling-qualifies analysis and design draws on the classical control theory which emerged in the middle of the twentieth century (for a more detailed description of handling qualities, see Hodgkinson, [38] ). This approach, with its insight into the dynamics of the aircraft, pilot and control system, builds on the approach to specifying handling qualities which Vincenti [39] said 'illustrates the intellectual and practical richness of engineering knowledge'.

4.11 References [1] CHALK, C.R., NEAL, T.P., HARRIS, T.M., PRITCHARD, EE., and WOODCOCK, R.J.: Background information and user guide for MIL-F-8785B(ASG), 'Military specification--flying qualities of piloted airplanes'. AFFDL-TR-69-72, August 1969 [2] MCRUER, D.T., ASHKENAS, I.L., and GRAHAM, D.: 'Aircraft dynamics and automatic control'. (Princeton University Press, 1973) [3] HODGKINSON, J., LAMANNA, W.J., and HEYDE, J.L.: 'Handling qualities of aircraft with stability and control augmentation system--a fundamental approach'.J. Roy.Aeronaut. Soc. February 1976 [4] WOOD, J.R., and HODGKINSON, J.: 'Definition of acceptable levels of mismatch for equivalent systems of augmented aircraft'. McDonnell Douglas Report A6792, 19 December 1980 [5] NEAL, T.P., and SMITH, R.E.: 'An in-flight investigation to develop control system criteria for fighter airplanes'. U.S. Air Force Flight Dynamics Laboratory report AFFDL-TR-70-74, December 1970 [6] HOH, R.H., MITCHELL D.G., and HODGKINSON,J.: 'Bandwidth--a criterion for higly augmented airplanes'. Criteria for handling qualities of military aircraft, AGARD-CP-333, Apr. 1982, pp. 9-1-9-11 [7] HOH, R.H., MITCHELL, D.G., ASHKENAS, I.L., KLEIN, R.H., HEFFLEY,R.K., and HODGKINSON,J.: 'Proposed MIL standard and handbook--flying qualities of air vehicles'. USAF Wright Laboratory Report AFWALTR--82-3081, November 1982 [8] RICKARD, W.W.: 'Longitudinal flying qualities in the landing approach'. Douglas paper 6496, 12th annual conference on Manual control, 25-27 May, 1976 [9] GIBSON, J.G.: 'Handling qualities and the fly-by-wireairplane'. Proceedings of the AGARD flight mechanics symposium on Stability and controlAGARD CP-260, September 1978 [10] HOH, R.H., MYERS, T.T., ASHKENAS, I.L., RINGLAND, R.E, and CRAIG, S.J.: 'Development of handling quality criteria for aircraft with independent control of six degrees of freedom. Ab3NAL-TR-81--8027, April 1981 [11] HOH, R.H., and MITCHELL, D.G.: 'Short take-off and landing (STOL) criteria for precision landings'. USAF Wright Laboratory Report AF~AL-TR-86-3050, 1986 [12] 'Flying qualities of piloted aircraft'. Department of Defence interface standard, MIL-STD-1797A, revised notice 1, June 1995 [13] National Research Council, Committee on the Effects of Aircraft-Pilot Coupling on Flight Safety, Aviation Safety and Pilot Control: 'Understanding and

168

[14] [15] [16] [ 17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]

Flight control systems preventing unfavourable pilot-vehicle interactions'. (National Academy Press, Washington, D.C., 1997) DORNHEIM, M.A.: 'Report pinpoints factors leading to YF-22 crash', Aviation Week & Space Technology, 9 Nov. 1992, pp. 53-54 HARRIS, J.J., and BLACK, G.T.: 'F-22 control law development and flying qualities'. AIAA Atmospheric flight mechanics conference, San Diego, CA, July 1996, pp. 155-168 KULLBERG, E., and ELGECRONA, P.O.: 'SAAB experience with P I t ' . Flight vehicle integration panel workshop on Pilot-induced oscillations, AGARD-AR-335, Feb. 1995, pp. 9-1-9-9 ILOPUTAIFE, O.: 'Minimizing pilot-induced-oscillation susceptibility during C17 development'. AIAA Flight mechanics conference, New Orleans, LA, Aug. 1997, pp. 155-169 NELSON, T.A., and LANDES, R.A.: 'Boeing 777 development and APC assessment'. Presented at the SAE Control & Guidance Systems committee meeting, March 1996 KEMPEL, R.W.: 'Analysis of a coupled roll-spiral mode, pilot-induced oscillation experienced with the M2-F2 lifting body'. NASA TN D--6496, Sept. 1971 SMITH, J.W.: 'Analysis of a lateral pilot-induced oscillation experienced on the first flight of the YF-16 aircraft, NASA TM-72867, Sept. 1979 ASHKENAS, I.L., JEX, H.R., and MCRUER, D.T.: 'Pilot-induced oscillations: their cause and analysis'. Northrop Corp. Norair report NOR-64-143, June 1964 CRAIG, S.J., and ASHKENAS, I.L.: 'Background data and recommended revisions for MIL-F-8785B (ASG), military specification--flying qualities of piloted aircraft'. Systems Technology, Inc., TR-1-89-1, Mar. 1971 A'HARRAH, R.C., and SIEWERT, R.F.: 'Pilot-induced instability'. Stability and control, part 2, AGARD CP 17, Sept. 1966, pp. 703-727 MITCHELL, D.G., and HOH, R.H.: Low-order approches to high order systems: problems and promises, J. Guid. Control.Dyn. Sept-Oct. 1982 5 (5) pp. 482-489 MITCHELL, D.G., HOH, R.H., APONSO, B.L., and KLYDE, D.H.: 'Proposed incorporation of mission-oriented flying qualities into MIL-STD-1797A'. WI~ TR-94-3162, Oct. 1994 MITCHELL, D.G., APONSO, B.L and KLYDE, D.H.: 'Feel system and flying qualifies'. AIAA-95-3425, AIAA Atmosphericflight mechanics conference, Baldmore, MD, Aug. 1995 pp. 1-13 MITCHELL, D.G., HOH, R.H., APONSO, B.L.,and KLYDE, D.H.: 'The measurement and prediction of pilot-in-the-loop oscillations'. AIAA Guidance, navigation and controlconference, Scottsdale, AZ, Aug. 1994, pp. 1167-1177 SMITH, R.H.: 'A theory for longitudinal short-period pilot induced oscillations'. AFFDL-TR-77-57, June 1977 SMITH, R.H.: 'The Smith-Geddes criteria'. Presented at the SAE Aerospace Control and Guidance Systems committee meeting, Rent, NV, Mar. 1993 MCRUER, D.T., and KRENDEL, E.S.: 'Mathematical models of human pilot behaviour'. AGARD AG-188, Jan. 1974 GIBSON, J.C.: 'The prevention of P I t by design'. Active control technology: applications and lessons learned, AGARD--CP-560, Jan. 1995, pp. 2-1-2-12 MITCHELL, D.G., and KLYDE, D.H.: 'A critical examination of P I t prediction criteria'. AIAA-98-4335, presented at the AIAA Amospheric flight mechanics conference, Boston, MA, Aug. 1998 SMITH, R.E.: 'Effects of control system dynamics on fighter approach and landing longitudinal flying qualities'. AFFDL-TR-78-122, Mar. 1978 BJORKMAN, E.A.: 'Flight test evaluation of techniques to predict longitudinal pilot induced osciUations'. Master's thesis, AFIT/GAE/AA/86J-1, Dec. 1986 WEINGARTEN, N.C., BERTHE, JR., L.J., RYNASKI, E.G., and SARAFIAN, S.FL: 'Flared landing approach flying qualities, vol I--experiment design and analysis'. NASA CR-178188, Dec. 1986 KISH, B.A., et al.: 'A limited flight test investigation of pilot-induced oscillation due to elevator rate limiting. AFFTC-TR-97-12, June 1997 MITCHELL, D.G., KISH, B.A., SEt, J.S., and MOSLE III, W.B.: 'A flight

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investigation of pilot-induced oscillation due to rate limiting'. IEEE 1998

Aerospaceconference proceedings, Paper 270, Snowmass, CO, Mar. 1998

[38] HODGKINSON, J.: 'Aircraft handling qualities'. (Blackweil Science, 1999). [39] VINCENTI, W.G.: 'What engineers know and how they know it'. (Johns Hopkins University Press, 1990)

© Institution of Electrical Engineers, 2000.

Chapter 5

Automatic flight control system design considerations j. F e n t o n

This chapter introduces a n u m b e r of the issues which must be addressed during the design and development of an automatic flight control system, (AFCS). It does not make a comparison of potential system architectures nor does it suggest an optimum approach because each AFCS is different, d e p e n d i n g upon the airframe and application. However, there is a c o m m o n theme associated with an AFCS development programme that can be introduced and used to familiarise the reader with some of the concepts which must be addressed during the design evolution.

5.1 AFCS development programme Figure 5.1 depicts a typical AFCS development programme with the associated activities provided in months of elapsed time for indicative purposes. The duration of any particular activity is d e p e n d e n t on the complexity of the system being designed and developed together with the associated contractual requirements for the data items or documentation. The figure illustrates the main activities undertaken in the development programme and identifies the basic systems considerations which must be accommodated within the AFCS design.

5.1.1 Study phase~vendor selection T h e AFCS development programme will c o m m e n c e with a study period, during which the high-level aircraft requirements will be established and a preliminary AFCS design proposed to allow selection of the successful vendor. The design proposal will take the form of a n u m b e r of b o u n d volumes of design data which will address each of the high-level requirements and explain the m a n n e r in which compliance will be achieved. This proposal will also detail the company organisation, financial performance, commercial terms, quality procedures and past achievements in this and other relevant © 1998: Smiths Industries PLC, reproduced with permission.

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projects. At the end of this phase a contract is awarded to the successful candidate for the design and development of the AFCS and the supply of the e q u i p m e n t to support the programme

5.1.2 Interface definition The selection of a vendor for the AFCS will probably take place slightly ahead of, or in parallel with, the selection of other suppliers for the supporting sensor equipment. Once contractual arrangements are established with all of the other vendors, a full definition of the AFCS interfaces may be commenced. This task is critical if system design pitfalls are not to be e n c o u n t e r e d downstream, requiring considerable attention to both the sensor characteristics and electrical interfaces to ensure that the AFCS receives and transmits acceptable operating data.

5.1.3 System definition At the same time as the interfaces are being developed, system-definition documentation will be compiled, including the partitioning of the AFCS functional requirements and resulting in the high-level architecture. The system design considerations will be addressed during this phase of the programme which is the foundation for the successful implementation of the AFCS. The control laws will also be developed now.

5.1.4 Software design and code Following the interface, systems and control law definition, the software which provides the AFCS implementation is partitioned within the hardware architecture and segregated into higher and lower integrity software tasks, as appropriate. A major consideration is that there is a consistent theme within the AFCS development concerning the verification and validation of the operational design. This will be addressed in more detail later in the Chapter.

5.1.5 Hardware design and development The AFCS will be partitioned into a n u m b e r of line-replaceable units (LRU) which will perform the interface, control and actuator drive as c o m m a n d e d by the e m b e d d e d operational flight programme (OFP). Each LRU comprises a n u m b e r of modules such as input/output, central processor unit, power supply and conditioning units etc. The hardware design and development task addresses all of these modules with the aim of providing the prototype units upon which the software-based control laws will be ultimately tested.

5.1.6 System integration and test The hardware and software are integrated together incorporating progressively more and more functionality until the whole system is tested in a

Automaticflight controlsystemdesign considerations

173

specially designed system rig. This provides a closed-loop environment which enables the system design team to simulate the aircraft dynamics and control them using the AFCS.

5.1.7 Qualification testing Qualification testing is used to determine the flightworthiness of the LRUs which comprise the AFCS. A n u m b e r of tests are undertaken, such as vibration, temperature/altitude variation, humidity, electromagnetic interference, crash/shock testing, contamination and fungus-resistance growths, plus others d e p e n d e n t on the application. This testing uses selected units identical to the type which will ultimately fly and is c o n c e r n e d with proving that the performance of the hardware will not degrade when in a typical aircraft environment.

5.1.8 Preliminary (final) declaration of design and performance (PDDP/FDDP) T h e PDDP and FDDP are documents which.draw together the documentation for the LRUs and the system in order to make a declaration of the testing which has been undertaken, together with the associated results which prove that the e q u i p m e n t is flightworthy. The PDDP contains a subset of the testing and is used to allow flight testing to commence in parallel with longer duration testing or verification exercises which are d o c u m e n t e d in the FDDP.

5. I. 9. Flight testing The aircraft manufacturer will perform a series of tests to prove the airworthiness of the airframe and the AFCS. There will be a parallel exercise undertaken by the AFCS vendor to implement modifications or rectifications during this activity, if needed.

5.1.10 Certification T h e data that has been compiled and d o c u m e n t e d during all phases of the AFCS project will be presented to the appropriate airworthiness authorities, which certify that the AFCS/aircraft is fit for flight operations when they are satisfied that the design pedigree is acceptable.

5.1.11 Design reviews Reviews will occur at various stages of the development programme to ensure that one phase of design is completed and the next phase can be commenced, see Figure 5.2. Generally, the AFCS customer will request a minimum o f two contractual reviews namely, the preliminary design review (PDR) and the critical design review (CDR) which address the design concept and design

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detail, respectively. These are shown at salient points on the development programme. 5.2 R e q u i r e m e n t s definition a n d verification 5.2.1 Introduction There are two primary considerations that must be satisfied by the AFCS design team which are: • that the equipment fulfils the requirements specified by the customer/

Automatic flight control system design considerations 175 airframe supplier n e e d e d for a product which is fit for purpose; • that the e q u i p m e n t is certified as safe to fly. Both of these considerations result in the design team adopting a n u m b e r of measures in order that they may be satisfied. Broadly speaking, these measures fall into one (or both) of two groups: • overall design methodology and testing; • specific design considerations to implement necessary safety features or satisfy specific requirements. This section will address the overall design methodology and testing philosophy used in a typical AFCS development. The next section will look at the specific design considerations made on an AFCS development.

5. 2.2 Design and test methodology Each AFCS is different, tailored to the airframe which it will control and the overall mission of the aircraft. The complexity of the AFCS is to a great extent d e t e r m i n e d by the a m o u n t of systems, software or hardware functionality which is included to provide the necessary redundancy within the system in order to satisfy the safety and availability considerations. The development methodology is c o m m o n for all types of AFCS, it is merely the a m o u n t of design, testing and documentation activity which varies in order to fully satisfy the verification criteria used to sign off the system. Figure 5.2 presents the V diagram which is used as the basis for the development of many aerospace products. It operates on the simple principle o f progressive breakdown of the functional requirements during the design phase followed by progressive build up of the testing of these requirements during the proving phase. Design reviews are held at the transitions between levels on the diagram. The left side of the V follows design decomposition, the bottom of the V is the implementation of the software code and the righthand side the progressive build up of testing. The diagram is equally valid for the development and testing of hardware. This is achieved by equating the software module to an element of an electrical circuit card design which would be progressively tested at higher and higher levels of functionality. T h e r e are two key items that must be addressed within this methodology and these are: • traceability; • configuration control.

5.2. 2.1 Traceability It is o f p a r a m o u n t importance that a high-level requirement can be traced down through the design to the lower-level requirements which evolve during the functional decomposition, and then back through the various levels of testing to prove that it has been fully satisfied. One way of ensuring that

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traceability is satisfied is to compile a large matrix. This takes all of the references of the requirements in the higher-level specification together with those derived in the lower levels of documentation so that the paths of design and testing can be followed. This is completed when all the design and test activity is finished and used to aid the flightworthiness sign off. Figure 5.3 illustrates the design and verification process which includes the production of the traceability matrices, the software-accomplishment summary and culminates in the issue o f the final DDE

5.2.2.2 Configuration control All of the design documentation, software and hardware building blocks of the AFCS need to be retained u n d e r configuration control. This is to ensure that correct and compatible software and hardware build standards which are fully tested are used for flight. In the event of any anomaly requiring further investigation, the AFCS configuration could be replicated and subjected to the appropriate level of testing. During the development phase, the primary purpose of configuration control is to ensure that formally controlled design changes are implemented into the system and that all associated documentation and testing completed before the change is signed off.

5.2.3 Safety considerations Safety during flight is the primary consideration that must be achieved within an AFCS design. The next section will address methods by which the AFCS is made more robust and available to the pilot in the event of failure. This section is c o n c e r n e d with the use of hazard assessments and failure-modeeffect criticality analysis in order to assess the severity and likelihood of a failure. The AFCS design team will identify the hazards at a systems level which may occur as a result of a failure of some part of the AFCS. These are then categorised d e p e n d e n t on the severity and investigated using a detailed failure-mode-effect criticality analysis (FMECA). The FMECA traces the causes of the possible failures through the system and the individual LRUs using fault-tree analysis. The probable rate of occurrence of the identified high-level failures is derived from the arithmetic combination of the failure rates of the components which make up the overall circuit or part of the system. The data is derived from data handbooks and the failure rates must be aligned with the categorisation of the hazards to ensure that the rate of occurrence is commensurate with the achievement of safety of flight over the life of the aircraft. If this is not satisfied, further design analysis is required to investigate the failure which may result in a systems modification.

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5.3 System design considerations Figure 5.4 illustrates the design considerations that flow from the overall consideration which is to achieve automatic flight control. The list of considerations may not be exhaustive and probably could be grouped or segregated u n d e r different headings. However, the reader can gain a basic understanding of how the considerations grow and become i n t e r d e p e n d e n t as the design is decomposed. The interdependency between levels is emphasised by the databus notation rather than connecting individual boxes which would have resulted in a confusing diagram.

5.3.1 Primary considerations T h e primary considerations from which others are derived as a consequence are listed below: • • • • • • • •

aircraft dynamics; safety; h u m a n interface; performance; environment; physical constraints; logistics support; cost.

T h e effect of each of these is discussed below.

5.3.1.1 Aircraft dynamics The resultant considerations influence the design of the flight control computer in the areas of processing power, the speed and authority of actuators and the speed of execution of control laws and the associated actuator drives. The aircraft dynamics have a direct impact on the stability, determining whether the pilot can fly the aircraft without the AFCS engaged. Highly agile fighter aircraft, such as Eurofighter, are designed to be unstable without the influence of the AFCS in order to achieve the manoeuvrability that is required. In this case a loss of the AFCS function has a catastrophic effect.

5.3.1.2 Safety T h e AFCS design is greatly influenced by the results of the hazard assessment. This may r e c o m m e n d levels of redundancy and dissimilarity in either the system or sensor elements to eliminate common-mode failures. Additionally, the control laws may be segregated on an axis-by-axis basis across processor modules or flight control computer units necessitating mode logic and voting strategies to effect a change or a system reconfiguration. This has the

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undesirable effect of making the system m o r e sophisticated, complex and costly which must be traded off against the increase in fault tolerance.

5.3.1.3 H u m a n interface T h e h u m a n interface to the AFCS is one of the areas that receives severe scrutiny. T h e r e is the need to minimise the workload of the pilot, maximise the information which he receives and ensure that he can take simple, p r o m p t action in the event of fault conditions being enunciated. T h e display of events, the pilot aircraft interface, the position and configuration of AFCS control units b e c o m e major design considerations. T h e repeatability of the system behaviour and outputs is i m p o r t a n t to the pilot who may have to react quickly to certain warnings in order to avoid a hazardous situation. Figure 5.5 shows the AFCS pilot control unit (PCU) in use with the EH101 helicopter. T h e PCU has a n u m b e r of design features which have been included to

Automatic flight control system design considerations 181 assist the pilot and minimise the workload. The autostabiliser channels are engaged by depressing the engage button at the top of the unit. To the left of this is the test button to actuate built-in test and the couple button to display the flight-director bars on the electronic instrument system. A display of actuator positions is provided in the top right-hand corner of the unit which is selectable by using the knob u n d e r n e a t h to choose the axis of interest. The eight buttons to the left of the actuator position display can be used to individually engage/disengage actuators in the appropriate areas of the autostabiliser. Below these buttons is the means of activating the autopilot functions of: B A R - - b a r o m e t r i c altitude hold; • RAD--radar-altitude hold; • VS--vertical speed hold; • IAS--indicated air speed hold; • H D G - - h e a d i n g hold; • NAV--Steering from an external navigation computer; • APPR, BC, G A - - s e l e c t i o n of an approach, back course or go around at an airport.

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Displays of selected targets for hover height, radar height and airspeed are provided, with each target being adjusted using a dedicated knob. Each knob is designed to provide a different tactile feedback to the pilot to avoid errors when wearing gloves. Finally, the bottom face of the unit has space allocated for selecting some of the modes specific to the military version of the EH101 which are automatic transition up and down (TDN, TUP) to target altitudes or speeds and hover modes. The switches light up to provide the pilot with information on the appropriate action to take. The displays are colour-coded amber to provide a warning and green to confirm correct operation. The equivalent PCU for a fixed-wing aircraft would not include the actuator position display, have four axes or the hover modes. The principle of operation using buttons to actuate modes and knobs to select targets would be very similar.

5.3.1.4 Performance The performance of the AFCS in achieving the required stability or autopilot operations is specified by the airframe manufacturer as a result of analysing the overall mission requirements. The AFCS performance is a function of the airframe dynamics, the equipment architecture, sensor configuration and the actuation of the control surfaces. The choice of sensor plays a major role in achieving the performance criteria which can require particular accuracies to be achieved in certain manoeuvres. Signal content/accuracy, noise suppression and latency are all items that the AFCS designer must consider. The choice of sensor for any

182


particular application is often best achieved by a combined approach between the airframe manufacturer and AFCS designer.

5.3.1.5 Environment~physical constraints The physical constraints on the size, weight, power consumption of the equipment, coupled with the specification for the operating environment, can influence the architecture almost as much as the aircraft dynamics and safety aspects. In helicopter applications, where weight and space are at a premium, it is highly improbable that a quadruplex/triplex architecture will be installed. The AFCS could be duplex or simplex and may have multiple processing paths with monitoring to achieve the necessary safety standard. If the equipment needs to operate in a high-vibration, high-temperature installation with the possibility of air contaminated with sand, salt or sea water, then the design must accommodate this while still ensuring maximum reliability. Key considerations in this case include the mechanical design, the component technology to be used, the segregation of electronically clean areas from dirty areas to minimise electromagnetic interference and the method of cooling. The packaging of the modules required to ensure adequate redundancy within a flight control computer without contravening weight, size and power consumption and ensuring adequate cooling is a particularly demanding design compromise to achieve.

5.3.1.6 Logistic support The support of any avionics equipment when it is operating on a fleet of aircraft is a major consideration for all suppliers. The concepts of reliability, maintainability, testability and manufacturability all have to be addressed as part of the AFCS design. Reliability figures are usually included as part of the AFCS performance specification in terms of maximum number of failures per thousands of operating or flight hours. The hardware design must therefore use components which support the required reliability figures. Maintainability must be relatively simple and easy to accomplish by a trained operator. The end user of the aircraft will specify the requirements which may vary from returning the AFCS units to the supplier for repair or using internal maintenance staff to perform levels of repair before this stage is reached. Testability is the concept of being able to diagnose the existence of faults by external or internal testing of the equipment. It is generally specified in terms of percentage coverage of the equipment. The AFCS hardware and software design team will be tasked with the development of external special-to-type test equipment, module test equipment and built-in test software to be executed in the AFCS units. A testability analysis will be performed to confirm the satisfaction of the specification requirements.

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5.3.1.7 Cost Cost is always a major consideration in all aspects of our daily life. In an AFCS design where safety of flight is of paramount importance, the most cost-effective solutions must be applied to ensure that fitness for purpose is achieved. Figure 5.6 illustrates the effect on the cost of implementing a design change at different phases of the AFCS design and development. Clearly a logical well-controlled design phase geared to a rightfirst-time philosophy will minimise the number of late changes and the associated additional cost. The more sophisticated the AFCS design, the more important it is to design the test methodology at an early point in the

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programme so that omissions can be detected and manual testing minimised. Anything that is planned to be included in an AFCS to enhance safety which cannot be easily tested and fully verified is itself a potential cause for concern. The AFCS must provide a compromise between achieving all o f the performance and safety requirements and operating so actively that it is in danger of wearing out the actuators in response to small perturbations. In this respect, the actuator lifecycle cost driver must be traded off against the bandwidth of the overall AFCS.

5.4 AFCS architecture

5. 4.1 Introduction The AFCS provides inner-loop stabilisation as shown in Figure 5.7 by undertaking the signal processing necessary to convert the data received from attitude sensors, autopilot mode selections and manual pilot inputs to actuator drive commands. These, in turn, act upon the mechanical interface between the actuator and the control surface to counter any perturbations.

5. 4.2 AFCS flying control interfaces An example of the AFCS and the flying-controls interface for a helicopter is presented in Figure 5.8. It is notable that the AFCS directly drives the shortterm high-dynamic actuators which are in series with the power controls, together with long-term trim actuators. These act in parallel to the short-term actuators and adjust the trim datum so that the high-dynamic actuators can compensate perturbations about the new baseline. This diagram illustrates the mixing of the axis controls which are necessary for the correct operations of a helicopter. The arrangements of similar interfaces on fixed-wing or highly agile jet aircraft is d e p e n d e n t on the inherent stability of the airframe and the operating requirements for the vehicle.

5.4.3 AFCS system interfaces Figure 5.9 provides a typical AFCS interface with the sensors and other systems on the aircraft. The n u m b e r of sensors, the complexity and m o d e of operation may be different from aircraft, but all AFCS will have similar interfaces. The motion and navigation sensors will provide attitudes, acceleration and rates for stabilisation purposes. The air data computer or transducers will provide altitudes and airspeed for control law gain scheduling and autopilot control laws. The radar altitude is used in precision low-level mission control such as hover in a helicopter. The landing-system and navigation-aid data will support

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autopilot modes associated with the terminal and enroute sections of a flight plan. Electrical power is necessary to drive the pilot's interface unit and flight control computers. The input from the central dimming system is used to dim the blacklight legends on keys on the pilot's interface/control unit at night. Two-way interfaces are maintained with a n u m b e r of other systems such as a flight or aircraft m a n a g e m e n t system which can c o m m a n d the AFCS to fly p r e d e t e r m i n e d routes or manoeuvres. The aircraft displays will receive output data from the AFCS to display warnings, flight-direction information and other system datums. The AFCS will automatically respond to requests from the display controllers to modify the content of the output data. T h e r e are interfaces with the aircraft controls, the trim system and the drive actuators. There is also a safety-critical interface with a hard-wired central warning system which will light attention getters should the AFCS detect and enunciate a failure. Generally, the pilot must acknowledge warnings before they are cancelled and the fault condition acted upon, or a subsequent warning may be generated.

5.4.4. AFCS configurations T h e system configuration for the AFCS installed on the GKN Westlands Merlin EH101 helicopter, supplied by Smiths Industries Aerospace, is shown in Figure 5.10. This system comprises five line-replaceable units, namely, a pilot's control unit, two flight control computers, a dynamic sensor unit used to increase the availability of attitude data and a hover-trim controller for the military variants of this helicopter. Figure 5.11 illustrates how the level of redundancy can be increased in an AFCS by using progressively more flight control computers. After the first miscomparisons between two flight control computers in a duplex configuration, the system must either shut down or the pilot arbitrate. In the EH101 configurations there are dual computing paths in each of the FCCs using dissimilar microprocessors. This significantly increases the level of redundancy and makes the system tolerant of two failures, see Section 5.4.5.8. Clearly, a triplex or quadruplex AFCS will have significantly more redundancy than a simplex or duplex configuration, but there are trade-offs which must be considered. A quadruplex/triplex configuration requires more LRUs, space inside the aircraft, more power, more complex testing and is significantly more expensive. The voting strategies with the synchronisation required across the system is a significant overhead. A highly r e d u n d a n t system is extremely fault tolerant which means that the testing required to release the equipment back on to the aircraft following repair must be exhaustive and require special equipment. The simplex AFCS is easy to repair and generally tends to be the older analogue design. It is used on airframes where the pilot can fly home, or land, following a failure without a major concern.

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Figure 5.10 EHI01AFCS configuration 5.4.5 Flight control computer data processing The major activity of the A r c s is to process data from sensors and derive actuator commands. The intelligence for the system is contained within the flight control computer and is achieved through a combination of hardware and software. Figure 5.12 provides a schematic of the FCC in terms of the software activities, and will be used to discuss the basic functions surrounding the A r c s control laws.

5.4.5.1 Start-up processing When power is applied to the Arcs, each LRU must determine whether or not it is undertaking a cold start or has suffered a short power interruption.


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In the event of a cold start, as d e t e r m i n e d from discretes 1 provided by the power supplies, the FCC will proceed through a start-up routine initialising data areas and will enter a built-in test task which is used to d e t e r m i n e the validity of the overall computer.

5.4.5.2 Power-interrupt processing In the event of a short-term power interrupt of less than 50 milliseconds, for example, this software will restore data from m e m o r y and continue processing from the last recorded point. The detection of the power failing by certain discretes provided by the power supplies will be flagged to the failureanalysis modules. 1A discrete involvesthe setting of a flag which is dependent on the relevant voltage transient.

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5.4.5.3 Built-in test The FCC will contain built-in test (BIT) software and hardware circuitry. This will be used to test out the validity of each of the subsystems within the FCC so that faults may be flagged. Generally, BIT will be segregated into the following areas: • power-up BIT; • run-time BIT; • requested BIT. Power-up BIT will operate after a cold start and check out basic circuitry of the FCC. Run-time BIT will operate continuously while the unit is running using spare capacity in the processing cycle when other tasks are not scheduled by the operating system. The results of run-time BIT will be used to reconfigure the system or provide warnings in the event of a fault being detected. Requested BIT is a long-term activity taking up to five minutes to complete and will be used by the maintenance groundcrew. It will be inhibited in the air and will perform exhaustive wrap-around testing of the modules within the FCC, exercise the processor units, check the memory-protection facilities, check out the actuator drives and finally output a data log for the groundcrew.

5.4.5.4 Failure analysis Failure analysis uses the results derived from BIT, power-interrupt processing and sensor management to determine failure situations. These may cause the disengagement of actuators and warnings to be displayed to the pilot.

5.4.5.5 Sensor management The sensor m a n a g e m e n t p e r f o r m e d by an FCC typically has to determine the validity of the data source and then condition or mix the data with similar signals from other sources. The key design considerations in sensor management are: • • • •

sampling frequency; latency of data; rapid determination of the failure of a sensor; mixing of data to avoid transient effects.

These are addressed below.

Sampling frequency As the FCC will operate using a discrete frame time of a set n u m b e r o f milliseconds and the majority of m o d e r n aircraft operate using digital sensor outputs, it is important that the data sampled does not become aliased. This

Automatic flight control system design considerations 193 is achieved by a correct choice of sampling frequency coupled by anti-aliasing or noise-suppression filters. It is possible to have contamination of the aircraft accelerations, rates and altitudes by structural vibration which may be caused by interaction with a helicopter main or tail rotor. In this case, filters are employed to minimise this noise and will be tuned to match the vibration source, i.e. the rotor frequencies.

Data latency Latency in data must be minimised to avoid excessive phase lag within both the sensor and the FCC. The AFCS designer may choose to use applicationspecific integrated circuits in the FCC to rapidly sample and decode data used within the autostabiliser control laws. The AFCS designer will need to work closely with the airframe manufacturer and sensor supplier to ensure that latency is minimised within the dynamic sensors on the aircraft.

Determination of sensor failures Each FCC will receive digital data which usually includes some status bits set to indicate the failure status as d e t e r m i n e d by the BIT software within the sensor. This is used to exclude the data from this sensor when a fault condition is displayed. Generally, analogue sensors do not provide any indication of failure, and so the signals need to be mixed and the data equalised to minimise sudden transients which can then be used to d e t e r m i n e a voltage condition.

Sensor-data mixing T h e AFCS will usually have multiple sources of dynamic data and algorithms are used to mix or condition this data to exclude sudden fault transients. Typical examples of mixing are averaging the two middle signals from four sources or selecting the middle signal from three. Sometimes, the difference of each signal from the consolidated signal is retained and used to correct the raw data for a limited period after a sensor fault is detected. This reduces the effect of a sudden fault transient in the data source.

5.4.5.6 Mode logic Each FCC must d e t e r m i n e the m o d e in which it believes the AFCS is being asked to operate. All available data is used and includes aircraft switches, autopilot control-unit button presses, autostabiliser e n g a g e m e n t status, sensor status and the view of the outside world as seen by other microprocessors or flight control computers. The general theme followed is one of only allowing a m o d e to be available if fully supported by the necessary sensors and voted for by the majority of the microprocessors/flight control computers. T h e design and development of AFCS m o d e logic is a complex but

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5.4.5. 7 Control laws The control laws are the central feature of the FCC and are simply illustrated in Figure 5.13 which shows the typical response to a step change in roll

Automatic flight control system design considerations 195 attitude using a proportional-plus-velocity-plus-integral controller. This section will not address the methodology used in AFCS control law design apart from stressing that simplicity allows easy implementation, testing and validation. A n u m b e r of basic building blocks will be implemented in software and configured together to provide the desired control laws for a particular application, such as an airspeed hold by controlling the pitch channel by blending together all sources of available data in that axis. An example of some of these building blocks is shown in Figure 5.14 with typical i n p u t / o u t p u t responses.

5. 4.5.8 Actuator drive The primary objective of the control laws is to c o m m a n d the drive to the actuation system. This is always in a closed-loop configuration with the position (or velocity) of the actuator being fed back into the FCC so that the c o m p u t e d error may be driven to zero. Figure 5.15 presents a typical actuator drive and monitoring circuit which combines the output from the control laws in processor 1 and processor 2 to drive one of the actuators on the aircraft. Data is used from the drive to the actuator from another FCC to compare the drive signals and isolate a fault condition which may exist between the two processors. The faulty drive may then be excluded. A comparison is made between the actuator output and that predicted by a model of the actuator. In the event of this comparison failing, the actuator is disengaged. Other similar configurations can be found with differences which d e p e n d upon the application and the AFCS architecture.

5.4.5.9 Output routines The FCC includes software to control the required outputs to other systems in the aircraft d e p e n d e n t on the selected mode.

© Smiths Industries plc, 2000. Published with permission of the copyright owner.

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Ground and flight testing of digital flight control systems T. Smith

6.1 Introduction The final p r o o f of design of any control system is the demonstration of successful integration of the control system into the total vehicle of which it is a part. Such a demonstration of satisfactory and therefore safe design must include an assessment of the behaviour of the vehicle and its control system over the full range of normal and extreme environmental conditions to which it will be subject. Thus, in the case of an aircraft flight control system, this can only be achieved by testing the flight control system (FCS) when it is fully integrated into the aircraft and assessing it over the full operating envelope of the aircraft. Flight testing therefore represents the ultimate p r o o f that the design of the FCS is fit for purpose, meets the design requirements and verifies that the design requirements themselves were valid. Historically, the flight test process has been viewed as an i n d e p e n d e n t check of the whole aircraft and its systems by the flight test team of pilots and engineers whose task was to assess the aircraft behaviour and identify any problems with the design. Any problems identified had to be understood and resolved by the designers and the modified aircraft reassessed by the flight test team. Up to the 1950s, the a m o u n t of flight data obtained from test flights was comparatively small and was made up of a combination of pilot's notes (on a kneepad), photographs of banks of gauges and data recorded on ultraviolet trace recorders which typically would record ten parameters per recorder. Extraction of data from these sources was both labour intensive and time consuming so flight test programmes would extend over many years. The general test philosophy for a new aircraft design was to build a n u m b e r of prototypes and fly as much as possible over a wide range of conditions in o r d e r to demonstrate freedom from problems and good overall behaviour. From a flight test point of view, the 1950s and 1960s was a period o f rapid technological advance and this, coupled with the continual drive for improved aircraft performance, led to many new problems being encoun© 1998:BritishAerospacePLC Reproducedwith permission.

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tered. This inevitably resulted in incidents or accidents with a n u m b e r of aircraft being lost and test pilots being killed or seriously injured. When problems were encountered, further detailed flight testing had to be made in order to gain an understanding of these problems. The designers would attempt to generate fixes to solve each problem. Such fixes then had to be fully flight tested so as to determine their success or otherwise in order to develop and flight clear a final fix which gave acceptable characteristics. Over this period, aircraft flight control systems progressed from comparatively simple systems with cables or rods connecting the pilot's controls to the control surfaces, to more complex power-assisted systems. As the combat aircraft flight envelope increased, control surface loads increased to the extent that hydraulic actuators were necessary to assist and eventually replace the pilot control forces. This in turn led to the requirement for artificial feel systems to give the pilot the correct cues in terms of control forces. As the quest for improved performance continued, the aerodynamic characteristics of new aircraft became more complex and it became progressively more difficult to produce satisfactory handling characteristics by aerodynamic means alone. Autostabilisers were introduced to improve the poor natural damping of the aircraft but since these were simplex, they could only be of limited authority in order to survive in-flight autostabiliser failures. Autopilot functions were also included and these utilised either dedicated autopilot actuators or the autostabiliser sub-actuators in order to introduce the autopilot demands on to the control surfaces. The correct behaviour of these systems had to be assessed in flight and so the flight test programme had to include testing in both the normal failure free state and in each of the possible failure modes. In addition, system failure testing had to be p e r f o r m e d in flight because loss of a system could result in potentially hazardous conditions. For example, loss of an autostabiliser function or loss of a hydraulic system, in certain parts of the flight envelope, could produce a significant transient aircraft response or degrade the aircraft handling qualities to the extent that control of the aircraft could be lost. Such in-flight failure testing required special test equipment and had to be approached and conducted with great care. For example, on the SEPECAT Jaguar, a special autostabiliser failure injection unit was fitted to inject hard-over or null failures in each of the axes of the three-axis limited-authority autostabiliser system. Single hydraulic system failures were simulated in areas of the flight envelope where high actuator loads were experienced, in order to demonstrate satisfactory aircraft behaviour. Such testing had to be p e r f o r m e d in flight because of the relatively low level of confidence in the mathematical models of the aircraft and its systems at that time. In the 1960s and early 1970s, technological advances took place that were to significantly impact the flight test process. These advances included the development of realistic and effective flight simulators, the development of airborne data acquisition and telemetry systems and the development of powerful digital computers. Such computers could both process large

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amounts of test data and provide the ability to develop comprehensive models o f aircraft aerodynamics, structures and individual aircraft systems. These developments together with the rapid advances in the field of electronics led to the introduction of the concept of electrically-signalled flight control systems, that is, fly-by-wire. Since control of the aircraft is a fundamental requirement, i.e. the FCS is a safety-critical function, any such electricallysignalled system must be fail safe. Thus early electrically-signalled aircraft flight control systems had a mechanical backup mode to ensure that control of the aircraft would not be lost u n d e r failure conditions. This again impacted the flight test task because flight testing had to be carried out in all possible failure modes to ensure that the aircraft could be recovered safely when failures occurred. Such electrically-signalled flight control systems were multiplex analogue systems and the Panavia Tornado is typical o f such a system. T h e Tornado c o m m a n d and stability augmentation system (CSAS) is a triplex analogue system with a mechanical backup. However, the increased complexity of the flight control system meant that it was no longer feasible to inject worst-case failures in flight since this would involve a failure-injection device interfacing with all lanes of the multiplex system. Such a facility would have to be multiplexed in order to ensure that failures within the injection facility did not hazard the aircraft! Thus failure testing was done on a realistic flight controls rig as described in more detail later in this chapter. With the rapid advances in microprocessor technology, the move towards digital flight control systems became feasible. In addition, studies into the concept of active control technology (ACT) and control-configured vehicles had indicated that there were significant aerodynamic and structural benefits to be gained if these concepts could be incorporated into future combat aircraft. Such a step forward was considered so significant that a n u m b e r of research programmes were set in place both in the US and in the UK in order to safely develop such systems. The first UK aircraft with a full authority digital flight control system was the fly-by-wire (FBW) Jaguar demonstrator aircraft. The aim of this national research programme was the design, development and flight demonstration of a safe, practical, full-time digital flight control system for a combat aircraft. The prime objective was the identification of the design methodology and airworthiness criteria necessary for flight certification, and throughout the programme the FCS was to be treated in all aspects as though it were intended for production. Although it was not intended to demonstrate the aerodynamic benefits of ACT, the programme included flight demonstration of the aircraft in a configuration which was aerodynamically unstable in the longitudinal (pitch) axis, and demonstration of a stall departure and spin prevention system. These aspects were considered crucial to the practical realisation of ACT. It was also decided that the FBW Jaguar digital FCS would have no backup flight control system o f any kind from the outset of the programme. The reason for this was twofold. First, a mechanical system could not control an unstable configuration. Secondly, an independent electrical backup, whether analogue or digital, would introduce so much

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additional complexity both in the design of the system (hardware and software) and in the flight-clearance processes, that it would be counter productive. From the flight test point of view any such backup system would almost certainly have to be tested in flight with all the associated hazards that this would involve. In the event, the decision to have no backup system was fully justified since other demonstrator programmes (e.g. the US AFTI F-16) had significant problems with their backup systems. The FBWJaguar programme therefore provided the UKwith the vehicle to develop, in a cautious step-by-step approach, the ground and flight test clearance methodology necessary for a digital FCS-equipped aircraft. As a research programme, the FBWJaguar ground and flight trials were an outstanding success. The progressive approach provided a validated set of design, development, ground test and flight test techniques and procedures which could be used as the basis for all subsequent UK digital FCS programmes. Having proved the principles of the digital FCS on the FBW Jaguar, the way was open to fully utilise the benefits of digital flight controls by producing an aircraft which was designed from the outset to take full advantage of the benefits of active control technology. That aircraft design was the experimental aircraft programme (EAP) demonstrator. The objectives of this programme were much wider than the FBWJaguar programme since it was to bring together a number of key new technologies required for a future combat aircraft. However, the digital flight control system was crucial to the success of the aerodynamic, structural and avionics design and it fully utilised the experience gained from the FBWJaguar. It also provided a major challenge to the flight test process and heralded a significant change to the philosophy of flight trials. Previous UK flight trials programmes had utilised telemetry to monitor each test flight, both from a trials safety point of view and to improve the efficiency of flight trials. However, most, if not all, of the test analysis was performed post flight. The advances in computing and modelling techniques which had enabled the realisation of digital flight controls also made possible the concept of in-flight (i.e. r~al-time) analysis of flight test data. The EAP demonstrator programme provided the vehicle for the development of real-time analysis techniques for an aircraft with a digital FCS and these techniques have become the basis for flight testing the latest European combat aircraft, the Eurofighter.

6.2 Philosophy of flight testing As already indicated, the flight trials of an aircraft represents the only truly valid assessment of the performance and characteristics of the flight control system in the total vehicle operating in its true element. However, the modern digitally controlled aircraft is so complex that the flight trials now represent only one part of the assessment of the aircraft and its systems. With the increasing ability to accurately model both the aircraft's aerodynamics and its

Ground and flight testing of digital flight control systems 201 individual systems, the flight test programme is one part of an integrated development, flight clearance and flight certification programme. The main emphasis of the flight trials is now the validation of the models developed in the design and initial flight clearance of the aircraft as well as a demonstration of satisfactory characteristics throughout the flight envelope over the range of configurations and roles of the aircraft. As a consequence, the flight test task begins in the design stage of the programme and continues through simulation, rig test and aircraft ground test before proceeding to the actual flight trials phase.

6.2.1 Ground testing In order to understand the ground test process, it is necessary to consider what actually makes up the flight control system within the total aircraft. The vehicle to be controlled by the FCS has structural and aerodynamic characteristics which need to be defined prior to flight as accurately as possible as a prerequisite for the FCS design and clearance process. Theoretical methods and wind-tunnel tests of physical models are used to produce the structural and aerodynamic models required. These models need to be verified either on the ground or in flight. Clearly, the aerodynamic model can only be verified in flight but the structural model can be partly verified on the ground and so ground tests are performed as a part of the clearance-to-flight process. The flight control system requires electrical and hydraulic power supplies with levels of integrity comparable to those of the FCS itself. Electrical equipment requires cooling and so the environmental control system is also important from an FCS point of view. If the FCS is the main source of air data for the aircraft, then the FCS interface to the cockpit displays also needs to be of high integrity to ensure that the pilot always has the flight reference displays required (i.e. airspeed, altitude, Mach, angle-of-attack as well as normal acceleration, attitudes etc.). The flight control system itself is made up of a number of items of equipment. The heart of the system is the set of digital flight control computers (FCC) which are typically quadruplex (but may be triplex). These computers interface with a variety of input sensors, i.e. pilot's controls (stick, pedal, throttle positions and a variety of switches), inertial sensors (gyros, accelerometers etc.), air data sensors (pressures and flow angles to produce airspeed, altitude, Mach, angle-of-attack and sideslip), actuator position and status signals and signals from other aircraft systems (e.g. weight on wheels, hydraulic pressures etc.). The outputs from the FCCs are the actuator command and control signals and data required by other aircraft systems (e.g. air data signals for pilot displays and other subsystems). Each set of sensors and interfaces will have a level of redundancy appropriate to the requirement, so the primary FCS sensors will again be quadruplex. Within the flight control computers are a number of basic functions of direct interest to the test

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engineer. These are the control laws, the sensor processing functions, the actuator interfaces and the redundancy management, failure monitoring and reporting systems. All these functions must be fully tested on the ground, and test facilities are required to achieve this.

6.2.2 Simulator and rig testing The control laws are designed and developed using modelling and simulation. The design process requires both aerodynamic and FCS models. The FCS model contains the actuator, sensor and computer hardware/ software characteristics so that the control laws can be designed and developed for the real system, i.e. nonlinearities and computing delays are included. The aerodynamic models have a measure of uncertainty at this stage of the process and so each are represented by a nominal model together with a series of tolerances which define the level of uncertainty of the particular aerodynamic coefficients. Having completed the initial design of the control laws using unmanned, i.e. nonreal-time simulation, the full FCS and aerodynamic models are installed on the flight simulator for evaluation by pilots and engineers. Clearly, the simulation models must be validated against the design models to ensure correct implementation onto the simulator, which may have its own set of time delays. The flight simulator contains a representative cockpit with outside-world display to enable a detailed assessment of the control laws. This assessment is carried out over the full flight envelope for nominal and toleranced aerodynamic data so that any shortcomings in the control law design can be identified and rectified. This assessment can often be an iterative process as problems are identified by pilots and referred back to the control law designers. The controls laws are modified and reassessed using offline simulation before the updated laws are passed back to the flight simulator for pilot reassessment. Once a satisfactory standard is obtained, the control laws are released for coding into the FCCs. The simulation task does not end at this point but moves into the next phase where it is used to p e r f o r m a full assessment of the control laws over the full range of aircraft configurations planned for flight assessment in order to generate a flight clearance from a flight mechanics point of view. In the UK, a n u m b e r of m a n n e d simulation facilities have been used for the control law development process. For example, at BAe Warton, a n u m b e r of general-purpose simulators are available and initial control law design assessment can be p e r f o r m e d on these where a generic cockpit is used. The detailed control law assessment requires a more representative cockpit, particularly in terms of pilot controls, so this may be done on either a flight simulator specifically configured for the task or on the simulation facility contained in the FCS rig described in the next section. The advantage of the general-purpose simulator is the very high quality of both the outside-world


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displays and the computing capabilities contained in this facility. The FCS equipment is tested on a ground test rig. The rig itself can be as representative as considered necessary for the project involved. The most representative rig is the so-called iron bird where the FCS and all the interfacing functions replicate the aircraft itself. The iron bird will therefore have a configuration very close to that of the aircraft itself with the controlsurface actuators m o u n t e d in representative structures. All the cable runs and pipe runs will utilise aircraft standard equipment and will be laid out and m o u n t e d in a representative way. Aircraft standard electrical and hydraulic supplies will be utilised and the equipment racking will also be representative of the aircraft. Such an iron bird requires a considerable investment in e q u i p m e n t and facilities, and in the UK, recent practice has been to utilise a test rig that is less extensive in terms of representative aircraft structure but is fully representative in terms of the FCS. This type of test rig is made up of a series of individual test benches which can either be used independently or linked together to provide the complete system. It will also have all the interfaces (either real or simulated) that the FCS requires. Thus the test rig will be made up of the following items: • FCC test bench; • actuator test benches containing representative mounting structures and facilities to apply simulated aerodynamic loads; • inertial sensors' test bench; • air data sensors' test bench; • other sensors' test bench; • simulation benches for sensors and actuators; • cockpit with all FCS-related equipment, representative flight instruments and realistic outside-world display; • simulation computer capable of running the aerodynamic model, the FCS model and any additional model functions (e.g. undercarriage, atmospheric effects etc.) as well as supporting the cockpit outside-world display; • real or simulated engine control system; • real or simulated avionics and utilities control systems; • hydraulic and electrical supplies capable of reproducing the aircraft systems in terms of pressures, flows and redundancy; • data acquisition and analysis system. Figure 6.1 is a schematic of the FBWJaguar ground test rig and it can be seen that a high level of flexibility is provided by such a facility. For example, simultaneous testing can be carried out on each of the test benches. Alternatively, different groups of benches can be linked with simultaneous testing being p e r f o r m e d on each of these groups. Even for closed-loop testing (i.e. with a pilot in the loop) a n u m b e r of different combinations are possible. These range from pure simulation (where the cockpit is linked to the simulation computer which runs models of the full FCS and aerodynamics), through real FCCs with simulated actuators and sensors, to all real FCS

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Figure 6.1 FBWJaguar: schematic diagram of FCS ground test rig e q u i p m e n t with the simulation computer simply closing the aerodynamic loop. This level of flexibility and simultaneous test capability is essential if the large a m o u n t of testing required to clear the FCS is to be accomplished in the minimum possible time period. The principal tasks of the rig test programme can be summarised as follows: (i) (ii) (iii) (iv) (v) (vi)

to verify the control laws by pilot assessment before they are programmed into the FCCs; to integrate the FCS hardware and software; to validate the software actually implemented into the FCS; to integrate the FCS with other aircraft systems including the flight test instrumentation system; to gain a level of confidence in the overall system; to provide a facility for the pilots and engineers to prepare and train for flight trials.

6. 2.2.1 Control law verification As already indicated above, the task of designing and verifying the control laws before implementing them in the FCCs is often shared between the general-purpose simulators and the ground test rig. What is of vital importance is that each of the models used on both facilities is both identical and thoroughly verified. The standard of each model must therefore be clearly defined and tightly controlled using a master data file which is only released to the test facilities when it has been thoroughly checked. Once installed on the test facility, check cases are run to ensure that the model is

Ground and flight testing of digital flight control systems 205 operating correctly. Any change to the models is first installed and checked out in a new issue of the master data file before being formally released to all the test facilities. Only in this way can it be ensured that the correct standard of model is used to verify and validate the FCS as being fit for flight.

6.2.2.2 FCS hardware and software integration and testing The ground rig provides the first opportunity to run the FCS e q u i p m e n t together as a full set of hardware. The functionality contained within the software on first equipment delivery is usually low and simply enables the various items of equipment, to be powered up and run together. As each software function is implemented it is thoroughly checked out (and debugged where appropriate!) to ensure correct implementation and operation. The built-in test (BIT) functions, which will ultimately require a full set of FCS equipment, are also developed to ensure that they correctly identify all conceivable failure scenarios. The individual items of e q u i p m e n t are tested on their own benches. Thus performance testing (i.e. frequency and transient responses, impedance characteristics and rate into load tests) is carried out on each of the actuators m o u n t e d in representative structures. These results are used both to confirm that the actuators meet their specification and to update/validate the actuator models. The inertial sensors (i.e. those containing rate gyros) are tested on rate tables and the pilot inceptors (control-stick unit and sensors, rudder-pedal assembly and sensors, cockpit switches etc.) are tested to ensure correct force/displacement and switching characteristics.

6.2.2.3 Software validation testing This is the most demanding task placed on the rig as it is the final stage of an extensive software validation process. FCS software must be of high integrity and free of faults. It is therefore subjected to a series of tests of which the final phase is carried out on the rig. Before the formal rig test validation process can begin, the delivered software must be shown to be free of faults. Thus, as each function is introduced into the software, it is fully tested and any shortcomings are corrected with software patches. Once a satisfactory standard is achieved, a formal configured standard of software is defined and released for implementing into the equipment. The formal software validation testing on the rig can then begin. If any of these formal tests fail then a new standard of software must be produced and the whole process may have to be repeated. The actual formal test process contains the following aspects: (i) (ii)

Initial testing to ensure that all previous system queries have been cleared. Initial closed-loop evaluation where the rig is operated closed-loop using real FCCs p r o g r a m m e d with the formal software. This evaluation

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also uses all other appropriate real FCS hardware. An experienced test pilot then flies a series of flight profiles to assess aircraft handling and system behaviour over a wide range of flight conditions to identify any deficiencies and to give early warning of any possible software errors. This technique has been shown to be particularly effective in identifying potential errors in the new software release. Having established confidence in the system and its software, the full detailed test process can be initiated. (iii) Full evaluation of the BIT functions to ensure that no self-detected faults exist and a full sequence of failure tests to ensure that the BIT correctly detects and identifies each failure. These tests are of particular interest to the flight test engineers because the design o f an FCS is such that any BIT failure will normally prevent the system from being engaged into its flight mode. Thus the engineers need to understand the causes of BIT failures and the differences between nuisance and hard failures. (iv) Open-loop static, dynamic and transient testing to ensure that the endto-end characteristics of the system are correct. In this configuration, the aerodynamic loop is not closed (i.e. the system is open-loop) and each sensor to surface path is exercised over the full range of conditions. Static tests confirm correct gains, dynamic tests check gain and phase over the range of frequencies appropriate and the transient tests check the time-variant aspects of the different paths and individual control law elements. The results of each of these tests is compared with predictions from the FCS model. Since the n u m b e r of tests can be of the order of 100 000, they are automated as far as possible with the computer comparing each result with an acceptance band. Only when a test fails is operator intervention required! (v) Synchronisation testing to ensure that the system obtains synchronisation on start up and maintains or re-establishes synchronisation correctly. (vi) Timing testing to ensure that the time delays through the FCS meet the requirements and are correctly represented by the models. (vii) Open-loop failure testing to ensure that the failure monitoring functions correctly detect and identify each different type of failure, that the voter and monitor thresholds and timings are correct and that the correct system reconfiguration takes place. Again, this testing is of particular interest to the flight test engineers because the pilot's failure drills and procedures need to address all possible failure scenarios. The correct warnings must be shown to be generated for pilot displays and correct failure information generated for the failure recording and maintenance functions. Other aircraft system failures or specific FCS equipment hardware failures are also assessed where appropriate to ensure correct failure detection and system performance/reconfiguration.

Ground and flight testing of digital flight control systems 207 (viii) Closed-loop dynamic testing (i.e. with the simulation computer closing both the aerodynamic loop and the pilot loop to perform dynamic and transient tests the results of which are compared with the theoretical responses obtained from the model. (ix) Closed-loop failure testing to ensure that, when single or multiple failures are injected into the FCS, any. transients produced are at an acceptable level and handling qualities remain fully acceptable following any FCS reconfigurations. For this testing, the rig is operated fully closed loop with test pilots or experienced test engineers flying the rig. T h e types of failure and the flight conditions at which the failures are injected are defined by a team of flight test, aerodynamics and systems engineers to ensure that all possible failure cases are included and that the worst-case flight conditions and system configurations are assessed. (x) Closed-loop handling testing to ensure that the handling qualities produced by the control law software actually implemented in the FCCs are identical to those assessed during the simulation assessment and clearance process. This is done in all system modes and over the full range of mass and centre of gravity (cg) positions to be flown. Also included are assessments of the FCS behaviour following other aircraftsystem failures. For example, fuel system failures can result in large cg excursions and the behaviour of the FCS in these conditions can be assessed. In fact, the rig can be used to assess aircraft and real actuator behaviour u n d e r extreme conditions to ensure that there are no cliff edges present which could result in loss of the aircraft should they occur in flight. Only when the formal software tests have been successfully completed can partial retests be considered. In the UK, a limited change clearance process was developed during the FBW Jaguar programme. This process identified the minimum a m o u n t of software retesting which was required following a small change to a fully tested standard of software. The process has proved to be both safe and efficient in subsequent UK programmes.

6. 2. 2. 4 Intersystem integration testing The FCS will interface with a n u m b e r of other aircraft systems and such interfaces may be hardwired links or databus links. A typical example is shown in Figure 6.2 which illustrates the overall systems architecture of the EAP demonstrator aircraft. System integration testing is p e r f o r m e d to confirm correct operation of each of these interfaces u n d e r normal and failure conditions. In the case of the EAP facility, the FCS rig was capable of operating with simulated interfaces for the majority of the time but a series of tests was p e r f o r m e d with the FCS rig linked to the avionics rig and the utilities systems rigs for the final stage of the integration testing. Other aircraft programmes have a dedicated integration rig. If changes are made to the software or hardware in either the

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Ground and flight testing of digital flight control systems 209 FCS or in any of the interfacing systems, appropriate integration testing will have to be repeated. A vital part of the flight test programme is the aircraft flight test instrumentation system (FFI) which is used to record the data required for analysis. On m o d e r n aircraft the majority of the FFI is extracted from the various databuses on the aircraft and, in particular, from the FCS. Thus the FTI FCS interface must be thoroughly tested on the rig to ensure correct functioning u n d e r normal and failure conditions.

6.2.2.5 Confidence testing Confidence testing is p e r f o r m e d to generate operating experience with the FCS functioning as a complete system. It is p e r f o r m e d with a full set of real e q u i p m e n t and with the rig operating in the full closed-loop mode. A series o f representative one-hour sorties are flown by pilots and engineers with each sortie including power-up BIT checks, take-off, a formal handling test sequence, a period of free-style handling, approach and landing and system shutdown. This test sequence is flown as often as is considered necessary and is intended to exercise the system as fully as possible over as wide a range of conditions as possible. For example, prior to the first flight of a new aircraft, a minimum of 50 sorties is considered necessary. Following subsequent software upgrades a lower n u m b e r will be performed.

6. 2.2. 6 Flight trials preparation The rig can be used to provide the facility for the pilots and engineers to rehearse each test flight prior to execution. To do this, it can be used either in full simulation mode or with a full set of real hardware depending u p o n the state of the flight test programme and the trials being performed. For example, the first flight of a new aircraft will be rehearsed with a full set of real equipment. Subsequent flights may be practised on either the rig or on the flight simulator depending upon the actual flight trial involved. However, the simulator outside-world display will usually be of much higher quality than that on the FCS rig and so the flight simulator would be more appropriate for rehearsing handling-qualities testing. The rig (and simulator) can also be used to provide a realistic training facility for pilots and engineers to practice drills and procedures for all possible failure scenarios. Even the most convoluted and potentially hazardous failures and emergencies can be practised in complete safety!

6.3 Aircraft ground testing Before the aircraft is ready to c o m m e n c e the flight trials programme, a whole series o f ground tests is required. These comprise FCS build tests, groundresonance and structural coupling tests, aircraft systems testing and electromagnetic compatibility testing.

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6.3.1 FCS build tests The flight control system is fitted to the aircraft and fully functioned in the aircraft environment to ensure that the complete system design has been correctly implemented into the airframe. The build tests confirm that all the individual items of FCS equipment and all the FCS wiring are functioning correctly. The FCS build tests are integrated with the other system build tests to ensure that all the interfaces are correct. Thus the electrical, hydraulic, cooling, avionics and other systems must also be shown to be functioning correctly from a flight control system point of view. Within the FCS all the actuators, sensors and pilot's controls must be correctly rigged and harmonised and it must also be demonstrated that there are no sign reversals in any of the control paths. These build tests utilise an automated g r o u n d test facility (known as the A T E - - a u t o m a t i c test equipment) which contains its own computer and interfaces directly with the FCS computer hardware via suitably protected interfaces.

6.3.2 Ground resonance tests As already indicated, the design process involves the establishment of a series of models which need to be validated during the ground and flight test programme. G r o u n d resonance tests are p e r f o r m e d to identify the various structural modes of the aircraft (i.e. wing, fuselage, fin, tailplane/canard, f l a p / e l e v o n / elevator, r u d d e r etc.) and these provide the first set of data used to validate the theoretical structural model of the aircraft. For these tests, the aircraft is positioned in a suitable test facility (i.e. it may be suspended in a test frame or supported on airbags) so as to replicate the in-flight state. Suitable external excitation e q u i p m e n t is used on the different parts of the airframe and a large n u m b e r of accelerometers are fitted to the aircraft to measure the structural responses and hence identify the actual structural modes. The validated structural model is then combined with the aerodynamic and FCS models to predict the structural characteristics in flight.

6.3.3 Structural coupling tests Structural coupling (or aeroservoelasticity as it is also known) is the p h e n o m e n o n associated with the introduction of a high-gain flight control system into a flexible airframe. The FCS sensors (both motion and position) will detect not only rigid body motions (used to control the aircraft) but also any structural-mode oscillations (generated by the flexible structure) superimposed on these signals. If the attenuation and phasing o f the structural signals are inadequate, then instabilities can occur. Such an instability is potentially catastrophic because it can result in either loss of control or severe structural/fatigue damage to the aircraft. T h e flight control system is designed such that structural-mode filtering is


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included in the control paths where the structural model of the aircraft indicates that potential instabilities can occur. A series of structural coupling ground tests are p e r f o r m e d to identify the characteristics of relevant structural modes and to test the implemented structural notch filters. Suitable test e q u i p m e n t is used to drive the FCS actuators over the required range of frequencies and each FCS sensor is monitored to determine the characteristics of any structural response. The tests have to be d o n e in a variety of aircraft configurations (i.e. different fuel states, a selection of external (or internal) store configurations and various FCS states) in order to determine the full filter requirements. This data is used to update the aircraft structural and FCS models. Structural notch filters are then designed using the complete aircraft structural/aerodynamic/FCS model. Further on-aircraft tests are then p e r f o r m e d with the notch filters implemented in the control laws in order to demonstrate satisfactory stability margins with the full flight-standard equipment. For all these tests, the aircraft has to be in as close to the flight-ready condition as possible so that the test results are fully representative.

6.3.4 Electromagnetic compatibility testing Electromagnetic interference (EMI) represents a serious problem for an electronic flight control system since it provides a mechanism for potential c o m m o n - m o d e failures in a multi-redundant FCS. Malfunctions caused by EMI can range between being insignificant in nature to causing catastrophic failures. EMI can be both internally and externally sourced and the FCS design process must address these issues. The flight control computers, control surface actuators, sensors units (inertial, air data etc.) as well as all pilot inceptors, switches and all databus inputs and wiring associated with the FCS must be designed to be resistant to all forms of electromagnetic interference. This will include radiofrequency (RF), microwave, lightning and EMP (electromagnetic pulse) sourced interference. Before the aircraft is flown for the first time, sufficient electromagnetic compatibility (EMC) testing is p e r f o r m e d on the complete aircraft to ensure that it can be flown safely in the local electromagnetic environment. As the test programme continues, EMC testing to clear the aircraft to the full electromagnetic threat levels is performed. Initial on-aircraft testing will commence with the aircraft in an unpowered condition and either single loom or multiloom bulk current-injection tests may be performed. External antennae can also be used to radiate the aircraft at a n u m b e r of different aircraft orientations and over a range of frequencies and transmitter characteristics (e.g. horizontally and vertically polarised etc.). Measurements are taken at the FCS equipment to determine the level of current induced per unit of field strength. These results can then be compared with the results of equipment bench-test results done at much higher test levels. Testing will then progress to the powered aircraft

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configuration and a range of tests will be performed. Typical tests are system interaction tests, onboard transmitter tests and external transmitter tests. System interaction tests are p e r f o r m e d to ensure that all aircraft systems are mutually compatible with each other, and in particular with the FCS. Thus all modes of operation of each aircraft system must be selected and exercised during engine-running tests to ensure freedom from cross-system interactions. Where appropriate, measurements may be made o f transients produced on the aircraft electrical busbars as manually or automatically-switched functions are operated. All onboard transmitters are exercised across their frequency range at normal and, where possible, at enhanced power levels, to ensure freedom from EMI. Testing against external transmitters can also be p e r f o r m e d in a n u m b e r of ways. Traditionally, the aircraft u n d e r test has been exposed to each type of external transmitter likely to be encountered during its development and then ultimately its service life. Current test techniques utilise a test site with antennae capable of exposing the live aircraft to radiation over the appropriate range o f frequencies. Monitoring the behaviour of the FCS during these tests can be done in variety o f ways. One option is to use the instrumentation system but this requires careful interpretation since the FTI system on an aircraft can itself suffer from EMI. (In fact, it may be more likely to suffer from EMI because it is not necessarily designed to the same high levels of EMC hardness as the actual aircraft systems.) A better option is to use fibre-optic links from the FCS computers to a remote computer monitoring facility which can be used to monitor a large n u m b e r of FCS signals against thresholds agreed in advance. The generation of a clearance to fly in conditions of high lightning risk is also very important in an aircraft development flight programme and is essential for a service aircraft. Such a clearance requires an FCS which can survive lightning strikes. When digital computers were first used in flight control systems, there was concern that their processors could be c o r r u p t e d by the electrical pulses generated by lightning strikes. System hardware and cable-loom screening design processes have been developed to protect such e q u i p m e n t from lightning-strike effects and these are particularly important on aircraft with composite structures. Although equipment bench tests can be used to demonstrate equipment resistance to lightning strikes (and EMP), it is now often considered necessary to perform whole-aircraft lightning-strike tests to validate the design and clearance process. Such a series of tests requires a dedicated test facility including a test frame tailored to the particular type of aircraft u n d e r test. Although such testing is usually carried out with an unpowered aircraft, there are occasions where some testing is p e r f o r m e d with a live flight control system. Whole-aircraft lightning testing was carried out on both the FBW Jaguar and the EAP demonstrator and Figure 6.3 illustrates the test configuration used for the FBWJaguar.

Ground and flight testing of digital flight control systems 213

Figure 6.3 FBWJaguar: first longitudinally unstable aerodynamic configuration 6.3.5 Engine-running tests T h e final g r o u n d tests are a series of engine runs when the FCS and all other aircraft systems are functioned with the aircraft providing its own internal power. (Hangar checks utilise external rigs to provide electrical and hydraulic power to the aircraft systems.) These tests represent the first opportunity to function the complete aircraft in a fully representative flight condition. For the FCS, the full power-up and built-in test functions are assessed together with the FCS interaction with the hydraulic, electrical, avionic and engine systems.

6.4 Flight test tools and techniques In order to assess the p e r f o r m a n c e and behaviour of an aircraft, an extensive instrumentation system is required. Until recently, the instrumentation system comprised a full set of i n d e p e n d e n t sensors which recorded the state of the aircraft and its systems. With the introduction of electronic flight control systems and digital buses, most of the data required by the instrumentation can be recorded directly from the aircraft systems. Some additional i n d e p e n d e n t sensors are still required, such as accelerometers for flutter/vibration measurements, strain gauges and pressure transducers for load measurements, and other specific sensors such as t e m p e r a t u r e transducers. Telemetry is also required to make the flight test p r o g r a m m e both

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safer and more efficient. In particular, telemetry makes possible the in-flight analysis techniques described below. In addition, a n u m b e r of specific flight test facilities are required in order to carry out the flight test programme. Such facilities will usually include a flight test nose boom and some form of flutter-mode excitation equipment. The nose b o o m (which will contain pressure sensors and be fitted with flowdirection sensing vanes) is used to provide an i n d e p e n d e n t measure o f aircraft flight conditions (airspeed, altitude, angle-of-attack and sideslip) in order to facilitate calibration of the FCS air data sensors. T h e flutter-mode excitation equipment is used to excite the various flutter modes of the aircraft in flight in order to demonstrate adequate levels of damping and hence validate the structural model of the aircraft. Other special flight test facilities are fitted for specific flight trials. For example, when high angle-of-attack trials are performed, there is a risk of departure from controlled flight and spin entry. Prior to the start of these trials, emergency recovery devices including a spin-recovery parachute and alternative hydraulic and electrical power sources are fitted. These, of course, have to be tested on the g r o u n d and in the air before the start of the trials. The current UK flight test philosophy of'fly to validate the model' requires a n u m b e r of novel test facilities as well as new excitation and analysis techniques. These were developed over the flight test programmes of the Tornado, FBWJaguar and the EAP demonstrator as described below.

6.5 Flight testing T h e flight trials assessment of an advanced digital flight control system involves a wide range of test disciplines. These include aerodynamic stability and control, aerodynamic loading, dynamic characteristics (flutter and structural interaction), air data sensors, hydraulic and electrical systems as well as the total flight control system. Thus, from a flight control system point o f view, the objectives and sequence o f the flight test programme will be d e p e n d e n t upon the aircraft to be evaluated. The two flight test programmes described illustrate the evolution of the flight test techniques now in use on the Eurofighter.

6.5.1 FBWJaguar demonstrator flight test programme Full details of the very successful FBWJaguar demonstrator programme can be found in References [1--4]. The flight trials took place between 1981 and 1984 and telemetry was used throughout. Although the telemetry system was limited, it enabled efficient sortie management as well as providing safety monitoring and engineering backup for the.test pilot. Detailed analysis was p e r f o r m e d between flights to ensure satisfactory behaviour o f the FCS and to


Figure 6.4 FBW Jaguar: straked configuration with high level of aerodynamic instability

further validate the aerodynamic models. T h e FBW Jaguar c o m m e n c e d the flight trials phase as an aircraft which was aerodynamically u n c h a n g e d f r o m a standard Jaguar and so the aerodynamic and structural models did not require validation. However, the aircraft was equipped with new p r i m a r y control surface actuators, the control laws were completely new and the air data sensors were new. Thus the initial objectives of the flight test p r o g r a m m e were not only to demonstrate the basic p e r f o r m a n c e and integrity o f the FCS, but to carry out an assessment of the aircraft handling-qualities, calibrate the air data system and validate the impact on the aircraft flutter characteristics of the new actuation system. Once the air data sensors were fully calibrated, the control laws were u p d a t e d to use the validated air data signals and the flight test p r o g r a m m e m o v e d into the next phase. This involved a full handling-qualities assessment including high angle-of-attack testing where the stall departure and spinprevention function of the control laws were fully evaluated. It also included the first flight trials assessment of the aircraft in a longitudinally unstable aerodynamic configuration (achieved using a large a m o u n t of lead ballast in the rear fuselage). Figure 6.4 illustrates the aircraft in flight in this configuration. Up to this point in the p r o g r a m m e , the d e m o n s t r a t o r aircraft had b e e n a standard J a g u a r with aerodynamic characteristics which were well established both from wind-tunnel and flight data. However, the final phases of the

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Control Input Amplitude

3t ¢

t

I,

| Time

2t

(secs)

t

Figure 6.5 3-2-1-1 control input

programme involved the fitting of large wing leading-edge extensions (strakes) in order to generate high levels of longitudinal instability. Since this resulted in significant changes to the aerodynamic characteristics, a new aerodynamic model was generated from theoretical and wind-tunnel data. This was used in the control law design and flight clearance process but required in-flight validation before maximum levels of instability could be flown. Since the demonstrator aircraft was highly augmented, conventional control inputs did not provide adequate excitation for extraction of aerodynamic characteristics (parameter identification). A new excitation technique was therefore assessed on the FBW flight simulator and validated in flight on the FBW demonstrator aircraft while it was still in the well defined standard Jaguar aerodynamic configuration. This technique required the pilot to apply a 3-2-1-1 control input which would provide excitation over a range of frequencies and so enable successful aerodynamic parameter identification. The name 3-2-1-1 was derived from the fact that the duration of the pilot inputs was defined by the time signature 3t-2t-lt-lt seconds as illustrated in Figure 6.5. When the large wing leading-edge strakes were fitted, this technique was used to validate the new aerodynamic model of the aircraft. Initial flight trials were p e r f o r m e d in a configuration with low levels of aerodynamic instability where the control laws were comparatively insensitive to tolerances in aerodynamic derivatives. Once the aerodynamic model had been shown to be within the tolerances used in the control law design process, flight testing progressed rapidly to the maximum levels of instability. Figure 6.6 shows the

Ground and flight testing of digitalflight control systems 217

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i i!!!!ii!iiiii!iiii iiii

Figure 6.6 EAP demonstrator manoeuvering

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aircraft in this configuration and clearly illustrates the size of the wing leading-edge strakes. The aircraft was successfully flight tested to high levels of longitudinal instability. The actual highest level of aerodynamic instability flown had a time to double amplitude of 250 ms. This was completely transparent to the pilot since the FCS provided a very stable and manoeuvrable aircraft with excellent handling qualities. The step-by-step flight test programme was fully vindicated and gave great confidence for subsequent digital FCS-equipped aircraftdevelopment programmes.

6.5.2 The EAP demonstrator flight test programme The experimental aircraft programme (EAP) evolved from a number of European studies into future combat aircraft requirements. These studies identified that a major requirement would be for a highly-manoeuvrable aircraft for close and medium-range air combat with a secondary, but effective, capability for air-to-surface battlefield support. This, in turn, would require a lightweight single-crew aircraft capable of carrying a wide variety of stores and which was twin-engined so as to provide a high level of survivability. To produce this within an acceptable cost would require extensive use of new technologies, many of which were either still at the conceptual stage or in the early stage of development. In 1983, British Aerospace and the United

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Kingdom government signed a partnership agreement for a programme to design and manufacture a demonstrator aircraft which would integrate the new technologies. This experimental aircraft programme included an extensive flight test development phase to assess and prove the viability of the new technologies as a complete concept. A more detailed description of the programme and its objectives can be found in References [5,6] but the following details are of particular relevance to this Chapter.

6.5.2.1 The demonstrator aircraft The aircraft, designed, built and flown during the programme, was known as the EAP demonstrator. The airframe was a canard--delta configuration with a structure containing widespread use of carbon-fibre composites and manufactured using an advanced cobonding technique. The cranked delta wing with full span trailing-edge flaperons and leading-edge droop together with large authority moving canards (foreplanes) and a single fin and rudder resulted in an aerodynamic configuration which was inherently very unstable (both longitudinally and directionally) and nonlinear. A full authority quadruplex digital flight control system was designed to stabilise the airframe and to provide optimum level 1 handling characteristics which would allow the pilot unrestricted use of controls, i.e. carefree handling. This FCS was a further development of the FCS designed for the FBWJaguar and as such had no backup electrical or mechanical system. More detailed descriptions of both the FCS and of the digital cockpit, avionic and aircraft systems can be found in References [5,7]. The initial objectives of the EAP demonstrator flight test programme could be summarised as: * a progressive expansion of the flight envelope to establish confidence in the overall design of the aircraft and its systems; • a progressive assessment of the manoeuvring capability of the aircraft provided by the combination of the advanced aerodynamic and structural configuration and the active flight control system. In order to achieve these objectives, a test to confirm satisfactory flight trials philosophy was to be used, the development of which is given in Reference [8]. This philosophy can be described as an integrated flight clearance and flight assessment process whereby the aircraft is cleared to fly over the full flight envelope provided that the flight measured data can be shown to validate the toleranced aerodynamic models used in the clearance process. Such a philosophy requires analysis tools which can analyse flight data in near real time (i.e. in flight) and provide the ability to compare the results with equivalent data generated from both the nominal and the toleranced aerodynamic models. In this way, if the flight data can be shown to lie within the predetermined model-generated boundaries of acceptability, the flight

Ground and flight testing of digital flight control systems 219 assessment programme can continue without the delays associated with postflight analysis.

6.5.2.2 Analysis techniques The new analysis techniques set in place for the start of the demonstrator flight trials were designed to enable validation of the stability and control and loads models of the aircraft in flight (i.e. in quasi-real time). These techniques are described in References [8,9] but can be summarised as follows.

Transform analysis--this technique determines the frequency or real root positions for longitudinal and lateral/directional modes from smallperturbation manoeuvres such as 3-2-1-1 inputs or doublets. By comparing the in-flight results with data from the nominal and toleranced aerodynamic models, the aerodynamic model could be validated at each test condition within two minutes of the test input. (ii) Comparison of aircraft response data with predictions--this technique compares the aircraft flight-response data from large-perturbation manoeuvres with preflight prediction data for the nominal aerodynamic model at the test condition. The results were obtained immediately the manoeuvre was p e r f o r m e d by crossplotting specific response parameters in real time for comparison with the preprepared boundaries. (iii) Aerodynamic loads analysis--aircraft loads were computed from telemetered aircraft response data using the loads model hosted on the mainframe computer (which was linked to the telemetry facility computers via a fibre-optic link). Computed loads were compared with maximum allowable loads and results were available less than 30 seconds after completion of the test manoeuvre. (iv) Parameter identification--although this could not be accomplished in real time, the transmission of telemetered data to the mainframe computer made it possible for the process to c o m m e n c e as soon as the test manoeuvre was completed. Thus initial results could be available by the end of the test flight with full results a few hours later. However, this level of detailed analysis was not necessary if the techniques described above showed that the aircraft was within tolerance. (i)

6.5.2.3 Flight trials The flight trials of the EAP demonstrator aircraft c o m m e n c e d in August 1986 and the new analysis techniques enabled a rapid expansion of the flight envelope [5]. In less than three weeks, 20 flights were p e r f o r m e d validating the aerodynamic models to the extent that a full display sequence was cleared for the aircraft to fly at the Farnborough air show which c o m m e n c e d three weeks after the first flight. The demonstrator flight trials continued until May 1991 [6] during which period significant development took place of both the flight control system

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and the real-time analysis techniques. Since the aircraft and FCS configuration were very similar to that proposed for the Eurofighter, the EAP flight test programme proved to be an effective risk reduction exercise for the Eurofighter development programme as described in Reference [10].

6.5.2. 4 FCS development during the flight test programme As already indicated, the EAP demonstrator FCS was a quadruplex digital system with no electrical or mechanical backup. The core of the system (rate and acceleration sensors, computing, actuator interface, pilot inceptors and switches) was quadruplex but the air data system (which was integrated within the FCS) was effectively triplex. Triplex pitot static data was provided by a nose probe and two foreplane tip-mounted probes with the nose probe acting as the primary source. Triplex angle-of-attack and sideslip signals were derived from four airstream direction detector probes m o u n t e d around the lower surface of the nose. A double failure of the angle-of-attack/sideslip sensors would put the FCS into its reversionary mode. Loss of any two o f the three pitot static probes would put the FCS into its fixed-gains mode. The aircraft could be recovered from any part of the envelope following failure into the reversionary mode. However, the level of instability of the basic airframe was such that there were parts of the envelope where it could not be recovered in the event of a failure into the fixed-gains mode. For a demonstrator aircraft this was d e e m e d to be an acceptable situation since the fixed-gains mode had been originally conceived as a safe ejection platform only. This was because the air data system was designed to be sufficiently robust as to make the likelihood of a reversion to fixed gains very remote. However, recovery procedures were developed on the ground test rig with the pilots such that an optimum recovery profile was devised to ensure safe recovery following an air data system failure. In the event, the design assumption was fully justified since there were no failures of the pitot static system t h r o u g h o u t the flight trials programme. The initial flight trials of the aircraft were p e r f o r m e d with the FCS in its reversionary mode, i.e. the angle-of-attack and sideslip sensors were not used by the control laws but were fully active so that the wind-tunnel-derived calibration could be validated in flight. In addition, the aircraft was ballasted to a forward centre of gravity position to reduce the level of instability. (Even in this configuration the level of longitudinal instability was such that the time to double amplitude was of the order of 250 ms, i.e. similar to the most unstable condition flown on the FBWJaguar.) Once the air data sensors had been calibrated over the initial flight envelope [10], the full system control laws were p r o g r a m m e d into the FCS, the forward ballast removed and the first phase of the carefree handling flight trials performed. (The level of longitudinal instability in this configuration was equivalent to a time to double amplitude of the order of 180 ms.) Again, using the real-time analysis and model-validation techniques described above, the initial carefree


Figure 6. 7 FBWJaguar: whole-aircraftlightning-strike test configuration envelope was successfully cleared in 25 flights over a period of four weeks. Such a high-risk flight trial meant that the aircraft was equipped with a spinrecovery parachute and appropriate emergency power supplies as well as a spin-recovery mode within the FCS. These facilities were never used in anger t h r o u g h o u t the demonstrator programme and this was due primarily to the success of the model-validation techniques developed and used in the flight trials. Figure 6.7. illustrates the aircraft performing a typical manoeuvre during these trials. The last phase of the FCS development was the implementation of the final standard of control laws which enhanced the subsonic carefree-handling characteristics and introduced supersonic carefree handling. This was achieved by utilising a blend of angle-of-attack and normal acceleration limiting together with the introduction of inertially derived angle-of-attack and sideslip signals as well as attitude-scheduling functions within the control laws. The development of the control laws is described in Reference [11] and the carefree-handling flight trials in Reference [12]. Pilot c o m m e n t was extremely favourable [12] with quotes such as 'the aircraft and FCS withstanding the most savage abuse!'. The real-time analysis tools again enabled rapid and successful assessment over the full flight envelope.

6.5.2.5 Flight test and analysis technique development During the flight-trials phase of the EAP demonstrator, a n u m b e r of significant developments took place both in the provision of test facilities and

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in the use of real-time model-validation techniques. Of these, the provision of an in-flight structural-mode excitation system within the FCS and the use of a real-time air data system model validation analysis technique are of particular interest and are described below. Other developments included the provision of a synthetic target tracking system (designed to demonstrate good handling characteristics and freedom from pilot-in-the-loop oscillations in high-gain tasks) and the development of an in-flight pressure plotting technique (to validate the aerodynamic loads model). More details of these can be found in References [10,13].

(i)

In-flight structural mode excitation--a facility to excite the aircraft structural modes via the aircraft control-surface actuators was developed on the FCS ground test rig and implemented into the flight control computers [14]. This was achieved by generating quadruplex frequency sweep and impulse excitation signals within the computers and injecting them directly into the primary actuator control loops on to the foreplane and flaperon surfaces. Up to 63 pilot-selectable test cases were programmed in to give a choice of surface, amplitude, symmetric or antisymmetric excitation and frequency sweep/impulse profile. The facility was tested over a period of 15 flights and shown to be very effective [14]. In particular, it offered great potential to reduce overall test time when compared with conventional flutter-mode excitation techniques since it enabled a large number of test points to be performed per test flight. (In fact, 83 test points were flown on one flight using this system.) In addition, it provided flight data which was subsequently used in the development of quasi-real-time analysis techniques for use on the Eurofighter flutter flight test programme [15]. The same FCS test facility was used to develop new test and analysis techniques which could measure both on ground and in-flight structural coupling characteristics. These techniques would enable accurate dynamic structural models to be generated and subsequently verified in flight in order to determine optimum notch filter requirements within the FCS. The aim was to demonstrate that a number of store configurations could be cleared into flight with a common notch filter design. This was successfully achieved [16] and the methodology and inflight test philosophy developed were fed directly into the Eurofighter programme. (ii) Real-time air data model validation--the level of instability of the EAP demonstrator configuration resulted in high gains within the FCS control laws which were a function of flight condition. If airspeed errors were excessive then FCS stability would be significantly reduced, particularly in transonic and supersonic flight. Although the nose probe air data correction coefficients were comparatively small and predictable, the correction coefficients for the foreplane tip-mounted probes were both more complex and more difficult to predict since they were a function of


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foreplane incidence as well as flight condition. During the supersonic envelope expansion phase of the flight trials, the actual difference between the nose probe and foreplane tip probe sourced air data was compared in real time with predicted differences generated in advance from the air data model. Boundaries of acceptability were superimposed on the predictions which respected minimum FCS stability requirements. This proved to be very successful in that it identified errors in the foreplane tip correction coefficients but confirmed in real time that the errors were acceptably small and so flight envelope expansion could continue. Similar techniques were used later in the programme when manoeuvring to high angle-of-attack. The techniques developed fed directly into the Eurofighter flight test programme.

6.6 Conclusion The ground and flight test development of modern combat aircraft equipped with complex digital flight control requires a test philosophy which will be both safe and efficient in order to constrain the ever increasing costs of such programmes. Within the UK, British Aerospace experience on the FBW Jaguar and EAP demonstrator programmes has demonstrated that the concept of an integrated ground and flight test programme successfully provides such a philosophy. In the flight trials phase, the combination of realtime analysis and new test techniques and facilities have been shown to be effective in confirming the validity of the aircraft and systems models used in the design and flight clearance process. The techniques enable a more efficient and hence cost effective development flight test programme as is currently being demonstrated by the progress of the Eurofighter flight trials.

6.7 Acknowledgements The author wishes to acknowledge the contributions made by members of the BAe Warton Flight Test, Systems Test and Aerodynamic Design departments as well as the FBWJaguar and EAP demonstrator teams to the work described in this Chapter.

6.8 References [ 1] DALEYE. and SMITH R.B.: 'Flight clearance of the Jaguar fly by wire aircraft'. Proceedings of the Royal Aeronautical Society Avionics working group symposium Certification of avionic systems, 1982 [2] SMITH T.D.,.YEO C.J., and MARSHALL R.E.W.: 'Ground and flight testing on the fly by wire Jaguar equipped with a full time quadruplex digital integrated flight control system'. AGARD 35th Guidance and controlpanel symposium, Lisbon, Portugal, 1982

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[3] DALEY E.: 'An update on experience on the fly by wire Jaguar equipped with a full time digital flight control system'. AGARD 65th Flight mechanics panel symposium Toronto, Canada, 1984 [4] NELSON J.R. and SMITH T.D.: 'Improved combat performance using relaxed static stability and a spin prevention system (FBW Jaguar)'. AGARD 68th Flight mechanicspanel sym~osiu~ Venice, Italy, 1986 [5] HARTLEY R.A.: The experimental aircraft programme test programme'. A GARD 73rdFlight mechanicspanel symposium, California, USA, 1988 [6] Smith T.D.. 'The experimental aircraft flight test programme' FlEA J. Test and Evaluation (1991 ) [7] KAUL J., SELLA E, and WALKER MJ.: 'The flight control system for the experimental aircraft programme (EAP) Demonstrator Aircraft'. AGARD 65th Flight mechanicspanel symposium Toronto, Canada, 1984 [8] HARTLEY R.A.: 'The development and use of real time analysis'. AIAA 95-3877 First AIAA Aircraft engineering, technologyand operations congress,Los Angeles, USA, 1995 [9] SMITH T.D.: 'The use of in flight analysis techniques for model validation on advanced combat aircraft'. AIAA 96-3355, Second Test and evaluation international aerospaceforum, London, UK, 1996 [ 10] SMITH T.D.: 'The role of the demonstrator aircraft in the development of a new Aircraft/Weapon System'. FourthEuropean mini symposium of the SocietyofFlight Test Engineers, Rome, Italy, 1991 [11] McCUISH A.: 'Experimental Aircraft Programme (EAP) Flight Control System Design and Test' A GARD-CP-560, Flight mechanicspanel symposium, Turin Italy, May •1994. [12] ORME K.P.: 'EAP Carefree handling trials' 23rd symposium of the Society of Experimental TestPilots, Bath, UK, 1991 [13] WATSON GJ.: 'Development and flight testing of a surface pressure measurement installation on the EAP demonstrator aircraft'. AGARD-CP-519, Flight mechanicspanel symposium, Crete, May 1992 [14] RAMSAY R.B.: 'In-flight structural mode excitation system for flutter testing'. AGARD-CP-519, Flight mechanicspanel symposium, Crete, May 1992 [15] RAMSAY R.B.: 'Flight flutter testing of combat aircraft'. AGARD-CP-566, Flight mechanicspanel symposium, Rotterdam, Netherlands, May 1995 [16] CALDWELL B.D.: 'The FCS structural coupling problem and its solution'. A GARD-CP-560, Flight mechanicspanel symposium, Turin, Italy, May 1994

© British A e r o s p a c e plc, 2000. Published with permission o f the c o p y r i g h t owner.

Chapter 7

Aeroservoelasticity B.D. C a l d w e l l , R.W. P r a t t , R. T a y l o r a n d R . D . F e l t o n

7.1 Introduction Fundamentally, flight control system structural coupling (simply referred to as structural coupling in the UK, or more commonly in the US, aeroservoelasticity) is a p h e n o m e n o n associated with the introduction of a closed-loop flight control system into a flexible airframe. The flight control system (FCS) might be provided to enhance the natural stability of the aircraft or, in the extreme case, to provide artificial stability to a configuration which has been purposely designed to be unstable to achieve the required aerodynamic performance. In each case, the FCS augments the forces and moments produced by the vehicle's aerodynamics by deflecting the control surfaces. In order to supplement inherent forces and moments which are proportional to angle of attack (a) for stability, say, or pitch rate (q) for damping, the FCS-commanded control-surface deflection must be a function of the same quantities. Thus the FCS must comprise a sensor pack, to detect the appropriate measures of aircraft motion, a control algorithm or law, to compute the forces, moments and ultimately control-surface deflections required to augment stability as desired and an actuation system to convert the control law c o m m a n d into physical deflections of the elevator and ailerons. However, the FCS motion sensors will detect not only the rigid-body motion of the aircraft, but also the superimposed higher-frequency oscillations due to the resonances, or flexible modes, of the structure. It may be appreciated that, if the high frequency components of the sensor output are not attenuated, they will drive the aircraft's flying-control surfaces through the control law. Since the controls themselves may excite the resonances, a closed loop is formed, with an attendant potential for instability. For solution of this structural-coupling 'problem', attenuation of the high frequency oscillatory signal introduced into the FCS by the flexible-aircraft motion should be provided, such that the closed loop is stable and degradation of the performance of the FCS, or damage to the aircraft structure, is avoided. Design of the solution requires that a valid and appropriate representation of the FCS-flexible aircraft system is built up to facilitate understanding and analysis. The elements of the system will be

226


common to any application, and are described in the following Section, but the required detail and fidelity of the system model will be very project dependent, according to the degree of the structural coupling present and the cost of the solution in terms of the potential penalties in overall aircraft performance. The project dependency of structural-coupling methodologies and solutions, and the developing interdependence of the structural coupling and the FCS design processes resulting from increasing exploitation of the potential of active control technology (ACT), are demonstrated through examination of previous British Aerospace projects, culminating in a discussion of the state-of-the-art as applied to the current Eurofighter programme. Developments beyond Eurofighter will similarly be driven by project needs and the desire to minimise process costs and timescales; a number of development directions intended for implementation in future programmes are outlined in the concluding Section.

7.2 Elements of s t r u c t u r a l c o u p l i n g The key to solving many engineering problems lies in gaining an understanding of the system, eventually modelling it in an appropriate fashion and performing quantitative analysis. The elements of the FCS flexible-aircraft structural-coupling system are illustrated in Figure 7.1 and described below.

7. 2.1 Flexible-aircraft modal dynamics Aircraft, like any flexible structure, exhibit many modes of vibration, with each mode having a characteristic resonant frequency and mode shape. For example, Figure 7.2 shows a snapshot of a typical symmetric mode shape for fuselage bending which might have a resonant frequency of about 15 Hz. The plot of the mode shape indicates the relative motion between the various parts of the airframe when subject to excitation at the resonant frequency. Note the deflection in the front and mid sections of the fuselage, where the FCS sensors are located. An aircraft will have many modes within the bandwidth of the FCS, many of which will vary significantly in frequency and amplitude of response with the stores carried, fuel state and flight condition, and each of which will involve a different deflection at the sensor location.

7. 2. 2 Inertial excitation of the flexible-aircraft control surface The flexible modes may be excited or 'forced' by oscillating the aircraft's flying controls. Figure 7.3 shows the results of a ground test on the aircraft where the relative amplitude of the response of the aircraft to control surface excitation was measured as a function of frequency. Here, relative response is expressed in degrees per second of pitch rate (q) per degree of surface deflection, and was measured in the test by monitoring the output of the

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aircraft-motion sensor unit (AMSU) while injecting a test d e m a n d signal into the actuators. The peaks correspond to strucural-mode resonances, and the peak magnitudes depend on: (i) the efficiency with which each control surface excites a particular mode; (ii) the amplitude of motion generated at the location of the FCS sensor for each mode excited; both of which are a function of the mode shape.

7.2.3 Actuators, flight control computers and the aircraft-motion sensor unit The presence of an automatic flight control system links the response directly to the excitation through sensors, control laws and actuators. Even without the aerodynamic elements of Figure 7.1, the resulting closed loop has the potential for instability. The individual elements in the system may themselves be complex items, and all aspects which are relevant to the behaviour of the structural-coupling loop must be understood. These aspects will include the frequency-response characteristics of the elements, any nonlinear effects and effects of the digital implementation where appropriate. The degree of understanding required is very likely to exceed that n e e d e d for successful rigid aircraft control system design.

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7. 2.4 Aerodynamic excitation of the flexible-aircraft's control surface T h e excitation force which is applied to the structure by the oscillatory motion of a control surface has two components. The first, an inertial c o m p o n e n t described above, is due to the offset of the control surface's mass from its hingeline, and has a magnitude proportional to the acceleration of the surface as it oscillates. The second, an aerodynamic component, is due to the change of aerodynamic pressure distribution over the control surface's own and adjacent surfaces, which is caused by the surface's displacement from its datum position. The aerodynamic c o m p o n e n t is proportional, for small perturbations, to the magnitude of the displacement, and to dynamic pressure.

7.2.5 Flexible-aircraft modal aerodynamics In addition to the variation of the excitation force with airspeed, the response of the system to that excitation will be affected by the aerodynamic damping and stiffness forces associated with the induced oscillatory motion of the rest o f the aircraft. At lower airspeeds, however, where the critical flight conditions for structural coupling are often found, these effects are secondary, and the variation of structural-response characteristics with flight condition will largely mirror the trends in the excitation forces. The d e p e n d e n c e of the aerodynamic c o m p o n e n t of the excitation force on airspeed, and the fact that the aerodynamic and inertial components are out of phase, results in the variation of the response of the flexible aircraft with airspeed as shown in Figure 7.4. The figure indicates the important differences in characteristics depending on whether inertial excitation forces dominate, or whether the aerodynamic effects overpower the inertial input at relatively lower speeds. The f o r m e r case, in which the inertial effects dominate, is typical for an all-moving control surface, such as a foreplane or a taileron, and the latter case occurs with relatively lightweight, but aerodynamically powerful, wing trailing-edge controls.

7. 2.6 Formulation for solution and design trade-offs As already noted, the above elements are c o m m o n to any structural-coupling mechanism. By representing and combining the elements in an appropriate way, deriving a picture of the structural-coupling characteristics of the system and comparing with the design and clearance requirements, the severity of the problem can be assessed and the required solution established. At British Aerospace, structural coupling is addressed as part of the FCS design process, and thus the frequency-domain methods used in the analysis of the rigid aircraft, based on the Nyquist stability criterion in conjunction with Bode and Nichols plots, are extended and adapted to cover the regime for the higherfrequency flexible modes. Frequency-domain modelling and analysis of the

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will pull the frequency response locus to the left, to encroach on the box surrounding the 0 dB, - 180 ° point which defines the stability requirements. Thus, notch filters may be considered as destabilising influences on the dynamic behaviour of the rigid aircraft. Figure 7.5 also shows one of the usual means of improving rigid-aircraft stability margins; the phase advance filter. It can be seen from the figure, however, that the phase advance filter has a high gain at high frequencies, which will, of course, exacerbate the effects of structural coupling and lead to the need for more attenuation; an obvious design conflict. The characteristics of the high-performance actuator which are also plotted in Figure 7.5, indicate a further trade-off in the design hardware in the flight control system. The high bandwidth actuators, along with the high throughput of the flight control computers and fast databus communication, are selected to minimise the lag inherent in the FCS, and thus support instability of the vehicle as a fundamental design concept. High-actuator bandwidth and low lag generally go together with higher gain at high structural-mode frequencies, and hence, as in the case of the phase advance filter, conflict with the high frequency attenuation and low frequency lag of the notch-filter design. The expense associated with design, development and manufacture of high-performance FCS hardware is strong justification for careful examination of these design options. In difficult cases, where the flight control system is sensitive to phase lag and a significant level of structural coupling is observed or predicted, SC and FCS designers must clearly work closely together in order that a good solution to both rigid and flexible-aircraft control problems is achieved, while maintaining a balance in the overall design and clearance process. Filter design must be addressed with care, and an appropriately detailed and representative model of the structural-coupling characteristics must be assembled, but equally, the control law design must not neglect the SC implications of high FCS gain and bandwidth. The influence of the magnitude of the structural-coupling problem, required detail, data quality and their influence on the analysis and solution will be illustrated by examining a series of projects which have been carried out by British Aerospace. During the period covering the evolution of these projects, advancing exploitation of, and dependence on, active-control technology has required that the FCS and SC design tasks advanced together and become increasingly integrated, to the point where structural dynamicists form part of the FCS team for EF2000.

7.3. FCS-SC structural coupling: design examples As already noted, the potential for structural coupling exists in any flexible vehicle fitted with an automatic FCS. It is probable that the problem first became well known and analysed in guided-missile design [1,2], although it

Aeroservoelasticity

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was certainly anticipated, and has also been experienced, in aircraft control [1-4]. The total loss of guided missiles owing to poorly understood or inadequately analysed structural-coupling interactions is by no means unknown, although none of the obviously structural-coupling-related encounters experienced in manned aircraft has proved to be catastrophic [1,4-6]. The loss of X-15 number 4 and its test pilot Mike Adams in 1967 has been attributed to structural coupling by some sources, but the details generally available [7] are not conclusive. Notwithstanding the X-15 incident, structural failure in the manner of a flutter encounter is unlikely to occur as a result of structural coupling, since the FCS cannot, in general, input sufficient energy, and since FCS nonlinearities would limit the amplitude of excitation through the control surfaces anyway. However, structural coupling has been predicted to have a profound effect on fatigue life [8] even subject to these constraints, and this has been borne out by experience of airframe and actuator fatigue-life usage during typical ground tests. Further concerns are that coupling with flutter modes may occur [1,4] which could lead to structural damage, and that the propagation of high frequency signals through the FCS could seriously degrade actuator performance for rigid-aircraft control of the rigid-aircraft dynamics [9]. Development of tools and procedures for analysis to address the structural coupling problem, as experienced in aircraft flight control design at Warton, began in the early 1960s with the TSR2 aircraft, and have continued to the present day with EF2000. Specific examples are described here to highlight the connection between the functionality of the flight control system, the structural-coupling design and the analysis tools employed, and the degree of FCS--SC design integration required for success.

7.3.1 Jaguar--first flight 1968 The Jaguar (Figure 7.7) was designed to be a simple, rugged, ground-attack aircraft. Primary pitch control is effected through all-moving tailplane controls. The aircraft is fundamentally stable, but is provided with low-gain pitch and yaw autostabilisers to augment the system's damping. The combination of low control law gain (actually less than unity at low speed, and reducing further with increasing dynamic pressure), inertially-dominated SC characteristics (owing to the type of flying controls, as explained in Section 7.2.5), and the relatively modest capability of the actuators of the autostabiliser (which themselves attenuated any structural frequency feedback through the FCS), meant that Jaguar constituted a relatively easy structural-coupling problem. In addition, the Jaguar FCS was not sensitive to the additional phase lag from the structural-mode filtering introduced, which comprised nominal 10 Hz/20 dB notch filters and a 50 ms low-pass filter. Owing to the relatively benign nature of the problem on Jaguar, a correspondingly simple process of SC analysis, based fundamentally on

236


Figure 7. 7 limited ground testing, which was quite separate from the rigid-aircraft design, was wholly adequate and has provided a solution which has proved to be robust throughout the life of the aircraft.

7.3.2 Tornado--first flight 1974 The Tornado multirole combat aircraft (Figure 7.8) embodies a full-authority control and stability augmentation system (CSAS), again with relatively low gains (but not, in this case, less than unity), and which also features primary control through large, all-moving taileron control surfaces. As for the Jaguar, the combination of inertially-dominated SC characteristics and the gain scheduling of the control law with inverse dynamic pressure lead to the expectation of a zero-speed worst case, and this was confirmed through analysis. From this analysis it was known that absolute accuracy of the flexibleaircraft modelling was not an issue in the structural-coupling design, since ground tests would give direct measurement of characteristics of the worst case. The broad range of stores to be cleared for carriage on the Tornado complicated the design and clearance process for the structural-coupling problem. The addition of massive stores to the relatively flexible, high-aspectratio wing naturally caused significant variations in the dynamics of the flexible aircraft. In particular, variation of the resonant frequencies of the

Aeroservoelasticity

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Figure 7.8 flexible modes would potentially multiply the notch-filter requirement and the corresponding phase lag. In practice, this possibility was ameliorated by the fact that the primary flying controls were not m o u n t e d on the wing, to leave it clear for high-lift devices and to facilitate the wing-sweeping feature. This meant that the modes most affected by the stores fitted (wing and pylon modes) were not excited directly through the FCS, and were not the most critical for SC (which were modes excited by activation of the tailerons). Thus specific features of the design configuration lead to favourable and complementary effects in the variation of FCS gain and structural-coupling characteristics with flight condition. With the relative immunity from the effects of stores, a simple and robust structural-coupling solution, confidently based on ground-test data, proved adequate, as it had in the case of Jaguar, despite the adverse effects of increased FCS gain, the capability and authority of the hardware and the widely varying modal dynamics of the wing.

7.3.3 Experimental aircraft programme (EAP)--first flight 1986 T h e experimental aircraft programme was aimed at demonstrating a n u m b e r of new technologies applicable to a future combat aircraft, one of which was active-control technology (ACT). The desire from an aerodynamic viewpoint

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Figure 7.9 was to produce a configuration, shown in Figure 7.9, with good supersonic performance and exceptional turning capabilities. The enabling technology of a full-authority, digital FCS meant that this was achievable through a combination of longitudinal instability of the basic airframe and a canarddelta configuration. A carefully selected level of instability at subsonic flight conditions conferred: trailing-edge-down elevon to trim, increasing with increasing angle of attack in a manner giving a simple form of scheduling of wing camber for good lift-to-drag ratio throughout the range of angle-of-attack; • approximately neutral stability when the aerodynamic centre moved aft at supersonic flight conditions, requiring only small control angles to trim, and hence achieving low values for trim drag.

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The powerful FCS and delta planform with trailing-edge controls were thus central to the design concept, but brought a number of characteristics which led to a difficult structural-coupling problem, namely: (i) a high bandwidth for the combination of the actuators and sensors, (ii) high control law gains at structural-mode frequencies; (iii) trailing-edge flying controls able to generate high structural coupling excitation forces which were dominated by aerodynamic effects at airspeeds where the FCS gains are also high, indicating structuralcoupling characteristics which were dominated by aerodynamic effects and giving an in-flight worst case. Moreover, the high level of longitudinal instability (0.18s to double

Aeroservoelasticity 239 amplitude) also meant that the FCS was sensitive to additional low frequency phase lag, leading to a tight phase budget for solution of the structuralcoupling problem, and the digital implementation of the system which required full account to be taken of aliasing and frequency-warping effects in the design and clearance process. It was clear that the control law design for the rigid dynamics must recognise the difficulty of the structural-coupling problem from the outset. Otherwise emphasis would be loaded onto the structural-coupling analysis, perhaps to an extent beyond the state of the art, which would clearly lead to problems in flight clearance. Equally, it was obvious that a different structuralcoupling design process from previous projects would be required, because of the need to assess in-flight cases and the need to carefully minimise phase lag due to the filters.

7.3.3.1 Rigid FCS design--structural-coupling considerations At the early stages of the programme, insufficient data for the flexible aircraft was available to facilitate specific and quantitative trade-off studies, but Jaguar FBW experience allowed some a pr/or/judgements to be made regarding the design choices for the control law which would influence the structuralcoupling process. These are outlined below.

Notch-filter phase-lag assumptions An estimate of the low frequency phase lag to be introduced into the FCS by the notch filters was made, based on an extrapolation from experience gained from the FBWJaguar, and this was included in the control law design process along with the assumed actuator dynamics and computational delay in the flight control computer.

Feedback signal selection The maturation of active-control technology has made it feasible for the FCS designer to implement complex control laws with freedom to build in switching, scheduling and so on, between alternative sensor signals. Normal acceleration, angle-of-attack and pitch rate were all used in the EAP pitchcontrol system, a (angle-of-attack) feedback is the theoretically natural choice for stability augmentation, and this parameter was not recognised as a problem for structural coupling on account of the inherent damping and limited bandwidth of the airstream direction detector (ADD). Pitch-rate (q) feedback was used for both stability and damping augmentation. For stabilisation, q was filtered to form a pseudo-a signal. The filtering effectively eliminated structural coupling through this path but for damping proportional pitch rate was used directly and proved to be the most significant path for structural coupling. Use of normal acceleration (nz) for stability

240


augmentation entails division by a velocity-squared factor, again to give a pseudo-a term. Acceleration feedback gains would thus be very high at low speed, and it was recognised that this would cause structural-coupling problems. EAP's control law was therefore built around pitch-rate feedback; with a proportional term for damping and integrated for stabilisation, plus cr at low speed where n z gains would be too high, and nz at high speed where the resolution of the ADD was not adequate.

Aircraft motion-sensing unit (AMSU): positioning and mounting The benefits of positioning the FCS sensors in the aircraft-motion sensing units at a position of low deflection for particularly troublesome modes and of fixing of the units to the primary structure to avoid problems caused by local flexibility, had been learned well on previous projects. However, the nature of EAP forced a less than ideal compromise in these aspects, as illustrated by the magnitude of the 15 Hz peaks in Figure 7.3. Positioning of the AMSU for ease of supply of cooling air to its electronics took priority over the considerations for structural coupling, leading to the large response from the fuselage bending mode. Further, the high gain at 55 Hz in Figure 7.3 was traced to local bending of the AMSU mounting plate between the four units fixed to it.

Hardware design The obvious trade-off between the bandwidths of the FCS hardware and the notch-filter requirement and phase lag noted in Section 7.2.6 had not been explored at the time of the inception of the EAP. The frequency-response specifications for the actuators, sensors and computers were therefore based on the well known relationship between capability of the hardware and vehicle-controllable instability (faster actuators and computers being required as the degree of instability increases). However, the effects of structural coupling did influence the design of the digital signal processing (DSP) within the AMSU, where rolling-average and downsampling processes were arranged to provide anti-aliasing protection for the FCS against response in the very high frequency flexible modes.

Feedback gain and loop-shaping design As previously mentioned, relatively high control law gains were necessary to stabilise EAP in pitch. Feedback loop shaping was also necessary to achieve the required stability margins and, implemented as lead-lag or phase advance filters (Figure 7.5), this further increased the control law gain at high frequencies. However, an overall limit on the total high frequency gain of the control law was imposed from the beginning of the design in recognition of potential structural-coupling problems.

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Structural-coupling (SC) design Having recognised the strong cross influences between the FCS and SC design processes and taken steps to account for them from the outset, the goals in seeking an SC solution for EAP were to avoid exceedence of the phase lag due to the notch filter assumed in the design of the control laws and, of course, to meet the structural-mode design and clearance requirements agreed with the project customer. In particular, for this innovative programme there was a desire to make the structural-coupling design and clearance process as clear, open and easily assimilated as possible. The approach was therefore to keep the treatment of the SC problem as simple as possible while: (i)

meeting the design and clearance requirements and limits on the phase lag due to the filters; (ii) ensuring a demonstrably safe clearance covering all considerations; (iii) fully recognising the quality of the available information. The above factors directly influenced the detail of the process, the means of representing the structural-coupling characteristics of the system and the design and clearance requirements set, because, in contrast to previous projects: (i)

the in-flight worst case meant that ground-test measurements would not be sufficient on their own for design of the notch filters and structuralcoupling clearance; (ii) the accuracy of the model of the flexible aircraft available for the evaluation of the effects of structural coupling in flight was not known with confidence, particularly with respect to the prediction of the phase response; (iii) the effects of the digital implementation of the system with respect to the higher-frequency structural modes needed to be understood and accounted for; (iv) good structural-coupling information was needed at frequencies up to the sampling frequency of the flight control computer, since the tight budget for phase in the filter design meant that a solution with blanket high frequency range attenuation (e.g. anti-aliasing filters) could not be tolerated. These issues and requirements were addressed by evolving a process with a high degree of intervention and understanding on the part of the design team, in preference to monolithic automated procedures for analysis. The process involved an iterative approach, starting with broad assumptions regarding the elements of the problem, with patches of detail and refinement added to enhance the assessment in areas identified as being critical to the solution.

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Table 7.1 MIL-F-9490D gain and phase-margin requirements Modal

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Design requirements The structural-mode design requirements for EAP were based on MIL-F9490D [10]. This gives a frequency-domain specification (Table 7.1) of stability margins, consistent with the approach adopted at British Aerospace of integrating the rigid and flexible FCS design functions. Because of the factors noted above, the MIL-F-9490D stability specification was modified to set more conservative clearance requirements. For the initial phases of the EAP programme, the decision was made to: • specify a 9 dB stability-margin requirement for all structural mode frequencies; • exclude phase entirely from the structural-coupling analysis. The latter specification meant that all parallel paths in the FCS-structure loop were evaluated separately and added as scalars to form the open-loop system transfer function, and that any alleviation in attenuation requirements for modes with apparently good phase margins was not admissible. The stability margins derived from this approach automatically satisfied the (arguably inadequate) multiple-loop part of the MIL specification, which would otherwise have been difficult to address in the EAP application. The resulting stability-margin requirements are illustrated in Figure 7.10.

Structural-coupling system representation--aerodynamics and control laws The representation of the flexible aircraft required for assessment of in-flight conditions was based on the mathematical model created for flutter

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calculations. This model comprised the matrix equations of motion describing inertial, stiffness and aerodynamic properties of the flexible and rigid-aircraft modes. The structural elements of the model were derived from finite-element analysis (set up by the company's stress office and forming a common basis for the EAP structural modelling used in all disciplines for EAP), transformed to give adequate representation with relatively few degrees of freedom. The rigid-body aerodynamics were derived from wind-tunnel results and unsteady aerodynamics were derived from kernel-function-based tandem-surface methods at fixed Mach and frequency parameters. Actuator and sensor dynamics were included by augmenting the flexibleaircraft matrix equation with extra degrees of freedom, including the actuator demand and sensor-output signal interfaces with the FCS control laws. It is a characteristic of notch filters, particularly those designed for low phase lag such as the lower-frequency filters for EAP, that the rate of change of attenuation with frequency near the centre of the notch is very high. This places a high premium on accurate knowledge of the modal frequencies. However, zero speed calculations using the flutter model adequately reproduced the aircraft's structural-coupling characteristics as measured in ground tests for only some of the sensor output/actuator input combinations required, and only then up to modest frequencies. This meant that the flexible-aircraft model could not be used on its own for notch-filter design, and strongly influenced the form of the structural-coupling design procedure. Hence, for EAP, the model was used only to derive the effects of the flexible-aircraft aerodynamics and control-surface aerodynamic excitation in the structural coupling loop in Figure 7.1. The aerodynamic effects derived from the model were combined with the zero-speed structural-coupling characteristics as measured in ground tests, thus accounting for any poor matches in frequency and gain between zero-speed measurements and predictions. Before including the control laws in the representation, preliminary frequency-response analyses indicated FCS paths which, in combination with the structure and aerodynamics, had negligible gain at the frequencies of the structural modes. This eliminated integral paths and the outputs from the incidence and sideslip feedback sensors. For the remaining paths (proportional pitch, roll and yaw rates and lateral acceleration), inclusion of sensor and actuator dynamics as part of the flexible aircraft and separate consideration of digital effects, allowed representation of the control laws at a single high frequency (above 6 Hz, where the FCS phase advance filters' frequency dependence had run out) gain value at each point of a grid of flight conditions across the flight envelope. The maximum control law gain at each of these flight conditions was sought by consideration of all the effects of scheduling with angle-of-attack, nonlinear gearings and so on. Addition of the corresponding FCS gain and structural-mode gain and frequency trends built a mode-by-mode picture of the variation of the

Aeroservoelasticity 245 structural-coupling loop gain with flight condition across the flight envelope. For each significant FCS path, this indicated, in a very clear format, the critical flight conditions and the relative importance of modes and control surfaces.

SC system representation--structural dynamics and FCS hardware Because of the inadequacy of the flutter model noted above, the parts of the Figure 7.1 structural-coupling loop for the flexible-aircraft dynamics and control-surface inertial excitation were represented instead by data derived from ground tests, where frequency-response functions for each significant i n p u t - o u t p u t combination were measured (for example Figure 7.3). The digital signal processing in the aircraft-motion sensor unit effectively limited the feedback of high frequency modes, indicating a requirement for structural-coupling test data up to the sampling frequency of the flight control computers. This entailed provision of an analogue test input to the actuators and a high-rate digital output from the sensor processors. Since the test data was to form a central part in the design and clearance calculations for the notch filters, and the need for accurate knowledge of modal frequencies, great efforts were made to maximise the quality of the results. Some of the particular considerations were: (i)

Special gains were provisioned in the FCS software just upstream of the digital-to-analogue (D/A) conversion, to reduce the relative amplitude of the noise picked up on the test cabling and connectors, and to make the least significant bit of the 16-bit internal signals accessible through the 12-bit D / A provided for ground test. (ii) Frequency-response functions were referenced to the actuator demand, rather than the actuator position, thus including the actuator dynamics in the measurement, that is in the flexible-aircraft dynamics as part of Figure 7.1, which gave better results at high frequencies where the actuator position response was very small and not a good basis for analysis. (iii) Great care was taken with the cable routing, earthing arrangements and so on to minimise analogue noise pick-up. (iv) Constant reference was made to the sensor-response output waveforms, to ensure that an adequate response amplitude relative to the digitalsystem resolution was being achieved. (v) A Solartron Sl1250 TFA instrument was central to the structuralcoupling test equipment, implementing steady-state, single-frequency sinusoidal excitation and correlation analysis for excellent amplitude accuracy and noise rejection. The tests also addressed factors which could not be modelled, and included: (i) confirmation of actuator installed stability and performance; (ii) assessment of the impact of actuator-failure cases on the structural-

246


coupling characteristics; (iii) assessment of free-free compared with on-undercarriage aircraft support on SC characteristics; (iv) assessment of the effect of the trim position of the control surfaces; (v) structural linearity checks. Significant emphasis was placed on the linearity checks; in general the policy was to drive the structure hard enough to saturate structural nonlinearities, at the same time avoiding excessive fatigue damage and invoking the actuator rate limit and other nonlinearities. Investigation of excitation amplitude effects was an inherent part of this procedure. Fatigue life usage was a major constraint on the tests. The aircraft was comprehensively instrumented, and all response cycles above a negligible damage limit predetermined for each parameter were recorded for fatigue assessment. An absolute limit of a factor of three on negligible damage was never exceeded. Other test constraints were the need to rotate the engine spools at intervals, to prevent bearing damage, and the need to avoid scoring of the actuator cylinder bores, by periodically moving the controls over large amplitudes to lubricate the actuator seals. The test results, in the form of gain against frequency information for each significant FCS path (Figure 7.3), formed the absolute basis for extrapolation of the trends in modal gain to cover the in-flight worst cases for EAP. Following the extrapolation process, the contributions of the parallel path to the pitch (pitch rate/pitch-rate demand through the paths for the in-board flaperons, outboard flaperons and foreplane) and lateral FCS paths were summed as scalars to give the end-to-end pitch and lateral open-loop transfer functions. The resulting gain envelopes, covering all flight conditions, directly specified the attenuation required to meet the design and clearance requirements. It still remained, however, to include the effects of the digital nature of the FCS, prior to notch-filter design.

Treatment of digital effects Careful consideration of the sampling process [ 11 ], led to a simple treatment which included all of the important effects. First of all, design of the digital signal processing included in the AMSU in the form of rolling average and downsampling processes provided a very effective anti-aliasing function. Together with the characteristics of the flight control computer's (FCC) sampling and zero-order hold (ZOH), this effectively eliminated signal components at frequencies above the FCC's sampling rate. This defined the upper frequency of interest throughout the analysis. Secondly, analysis showed that the effects of the FCC's sampling and ZOH functions could be represented by applying the attenuating characteristics of the sample-and-hold to the overall envelope for the open-loop transfer function, then folding the data about the half-sampling frequency, summing

Aeroservoelasticity

247

Table 7.2 Notch-filter solutions Aircraft

Feedback

Solution

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all axes

1 1st-order lag (4 Hz), 1 NF (10 Hz)

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pitch roll yaw

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pitch roll yaw

0 0 0 0 0

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the upper and lower frequencies (as scalars), to represent the effects of aliasing. The treatment is explained more fully in Taylor, Pratt and CaldweU [12] (see also Kehoe et aL [6]). For EAP this resulted in the open-loop transfer functions for q/q, ¢ / ( and p / p over the zero-to-half-sampling frequency range, that is, representations of open-loop gain at strategic points in the control laws within the flight control computers. These data are then used directly for notch-filter design.

Notch-filter design As previously noted, the digital signal processing in the AMSUs provided an anti-aliasing function for frequencies higher than the FCC's sampling frequency (80 Hz for EAP). Conventional anti-aliasing filters proved, in this circumstance, to be a less efficient solution for attenuation in the 40 to 80 Hz band than broad notch filters, located, of course, upstream of the FCC's sampling in the AMSU. The high frequency response remaining after AMSU filtering was folded back and added to the 0-40 Hz data for FCC filter design. On the Experimental Aircraft Programme, advantage was taken of the exclusive excitation of some modes by particular control surfaces illustrated by Figure 7.3. Obvious examples are the excitation of the foreplane bending mode (18 Hz) by the foreplane, and excitation of wing bending (7 Hz) by the outboard trailing-edge flap. Positioning of notch filters in the actuator command paths, rather than on the sensor outputs, gave the required attenuation, but reduced the overall phase-lag penalty associated with the particular filters. This solution has the disadvantage, however, of adding lag to the control law, path between the pilot's command and control surface displacement. The lag in this path is a key consideration in the susceptibility to pilot-induced oscillations (PIOs), and the additional filtering must be

248


Figure 7.11 accounted for in PIO analysis. Table 7.2 compares the notch-filter configuration for EAP with those of previous projects, illustrating the magnitude of the structural-coupling problem addressed on the aircraft.

7. 3. 4 Eurofighter 2000 (EF2OOO)--first flight 1994 EF2000 (Figure 7.11) basically takes the design concept of the experimental aircraft programme (originally developed with partners DASA, then MBB) forward into a series-production weapons system. The unstable aerodynamic configuration and full-authority digital FCS are common with EAP, but the wide range of stores to be carried constituted a major development in the analysis of the structural-coupling problem. The resulting wide variation of structural dynamics was ameliorated on the Tornado because the FCS control surfaces were not wing mounted, but this was clearly not going to be the case for EF2000, and the structural-coupling problem was expected to be significantly more difficult than for the Experimental Aircraft Programme. It was thus recognised that the method which had been originally developed for EAP, although very satisfactory for the initial phases of the programme, would not be viable for EF2000. The low frequency phase lag from a set of notch filters designed to EAP margin requirements and to cover all configurations would be beyond that which could be tolerated by the FCS

A eroservoelasticity 249 without making radical changes elsewhere in the FCS design process. Solutions involving filters which were switched with the stores fitted was ruled out, since mechanisation would entail making the stores-management system critical to flight safety, and therefore more complex and costly. Nonlinear filters and other forms of filter scheduling (with flight condition, for example) were also discounted on the basis that developments of the EAP processes could provide a solution, without further complication of the filter implementation and design and clearance tasks, and therefore at an acceptable cost. Studies indicated that by effectively eliminating the fuselage bending m o d e (the troublesome 15 Hz mode on EAP) by careful positioning of the aircraftmotion sensor unit, and relaxing the stability-margin requirements for the modes most affected by stores, a notch-filter set could be designed that was both satisfactory for the control of the rigid aircraft and covered all the stores configurations. Clearly, a relaxation of requirements would be possible only with an e n h a n c e d representation of the flexible aircraft, coupled with the provision of additional evidence of validation, in the form, in this case, of confirmation of the predictions at the critical, in-air flight conditions. Part of the extension to the Experimental Aircraft Programme, EAP in support of EFA, was designed to test whether the relaxation of the margin could be justified. This programme had three aims: (i)

To demonstrate that a representation of the structural-coupling loop could be built which was sufficiently accurate and robust to allow relaxed stability-margin requirements to be applied to the fundamental wing modes in the pitch axis. (ii) To design, implement and demonstrate in flight a structural-mode excitation system built into the primary FCS, as a prototype for a similar system on EF2000. (iii) To demonstrate that the flexible-aircraft aerodynamics were conservative with respect to control-surface effectiveness, and that flexible-aircraft control effectiveness followed similar trends to the corresponding terms for the rigid-body aerodynamic as angle-of-attack increased.The control effectiveness is essentially a gain in both the rigid and flexible dynamics, and achievement of objective (iii) would allow the increases in gain in the control law with angle-of-attack (designed on the basis of rigid-body aerodynamic effects) to be offset with a reduction in the control-surface aerodynamic excitation force for the flexible aircraft in the evaluation of the structuralcoupling loop. Each of these aims was successfully achieved, and the EF2000 process outlined below reflects the developments made with the experimental aircraft programme.

7.3. 4.1 Rigid FCS design--SC considerations The structural-coupling considerations applied in the design for the Experimental Aircraft Programme were carried across directly to EF2000,

250


including the limit on high frequency gain, feedback-signal usage and the hardware design. The rigidity of the AMSU (known as an Internal Measurement Unit (IMU) on EF2000) mounting structure was guaranteed, and because of the known importance of the minimising pick-up of the effects of fuselage bending as part of the strategy to facilitate stores clearance, IMU positioning was given a high priority, leading to the selection of a position outside the main avionics bay. The experience gained on EAP allowed for a much more considered and integrated approach to control law design on EF2000. In the design of the control law scheduling, engineers were now aware of structural-coupling gain trends with flight condition and were able to exercise the option of higher gains at noncritical flight conditions. Further, it was now possible to integrate the design of phase advance, notch filters and feedback gains in a joint optimisation procedure, which achieved a better balance in the design tradeoffs noted previously.

7.3. 4.2 Structural-coupling design For Eurofighter 2000 the structural-coupling design process is basically that successfully deployed on the Experimental Aircraft Programme, but with a patch of more detailed analysis applied to the low frequency modes in the pitch axis, as necessary for clearance of the range of stores configurations envisaged. The patch involves increased dependence on the model predictions for the flexible aircraft, supported by matching the model to ground tests, carrying out sensitivity studies and, fundamentally, flight measurements of structural-coupling characteristics. Flight data were collected during specific structural-coupling flight tests, during which a test signal was injected into selected FCS actuators, and the aircraft response was recorded from the inertial measurement unit, thus making a direct measurement of the part of the system illustrated in Figure 7.1 which represents the flexible aircraft. This approach was preferred over the explicit measurement of stability margins for structural coupling, since it allowed the contributions of individual control surfaces to be measured separately, to the greater benefit of the model-validation exercise. Clearly, if flight measurements are required before the model can be used with confidence, a flight clearance based on more conservative assumptions and processes is necessary initially, so that the flight data required may safely be obtained. For Eurofighter 2000 the structural-coupling design and clearance process was therefore phased such that before new design and clearance refinements are introduced, supporting evidence is gained under a prior, more conservative, clearance. The phasing of the test programme will be synchronised with the development of the functionality of the FCS, and expansion of the range of configurations fitted. Major phases will be: (i)

Initial clearance to 'basic' design and clearance requirements (Figure 7.10). Limited air-to-air stores configurations, flight testing to support

Aeroservoelasticity 251 relaxation of stability requirements and matching of control effectiveness. (ii) Clearance to 'relaxed' SC stability-margin requirements. Air-to-air store subsets and underwing tank configurations. Flight testing to support the introduction of alleviation owing to tank effects on flexible-aircraft control effectiveness. (iii) Clearance to relaxed margins. All air-to-air tank and air-to-ground configurations. Tank alleviation effect introduced. (iv) Clearance to relaxed margins. All air-to-air, tank and air-to-ground configurations.

Design and clearance requirements The relaxation or refinement of the design and clearance requirements for structural coupling accompanied the expectation that additional evidence would be available from flight testing for the validation of the flexible-aircraft model. It was proposed to allow phase stabilisation of the modes for which appropriate flight test data would be available, thus making the design of the notch filters sufficiently tractable such that clearance for all of the desired store configurations could be achieved. Phase stabilisation means that the phase of the system frequency response is examined when determining stability, in addition to response gain. This obviously meant including phase in the modelling of the SC loop of Figure 7.1, which was specifically avoided for the Experimental Aircraft Programme. Clearly, if the closed-loop system is to be stable, the open-loop frequency response of the system must avoid the unity gain (0 dB), - 180 ° phase point on a stability diagram. On the Nichols plot showing the SC stability-margin requirements for EF2000, Figure 7.12, the enclosed areas denote regions to be avoided by the open-loop frequency response characteristics of the structural-coupling system, and encircle the sequence of unity gain, - 180 ° point (plus multiples of - 360 ° to allow for the cyclical equivalence of - 180 °, - 540 ° etc.). The size of the areas relative to the margin requirements for the rigid aircraft to the right of - 1 8 0 °, reflects the relative confidence in the modelling for the rigid and flexible aircraft, and the difficulty in defining sensible parameter uncertainties for the flexible aircraft, which might otherwise allow smaller prohibited areas subject to appropriate tolerance studies and validation evidence provision. Note that it is permissible for the magnitude of the frequency-response locus to exceed 0 dB for values of phase in the region of - 3 6 0 °. This is acceptable since, in the closed loop, structural feedback with this phase will actually act to stabilise the flexible modes. Other implications of this eventuality are considered later. The frequency range of application of phase stabilisation was limited by: (i)

The capability of the flight test techniques available. In this case in-flight structural-mode excitation was limited by the capability of the actuators

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and the system's digital effects. (ii) The benefit to be gained from phase stabilisation; to avoid additional complication and cost in the clearance process, the relaxed requirements were only to be applied to the modes most influenced by the stores configuration and which most affected low frequency lag in the FCS. Along with the undertaking to gain additional information, application of the reduced-margin requirement was further justified by the fact that the modes in question are dominated by the outboard flap excitation, leading to a pseudo single-loop situation and reducing the potential effects of interloop variability of phase. Also, at the low frequencies, the hardware elements of the SC loop are well known, are verifiable and relatively invariant and, furthermore, the effects of the digital implementation of the system are less significant.

Structural-coupling system representation For the bulk of the clearance task for structural coupling, the system is represented in just the same way as it was for the Experimental Aircraft Programme, being based on a combination of ground-test data and predicted aerodynamic effects, with phase being completely eliminated from the analysis. For the modes which are to be phase stabilised, however, the entire system is modelled as an extension to the matrix equations of motion for the flexible aircraft, that is the flutter model, and the model used directly to calculate structural-coupling gain and phase margins assessed against the stability requirements. The matrices comprising the flexible structural and aerodynamic model were augmented with additional degrees of freedom representing the variables of the control laws completing the link between the sensor output and actuator demand which were included for the standard analysis. The extra matrix elements then correspond to the filter time constants and gain elements comprising a model of the control laws linearised at a desired flight condition. The flexible-aircraft model itself may be subject to refinement to ensure that it is adequately representative for use in phase stabilisation. In practice, this means that a model is set up to replicate a ground-tested configuration and calculated zero-speed SC characteristics compared with test data. It is usual for the low frequency wing modes to need only minor adjustments to the modal frequency, made by factoring the structural stiffness matrix, with the amplitude of the response being well reproduced. In particular, the accuracy of the amplitude match to test measurements is broadly perceived to reflect the extent to which bending of the fuselage is present in the individual mode shape. The relatively better match where fuselage deformation is not an important part of a mode may be explained by the relative difficulty of modelling the very three-dimensional fuselage,

254


compared with the plate-like wing. For the fundamental wing modes on EF2000 the fuselage can be considered to be approximately rigid, explaining the good match noted above. In line with the additional demands placed on the model in this use for the direct prediction of stability, additional analyses, in terms of modal gain and phase sensitivity to variations in configuration (tip pod inertial properties on EF2000, for example), become part of the process, to establish the factors influencing gain and phase margins. Gain and phase variability of the FCS hardware must also be investigated thoroughly, and the effects of wear and ageing will have to be addressed for clearance of the service fleet.

Flight testing Aims Whereas ground testing for structural coupling was at the focus of the design and clearance process for the Experimental Aircraft Programme, flight validation of predicted structural-coupling characteristics is a central part of the approach applied to EF2000. Owing to the expense of a flight test programme, reliance on flight validation is accepted only with reluctance; for example, in this situation where the evidence is essential to the solution o f the structural-coupling problem. The purpose of the SC flight testing on EF2000 was thus to: • provide essential validation of the model used in the calculation of margins for phase stabilisation; • allow for assessment of the factors which had not been modelled; and was implemented, as had been prototyped in EAP, with an excitation injected into the actuator and the response being measured at the IMU, thus mimicking a ground SC test and measuring the flexible-aircraft part of the SC system. The control laws were fully validated in ground-rig tests, so direct measurement of SC stability margins was not the preferred approach. The validation exercise was particularly aimed at verifying the predicted phase characteristics at in-flight conditions for structural coupling, while confirming and quantifying the expected overprediction of the flexible aircraft's control-surface effectiveness. The second aim was primarily associated with the expected variation of the same control-power term with angle-of-attack. Both aerodynamic effects result from the relatively simple formulation for the aerodynamics used in the flexible-aircraft model, which assumes an inviscid flow and hence lacks boundary-layer effects which include reduced control-surface effectiveness, and cannot deal with separated flows typical o f delta configurations at high incidence. As noted, the control-power term is effectively a gain in the structuralcoupling loop, and the conservatism in the basic SC process was expected to show as a reduction of the SC gain when comparing the prediction with the

Aeroservoelasticity 255 measurement, corresponding to an alleviation factor which may be taken into consideration when assessing SC stability margins for the low frequency modes. Similarly, it was expected, with support from EAP flight tests, that the measured structural-coupling gain would reduce with increasing angle-ofattack. Some success in matching flight-measured alpha effects has been gained by modelling the variation in the unsteady aerodynamic term by corresponding variation in the wind-tunnel-measured steady-flow equivalent. The flight test programme was therefore planned around a n u m b e r of subsonic and supersonic flight conditions for identification of the conservatism in the aerodynamioc model, with constant angle of attack at selected conditions to investigate the effects of incidence.

Excitation system T h e frequency and bias injection system used for excitation in SC flight tests, (Reference [13] describes the system used for flutter-flight tests) is mechanised as a subsystem of the FCS, within the flight control computer. The frequency and bias injection system generates a high sampling rate (pseudo analogue) digital d e m a n d signal, synchronous with the actuator outer-loop closure and summed with the output of the control law before being transmitted to the actuator. The SC excitation signal is a swept-frequency sine wave, with parameters (start and stop frequencies, duration, amplitude against frequency, actuators to be driven) defined wholly in software to facilitate modification. A deterministic signal was preferred in order to aid understanding and visualisation, and a swept-frequency form was selected rather than the singlesine ground-test approach because of the obvious constraints on the time spent on one condition during a flight test, especially for the test cases for high angles-of-attack. Experience gained in the flight trials for EAP, as well as g r o u n d tests on EF2000 itself, lead to the selection of the values of the parameters for the test. In this application, a 60-second duration, logarithmic-frequency sweep over 2-15 Hz was chosen. The excitation amplitude was profiled with frequency to match the capabilities of the actuation system. One-third and two-third factors could be applied to the basic profile to account for the effect of dynamic pressure on the excitation generated, and to match the predicted amplitude o f the response as closely as possible to dynamic load limitations for each testflight condition.

Response measurement and analysis The excitation measurement and analysis route is illustrated schematically in Figure 7.13. Note that since data is not necessary for validation of the clearance phase u n d e r which the flight test is being performed, telemetry and real-time analysis are not required. The recorded time histories of the excitation and the response are analysed

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Implications of phase stabilisation The task of modelling accurately the structural-coupling loop for the low frequency modes, together with the necessary validation of each loopelement, constitutes a significant cost to the EF2000 programme which is

258


directly attributable to the adoption of phase stabilisation, in addition to the obvious expense of the flight testing itself. Further costs are associated with the wider implications of the implementation of the phase-stability margin criteria, as outlined below. With the Experimental Aircraft Programme gain stabilisation criteria (Figure 7.10), the minimum SC loop margins (maximum open-loop transfer function gain) is - 9 dB, and, in most circumstances, rather more. This means that the attenuation provided by the notch filters effectively negates the link between the response of the flexible aircraft and control-surface excitation through the FCS, or effectively opens the structural-coupling loop. This is convenient for the clearance for flutter and dynamic loads, since it means that predictions and clearance can be based on a flexible-aircraft model without the FCS being included, and the clearance processes are not dependent on the FCS in any way. The Nichols chart showing closed-loop gain and phase superimposed on the usual open-loop grid, Figure 7.15 shows a large area (hatched) where the magnitude of the closed-loop response will exceed that of the same system with the SC loop open. Thus any mode which has its peak open-loop magnitude within the hatched area is effectively reduced in damping by the action of the FCS when the loop is closed. Note that, in fact, a mode with an open-loop gain of - 9 dB at - 180 ° phase (and so meeting the EAP criteria) will show a closed-loop peak magnitude at - 5 dB, a 4 dB, or 60 per cent increase in response. The phase-stabilisation criteria were drawn to maintain this - 5 dB closed-loop peak gain to a phase margin of + 90 °, to give a closedloop response consistent with the worst possible under the gain-stabilisation requirements. A peak in the open-loop response which falls outside the hatched area will have a closed-loop response of lower magnitude than the open-loop, indicating that the FCS is acting in opposition to the excitation, to damp the response. Intuitively this latter situation would be expected to have a beneficial effect on the flutter problem, and dynamic loads in particular, but since the FCS control surface is now activated to modify the system's response, or to effectively increase modal damping, it is implied that the aerodynamic pressure distribution on the wing is modified from the open-loop case, which may result in different structural loads. In any case, unless the structuralcoupling margins are very large, the closed-loop system will behave differently from the open-loop, which means that dynamic loads and flutter analysis must model the FCS coupling. Furthermore, to correctly reproduce the closedloop effect, the magnitude and phase of the coupling must be accurately represented, implying that the SC flight and ground-test-matched flexible aircraft model used for phase-stabilisation margin prediction must be adopted. Traditional matching of the flutter model, extending only as far as adjustment of the modal frequency, and wing, fin and foreplane modeshape matching to ground-resonance test measurements, may no longer be adequate.

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7.4 Future developments T h e cost of a solution to the structural-coupling problem, in terms o f the additional phase lag introduced into the FCS, is not insignificant when compared with the lag from other sources such as primary actuators, as indicated by the example of Figure 7.5. As expensive development efforts are applied to reduce overall system lags in order to realise the p e r f o r m a n c e potential of the FCS, a commensurate effort must be made to minimise the cost of the SC solution. The approach to structural coupling at British Aerospace is therefore u n d e r continual review; a n u m b e r of the directions where work is required or underway are outlined below.

7.4.1 Limit-cycle prediction and specification of alternative clearance requirements For consistency with the factors motivating the design and clearance methodology applied to EAP, structural coupling has been treated as a flightsafety issue. As already described, however, it is unlikely that structural failure could result directly from a structural-coupling encounter, because of the limited energy which the FCS can input, and because of system's constraining nonlinearities. For a flexible aircraft, an unstable mode will manifest itself as a limit-cycle oscillation in these circumstances, which may be very undesirable, but is not necessarily critical to flight safety. The real concerns are with the coupling of the flutter modes, structural and FCS hardware fatigue and effects on actuator performance, which may themselves have safety implications. To fully understand these concerns, a m e t h o d must be devised for predicting the amplitude and frequency of a limit-cycle oscillation within the system. The following section investigates the case of a structural m o d e which is unstable in the closed loop, through an application of nonlinear system theory to both a simple example system, and a more representative aircraftsystem model. The possible advantage of such a consideration in terms of an alternative structural-mode clearance procedure will then be considered.

7. 4.1.1 Description of limit-cycleprediction technique Limit-cycle criteria and prediction The existence of limit cycles in a nonlinear system can be predicted from a solution of its characteristic equation, with the nonlinear elements replaced by their describing functions [22]. In order to simplify the analysis, the only nonlinearity that will be considered is the software rate limit function within the FCS. The purpose of the rate limiter within the control software is to prevent saturation of the actuator main valve and, as such, is the main nonlinearity which limits the performance of the actuator. This in turn dictates the amplitude of any limit cycle which may occur. Consider the system as shown in Figure 7.16 in which an actuator is used in

Aeroservoelasticity

r(t) ) ( ~

~

261

c(t)

Gn0tO,E) Ratelimit Actuator Load

Structural Filters

Figure 7.16 System block diagram a position-control system in which the load exhibits a structural m o d e within the bandwidth of the closed-loop system. In this case, the characteristic equation for the system can be written as:

1 + G,(jw, L) G1(jto) Gz(jto) Gv(jto ) = 0

(7.1)

T h e solution of the characteristic equation gives the limit-cycle condition, which can be predicted from a r e a r r a n g e m e n t of eqn (7.1) 1

G1(rio)G2(jw ) Gr(jto ) - Gn(Jt°, E)

(7.2)

Provided that the describing function for the rate limiter can be derived, and that the linear c o m p o n e n t s within the system can be adequately modelled, it will be possible to predict the existence of limit-cycling conditions within the system.

Derivation of describing function for a rate-limiting function In order to derive a describing function for the rate limiter, consider the i n p u t / o u t p u t characteristics of such a device as shown in Figure 7.17. In this case, the characteristics are shown after a length of time sufficient for a steady relationship to be achieved. In addition it is assumed that the input signal is a pure sinusoid which triggers the rate limiter to give an output waveform which is triangular [23]. From Figure 7.17, the amplitude of the triangular output waveform can be derived as:

Y=~fl

2w

where fl is the m a x i m u m rate as shown in Figure 7.17.

(7.3)

262

Flight control systems i

I

----

i Y

Input i

0

Figure 7.17

i

~

"~ tm

= ESino~t ~

i

i

i

~

"-6Time (s)

i

2~

co

I n p u t ~ o u t p u t characteristics o f rate-limit f u n c t i o n

Fourier analysis o f such a triangular waveform o f amplitude Y, reveals that the a m p l i t u d e o f the f u n d a m e n t a l is:

4/3

Y10,= - -

(7.4)

0)77

with an infinite n u m b e r o f harmonics. Neglecting these h a r m o n i c s , the gain o f the rate limiter can be expressed as" I G , ( j w , L) I -

4/3 wETr

higher-order

(7.5)

for an i n p u t sinusoid o f the f o r m as shown in Figure 7.17. In o r d e r to derive the phase response o f the rate limiter, c o n s i d e r the i n p u t / o u t p u t relationship o f Figure 7.17 o n c e again. F r o m the figure, it can be seen that the phase lag between the two signals can be r e p r e s e n t e d by the time delay, r. In o r d e r to obtain an expression for this time delay, it is necessary to locate the time at which the i n p u t signal is equal to the o u t p u t signal, such that: E sin cotm = 2-~

(7.6)

C o n s i d e r i n g that t moccurs after t = 7 r / 2 w , the above e q u a t i o n can be solved for t m such that 7r

1

7r/3

co

0)

2E0)

t m = -- - -- a sin - -

(7.7)

Aeroservoelasticity

263

Therefore, the time delay, r, can be expressed as

(7.8)

- a sin

r=--

¢.0

Finally, since the phase lag between the input and output signals can be expressed as

/_G,(jw, E) = - ~'w

(7.9)

the describing function of the rate limiter u n d e r the assumptions applied earlier is therefore

IGn(joJ, E)

I= 4fl

(7.10)

o~ETr

/_ G,(jw, E) = -

-asm~

+)

(7.11)

Since the gain of the rate limiter will never be greater than unity, and the phase o f the rate limiter will never be greater than zero, limitations can be applied to the above expressions. This results in the requirement that:

EoJ~ >4/3

(7.12)

/O

for the gain expression to be valid, and: EoJ~-2

(7.13)

for the phase expression to be valid. The above expressions therefore allow the prediction of the existence of the limit-cycling condition from the solution of the characteristic equation for the system as given in eqn 7.2. This is provided that the linear elements of the system can be accurately modelled, or a frequency response obtained from suitable testing.

Prediction of limit cycles in an example system In order to demonstrate the use of the describing function in the prediction of limit-cycles, consider the system as shown in Figure 7.16, with characteristic equation as given in eqn 7.2. Given that the linear elements of the system can be represented by the transfer functions:

264


20

'i

_

(:

.::

/

'-

! ---~

i

~ncreasing o

G1G2GF(j°))

..................

: .... ,

..... : ..... :

.... :

-~-s~ ..... ~ .......S01utipn at ~=9"6 HZ,.E=0"04 • ~

-40

-35

-30

-25

-20

-15

-10

-5

•......

0

5

Real

Figure 7.18 Nyquist diagram showing limit-cycle solution 1 G1(s) = (0.026s + 1) (0.00005917s 2 + 0.007693s + 1)

(7.14)

1 Gz(s) = s2 + s+ 4000

(7.15)

GF(S) = 1

(7.16)

where the e l e m e n t Gl(S ) represents a typical servo hydraulic actuator, and G2(s) represents a lightly d a m p e d modal system. In the absence of the rate limiter, the system is unstable in the closed loop resulting in an u n b o u n d e d oscillatory response in the presence of an initial disturbance. For the system including the rate limiter, however, the characteristic equation can be solved in order to predict any resulting limit cycle. O n e m e t h o d of solution of the resulting characteristic equation is to plot both sides of eqn 7.2 on a Nyquist diagram and find the intersection of the two loci. Unfortunately, the describing function for the rate limiter is both frequency and input-amplitude dependent, resulting in an infinite n u m b e r of loci. However, solutions of the characteristic equation can either be located through suitable iterative techniques, or through plotting the describing function for the rate limiter as a function of Eto. T h e intersection therefore identifies the frequency of the limit cycle on the loci of G1C~GF(to) and the value of Eto and hence to on the loci of the rate-limiter describing function. T h e corresponding Nyquist diagram for the example system is shown in Figure 7.18. In this case, the nonlinear characteristics have been plotted for a


10

,

!

........

.........

!

!

!

......

!

....... ,..........

, ................... .

265

,

........

5

_Fo -5

-10

: -15 -5

-4

i ~ S o l u t i o n at a h = 9 . 6 H z , E - - 0 . 0 4 -3

-2

-1

0 Real

1

2

3

4

5

Figure 7.19 Nyquist diagram showing limit-cycle solution single frequency, o~, which intersects the locus for Gl GzG~(jo2) at G1GzG3(jwl). This point represents the solution of the characteristic equation, and therefore predicts the frequency and amplitude of the resulting limit cycle. From Figure 7.18, the value of the frequency at which the two loci intersect is 9.6 Hz, and the corresponding limit-cycle amplitude, E, is 0.04. Figure 7.19 shows the intersection of the two loci in more detail. A simulation of the system results in the limit cycle shown in Figure 7.20. From the figure, the limit-cycle frequency is 9.64 Hz with an amplitude of E=0.038. These results match well those predicted by the describing-function technique. From this simple example at least, the prediction of limit cycles within a system involving a rate limiter seems feasible. The following section extends this analysis to consider a system based on a typical aircraft-system model.

Limit-cycle prediction in an aircraft system T h e previous section demonstrated an application of describing-function theory to the prediction of limit cycles. However, the example system used was relatively simple compared with an aircraft-system model. Assuming the aircraft flight control system to be analogue, and that the sensor dynamics can be neglected at present, the block diagram for the aircraft system can be considered as shown in Figure 7.21. The three control-surface actuators are assumed to be identical, and have been linearised in order to make use of the earlier describing-function analysis. T h e derivation of the characteristic equation for the system is straight


266

0.04

1

0.03

r

. . . . . . .

i

. . . . . . .

.

.

.

.

.

.

.

.

.

........ !....... "!""w -0 04 ~

0

0.5

1

.

.

.

~

.

.

.

.

.

.

i

.

i

. . . . .

i

t

I

. . . . . . . .

illvviltlillllHlllllIllllllllllll 1.5

2

2.5

3

3.5

4

4.5

5

T i m e (S)

Figure 7.20

Time-domain simulation results of example system

forward, and results in the equation:

1 - H(jw) GACT(JW)GT(jto, A l, A 2, A3) = 0

(7.17)

where

Gr(jto, A l, A 2, A3) = GAca(jtO)Gl(jto)Gu(jto, A 1) + Gacz(jto)G2(flO)GN(jto, A2") + Gac3(jto) G3(jw) GN(jto, As)

(7.18)

Now, the amplitude of the input signals to the rate limiters (A1,Az,A3) can be derived from the error signal and the particular FCS path-transfer function, such that for example: A

1 =

iG](jw)IE

(7.19)

This enables the characteristic equation for the system to be expressed as a function of 0J and Eonly, as was the case for the earlier example. Although the resulting equation is more complex than for the earlier example, the principle is exactly the same in that a solution of the characteristic equation will predict the existence of limit cycles within the system. The characteristic equation is therefore:

H( jto) GACT(jto ) = where

1

GT(jW, E)

(7.20)

~ / = 1

I

~

w

~f w

+

~F

~t

m

. . . . .

!, i

Aeroservoelasticity

-q

267

268


Table 7.3 Predictedaircraftsystem limit cycles w(Hz)

E(V)

16.0 16.4 24.0 66.0 73.6

0,0142 0.0332 0.0371 0.0040 0.0106

or(j,,,, E) = CAc~( jo~) 61( jo,) CM ( jo~, E) + C~c2( jo~) G2(jo~) CN2(jo,, ~ ) + Gac~(jw)G~(jw)G~(jw, E) (7.21) and

[GNx(JO,), E)

I=

Z-GNx(jw, E ) = -

4[3

(7.22)

)

-asin21Gx(jw)lE w

(7.23)

T h e solutions o f this characteristic equation for a reduced-order model of the flexible aircraft with ten modes are as shown in Table 7.3. These solutions were obtained using the same principle as shown in Figure 7.18. The results therefore predict that there exist five possible operating points for the system, each point representing a limit cycle of differing amplitude and frequency. A time-domain simulation of the system for an arbitrary initial disturbance, results in a limit cycle as shown in Figure 7.22. The amplitude and frequency of the actual limit cycle is 0.035 and 16.4 Hz, respectively. This compares well with the second of the predicted limit cycles in Table 7.3. The above results demonstrate that it is possible to predict the existence of limit cycles even in a complex system such as the aircraft model shown in Figure 7.21. In this case, the theoretical analysis predicted the existence of five possible limit-cycle conditions. In reality, the system will operate at only a single limit-cycle condition. Table 7.3 gives the values for the five solutions o f the limit-cycle analysis. The second pair of values, 16.4 Hz and 0.0332 V, correspond to the limit cycle which actually occurs. The practical significance of the other values was not investigated, but it is possible that they correspond to unstable limit cycles which could not, of course, be realised in practice.

7. 4.1.2 Prediction of limit cycles in the presence of phase uncertainty T h e above section has described a m e t h o d for predicting the existence of limit cycles in a nonlinear system. In this case the only nonlinear element that

Aeroservoelasticity 269 0.04

0.03

0.02

0.01

o

uJ

-0.01

-0.02

-0.0~

-0.04

0

0.5

1

1.5

2

2.5 Time (s)

3

3.5

4

4.5

5

Figure 7.22 Limit-cycle condition for reduced-order aircraft model has been considered is the software rate limiter. Comparison of the predicted limit cycles with those obtained from time-domain simulation has shown that a simplification of the nonlinearities still produces a good estimate of the limit-cycle frequency and amplitude. Unfortunately, this procedure relies on the existence of reliable frequencyresponse data for all the linear elements of the system. In the case of the real aircraft system, this is not the case as has been discussed earlier. Although ground vibration tests provide reliable measurements of the open-loop gain of the aircraft system, there exists a large degree of uncertainty in the phase response of the system. This is due in part to uncertainties in the modelling of the unsteady aerodynamics and also in the phase relationships between the many possible signal paths which exist within a typical flight control system. As has been discussed earlier, clearance procedures allow for this uncertainty in the phase by neglecting its influence on the stability of the system and by assuming in-phase addition of all the signal paths. If the phase response of the system cannot be relied upon, then the use of these limit-cycle prediction techniques is restricted. The following section discusses to what extent the limit-cycle condition can be analysed in the presence of such uncertainties.

Limit-cycle prediction in the presence of phase uncertainty Consider the characteristic equation of the aircraft system as given in eqn 7.20. If no phase information is available, then the solution of the characteristic equation yields only a value for the gain, such that:


270

]H(jw) it GACT(j0)) I -

I G T (j0), E)

(7.24)

where

IGT(j0), E) i = IGAcl(j0))IIGI(j0))IIGM(j0), E) + IGAc2(j0) ) IIG2(j0) ) IIG~(j0), E) I + ] Gac3(j0)) IIG~(j0))If Gin(j0), E) I

(7.25)

4[3 0)J Gx( j0) ) IETr

(7.26)

and

GNx( j0), E) -

Whereas in the earlier case there was a single solution, there now becomes an infinite n u m b e r o f possible solutions. In reality, the actual solution that exists is d e p e n d e n t on the phase response. Since this phase response is not reliably known, then it has to be assumed that a limit cycle could occur at all frequencies. Substituting for eqn 7.26 into eqn 7.25 where appropriate, the characteristic equation can be expressed as:

]H( j0)) [I GAcr( j0)) I = 4[3 -( I GAcl( j0)) I + I GAc2(j0)) I + I GAc3(j0)) I) 0)E~r

(7.27)

which can be rearranged to result in an equation for the amplitude of the limit cycle in terms of the error signal, such that:

E= 4fl IGAcT(J0))I(IGaca(Jw)l + IGAc2(joI + IGAca(J0))I)IH(j0)I

(7.28)

0)71"

Consideration of eqn 7.28 reveals that the limit-cycle amplitude at any given frequency is simply the maximum output of the rate limiter multiplied by the loop gain between this point and the point at which the limit-cycle amplitude is desired. In this case, where the limit-cycle amplitude is given in terms of the e r r o r signal, the amplitude is as given by eqn 7.28. In addition, the worst case is assumed where the three signal paths are considered to act in unison as in the current design methodology. It would also be possible to account for changes in flight condition within the form of eqn 7.28 by augmenting the aircraft gain terms accordingly. Now, consider that:

4[3

--

0,)71"

I GAcr(j0))l = X( j0))

(7.29)

Aeroservoelasticity 271 1 0 -1

10'

~ :~

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

. . . . . .

i. . . . . . . . .

~ . . . . . . . . . .

,

. . . . . . .

~ . . . . . . .

2

1 0 -3

EIO

-4

1 0 -s

. . . . . . . . . . .

1 0 -e

0

~. . . . . . . . . . . .

~ . . . . . . . . . . .

i . . . . . . . . . . . .

:. . . . . . . . . . . .

i

t

L

. . . . . . . . . . . .

I

. . . . . . . . . . . .

i

i

i

10

20

30

40

50

60

70

Frequency

:. . . . . . . . . . . . .

80

( H z )

Figure 7.23 Actuator performance limit, X(l'oJ) where X(jo) is the maximum output of the combination of the linear actuator and rate limiter at any given frequency. This enables the amplitudes o f the limit cycles to be predicted from the performance limit of the actuator and the gain response of the remaining linear elements of the system. In addition, the linearisation of the actuator is no longer necessary in order to predict such limit-cycle amplitudes. Instead, experimental measurement of the maximum output amplitude of the actuator as a function of frequency will suffice. The presence of uncertainty in the phase response has therefore restricted the prediction of the limit cycles within a system to the estimation of only amplitudes of the limit cycle.

Application of the prediction of limit-cycle amplitude to an aircraft system In order to demonstrate the prediction of the maximum limit-cycle amplitudes in a typical system, consider the aircraft-system model as shown in Figure 7.21. In this case, however, the model will contain a nonlinear actuation system model as opposed to the linear version used earlier. In addition, all of the structural modes will be included in the analysis. From eqns 7.28 and 7.29, the elements required to calculate the limit-cycle amplitudes at the error-signal position are as shown in Figures 7.23 and 7.24. Combining these two figures according to eqn 7.28, along with the necessary scaling between ram extension and control-surface motion, results in a maximum boundary for the limit-cycle amplitude at the error-signal location [23,24]. This boundary is as shown in Figure 7.25.


272

80] =

i

60

.....

.

4o

.........

i ........

.

.

i

.

.

.

.

.

.

.

.

:

.

.

.

i

.

.

.

.

.

i

.

.

i

0 F r e q u e n c y

Figure 7.24

100

$

(Hz)

Loop gain, (I Gacl~jOJ) l + I GAc2(l'oJ) l + I Cac3(joJ) I)IH(joJ)l

............

w. . . . . . . .

[

. . . . . . .

J ........

!. . . . .

!

. . . . .

~ . . . . . . . . .

L

.........

1 0 -1

1 0 -3 0

i 10

20

i 30

= 40 F r e q u e n c y

Figure 7. 25

50

60

(Hz)

Maximum limit-cycle amplitude at error signal, E

70

80

Aeroservoelasticity

273

The above theory has demonstrated that the maximum amplitude of the limit cycles within the system can be defined quickly using the p e r f o r m a n c e b o u n d a r y of the actuation systems and the gain response of the aircraft structure and flight control system. The ability to predict such limit-cycle amplitudes enables their effect on, and interaction with, other system elements to be assessed. In reality, the existence of limit cycles within the system would not be tolerated for long periods of time. Such conditions would have serious consequences both in terms o f the fatigue life o f the aircraft structure and in terms of the wear of actuator components. In addition, were a limit-cycling condition to arise, a large a m o u n t o f power would be dissipated within the flight control system in responding to it. As a result, it is vital to ensure that such limit-cycling conditions do not arise u n d e r normal flight operations.

7.4.1.3 Prevention of limit cycles Returning to the system of Section 7.2.4, the system as shown in Figure 7.16 has the characteristic equation: -1 G1(jw) G2(jo0 GF(jOJ) - Gn(Jw, E)

(7.30)

Consider now that the gain of the rate limiter, Gn(joo, E), which can never be greater than unity by definition. As a result, the magnitude of the right-hand side o f e q n 7.30 can never be less than unity. The result of this in terms of the Nyquist diagram is that the locus of the right-hand side of eqn 7.30 originates from the ( - 1,0) point and never enters the unit circle. In order to prevent a possible limit-cycle condition, it is therefore adequate to ensure that the locus of the lefthand side of eqn 7.30 remains within the unit circle. If this is achieved, then the two loci cannot intersect and no limit cycle can occur. This can be demonstrated graphically as shown on the Nyquist diagram of Figure 7.26. In this contrived example, the linear elements of the example system considered earlier have been attenuated by a gain sufficient to bring the response within the unit circle. Although the inclusion of such a gain in the system may not result in the required closed-loop response, it will ensure that a limit-cycling condition may not occur. Such a criterion may be satisfied in the case of the aircraft system even in the presence of phase uncertainty. Since the criterion only depends on the open-loop gain of the system, phase effects are unimportant. If phase information were available at certain structural frequencies, it may be possible to relax this requirement. For example, if reliable phase information was available for the 7 Hz structural mode, and it was found that it did not cross the locus of the rate-limiter describing function, then a limit cycle could not result.

274

Flight control systems 2

,

1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

..... 1

!

........

Unit Circle

. . . .

! n c r e g s m g (ii ........... :::.. i:..

0.5

.

.

.

.

.

:i"

i -1.5

,

. . . .

]

,

i

,. I . . . . . . . . . . . . . . . . . . .

. :_G_I G_2 G F (~,i 0 ) )

i . . . . . . . . . . . . . . .

: .......

: ....

I

i

-2 -

i -1.5

I i

-1

-0.5

0 Real

i

,

=

0.5

1

1.5

2

Figure 7.26 Nyquist diagram for arbitrary system In summary, provided that the open-loop gain of the system is less than unity, the Nyquist plot for the linear system cannot intersect the rate-limit describing function at any point. As a result, the existence of a limit cycle is not possible given the nature of this particular nonlinearity. As with the current clearance procedure, suitable filters introduced into the feedback path may be used to reduce the open-loop gain to the required level. It is i m p o r t a n t to note that, should the model of the aircraft be in error, then the nature of any potential limit cycle is predictable. In addition, if a limit cycle does occur, its effect in terms of actuator p e r f o m a n c e and h e n c e rigid-aircraft response can be quantified.

7. 4.1.4 Specification of an alternative clearance procedure T h e current clearance procedure as discussed earlier assumes that the aircraft system can be considered to be linear in the main. T h e result of this is that feedback filters are designed so as to ensure closed-loop stability by ensuring a m a x i m u m open-loop gain of - 9 dB for the majority of structural frequencies. This safety margin of 9 dB ensures, that even in the presence of significant modelling errors, closed-loop stability will be assured. This large safety margin was applied owing to uncertainty in the effect of an unstable structural m o d e on the aircraft as a whole. T h e previous sections have discussed in some detail the effect of the nonlinear nature of the actuation system on the structural-coupling problem. In particular, it has been d e m o n s t r a t e d that, owing to the existence of the rate-limiting function within the FCS, an unstable structural response may only result in a limit cycling condition. T h e criteria for the existence of such

Aeroservoelasticity

275

a limit cycle have been introduced earlier. In the presence of uncertainty of the phase response, however, it has been shown that limit-cycling conditions may arise wherever the open-loop gain of the system exceeds 0 dB. The effect of allowing limit cycles to exist in the nominal case has been discussed earlier, and as a result suitable filters should be incorporated into the system to give a maximum open-loop gain of less than 0 dB. The question that remains, however, is to what extent should the open-loop gain be attenuated below this level in order take account of possible modelling errors? Fortunately, in the event of modelling errors causing the open-loop gain to b e c o m e greater than unity, any resulting limit cycle can be predicted. For example, for the case of the system model being in error, any frequency at which the open-loop gain exceeds 0 dB may result in a limit cycle. Importantly however, the amplitude of such a limit cycle can be predicted and its effect on the satisfactory control of the rigid-body aircraft assessed. Suppose that the structural filters were designed so as to give a maximum open-loop gain of - 1 dB. As a result, the phase lag introduced by these filters will be significantly less than that introduced by the current - 9 dB filters. In the nominal case, these filters will ensure that a limit-cycling condition could not arise. One consequence of this action, however, would be that any error in the modelling of the system could result in a limit-cycling condition occurring. Consider a situation where an error in the modelling has indeed resulted in an in-flight limit-cycle condition. Such a condition would be more likely at high aircraft incidence where the FCS gains are highest. Provided that such a possibility has been investigated in terms of the limit-cycle amplitude and its effect on the actuator performance, rigid-body stability will be maintained. The aircraft incidence could then be safely reduced, whereupon the limitcycle would dissipate as a result of the reduction in FCS gain. If such an in-flight interaction were encountered, then it would be possible to correct the flexible aircraft model accordingly, redesigning the structural-mode filters so as to maintain the - 1 dB maximum open-loop gain for the nominal case. Provided that a suitable safety margin has been explored in terms of limitcycle amplitude and its effects, the implementation o f structural filters giving a - 1 dB open-loop gain should be free of risk to the aircraft. An alternative design procedure can be represented by the flow diagram given in Figure 7.27. The initial stages of the design process are identical to that currently employed. First, a flexible-aircraft model is developed, which when combined with a model of the flight control system allows the production of an envelope showing maximum open-loop gain against frequency. These results can be modified by actual ground-test data when available. As for the current design method, it is assumed that all the signal paths act in phase. The next stage in the design process is to design suitable structural-mode filters to meet the - 1 dB maximum open-loop gain requirement.

276

Flight control systems LinearModellingof FlexibleAircraftand FCS

"Nonl~ne~-M~odeHingof FCS

sumptions ~N~ Aliasing l In-Phaseadditionof I ignat paths 1 SU averaging] ZoH attenuation J

oxib,0Airora' o,FCS II O.ou.Stoao

1

~ ~ oUmVtions ~X ingleinput(worst[ ase) [ h signalwaveform[ o load /

Actuator/Rate/ [ActuatorBench LimitModellins~[ Test

Performancelimitsof [ ActuatorandRate Limit['--~ Combination 1

Envelopeof Maximun~ Open-LoopGain 1 versusFrequency[ Designfiltersto I InitiallyMeet-1 dB [ MaximumOpen-Loop Gain

MaximumPossible [ FilteredResponse(nominal) at Actuator/RateLimit

~[

NotchFilterDefinition I CheckBelowRate ] LimitThreshold

MaximumPossible [ FilteredResponse at Actuator/RateL mit Check Rigid-Body Stability-Margins

I

Figure 7.27 Proposed aeroservoelastic design and clearanceprocess In parallel with this work, the performance limit of the actuation systems is derived both from modelling and bench tests of the actual hardware. Once this has been obtained, it can be combined with the model o f the remaining

Aeroservoelasticity 277 elements within the system. This results in a specification of the maximum filtered-system response, assuming the system model to be correct. As a check that all is well at this stage, if the amplitude of the structural feedback signals at the rate limiter are calculated u n d e r these conditions, the rate limit should not be exceeded. The next stage in the design process is to consider the effect of any errors within the modelling of the system. This could be expressed in terms of an overall increase in gain, or a more specific increase in gain for each structural mode. For example, it may be felt that the system model might be in e r r o r by a certain factor. Alternatively, results from ground tests and where possible inflight tests, might lead to a greater confidence in the gain of particular structural modes. Once obtained, such an error model may be used to predict the maximum possible filtered-system response. This envelope will therefore permit the prediction of the amplitude of any limit cycle which may exist within the system. Assuming such a situation to be the case, the effect of these limit cycles on rigid-body performance can be assessed from a consideration of their effects on actuator performance. If it were found that none of the predicted limit cycles caused unsatisfactory rigid-body response, then it would be safe to proceed to flight testing. Alternatively, if it were found that a particular limit cycle had the potential for causing unsatisfactory rigid-body response, then the structural-mode filters should be compensated accordingly. Although in the presence of modelling errors the potential for limit cycles may exist, it is still not certain that they will occur. The discussion of the criterion for limit cycles made earlier in the chapter has highlighted the need for the correct phase response before a limit cycle occurs. Combining this requirement with the fact that the separate control paths will almost certainly not act in phase as is assumed makes the existence of an in-flight limit cycle a remote possibility. Such conditions for the actual occurrence of a limit cycle are highlighted within Figure 7.28. In the following section, the alternative design procedure is demonstrated using a typical aircraft-system model.

7.4.1.5 Demonstration of alternative clearanceprocedure on analogue aircraft system Design of structural-mode filters In order to design suitable structural-mode filters using the alternative design procedure, it is necessary to produce a model of the aircraft system as for the current design procedure. In order to prevent a limit-cycle condition arising, it has been discussed that it is sufficient to ensure that the open-loop gain of the system is less than unity. In order to achieve this, filters can be designed for implementation within the feedback path of the FCS. Although this is identical to the current design procedure, it is important to note, that in this case, filters are designed to give a maximum open-loop gain of - 1 dB. This

278


Conservative Design Process

Notch Filters Designed to Meet -1 dB Maximum Open-Loop Gain for Nominal Model

_] o dBOp~n-~op Yes

v ] Gain not Exceeded

No No

limit-cycle Possible I

No limit-cycle Possible ]

No Yes No

limit-cycleDoes Not Occur ]

I limit-cycleOccurs I Frequency and Maximum ] Amplitude, Effect on Rigid [ Body Stability Predictable ]

In-Flight In Tests: ] Change I e Flight Condition to I FCj Gain and Dissipate Reduce FCS limit-cycle

Figure 7.28 Conditions for limit-cycle oscillation and implications is in contrast to the c u r r e n t design p r o c e d u r e which results in a m a x i m u m o p e n - l o o p gain o f - 9 dB. P r o d u c i n g the m a x i m u m o p e n - l o o p gain for the earlier aircraft m o d e l for all flight conditions results in a specification o f the structural-mode filter a t t e n u a t i o n as shown in Figure 7.29.

A eroservoelasticity

i: ::::::::i~,:::::

~-,~ ..... t ,~ |

: i

.~.

~

..........

::i:...... : .... .......... :',. ....

'

:

/

~

...........

i

gain requirement

............

............

.......................

I

-%

10

....... ~.... ::::i

.

/

~............

"......

20

30

279

............

I

40 50 Frequency (Hz)

60

70

80

Figure 7.29 Maximum open-loop modal response envelope for full flexible-aircraft system model

If suitable s t r u c t u r a l - m o d e filters are d e s i g n e d so as to m e e t t h e a t t e n u a t i o n r e q u i r e m e n t s d e f i n e d in F i g u r e 7.29, t h e r e s u l t a n t filters are: s2 + 0.90s + 2018 Gqa (s) = s2 + 2.7s + 1968

(7.31)

Gsf2 (s) =

s2 + 1.62s+ 10250 s2 + 2s+ 9990

(7.32)

G~f3(s) =

s2 + 1 . 4 9 s + 8636 s~ + 7s+ 8420

(7.33)

0.1648 (s2 + 5.3854s + 113290) (s 2 + 2.2307s + 19437)

Gsf4(s) =

(s2 + 274s+ 29821)(s2 + 50s+13131e4)

(7.31)

where

Gsjq(s)

is a n o t c h filter c e n t r e d o n 7.15 Hz;

Gsf2(s)


Gsf3(s)


G~f4(s)

is a low-pass filter d e s i g n e d to a t t e n u a t e t h e h i g h f r e q u e n c y


280

.....

t ...... 1o-

~o

[ /

!

:

i

i

•

'

i. . . . . .

i ........

:

:

'

i

'

.

I~.

................

a ~

'

! f~l- ~ ......

'

]

..........

0

"0

' ....

Before filtering

I ~ - .

-+o

..........

: ~..~1 :

i ........

I

:I ~

I/

4. .~.,~ ~ :

". ::.

•

_ 3 0....... -20 1 ~ ....~ :

4.

;_

..~. :

~/ ~4.;..:~.

:

.i . . . . .

: ----7"--

~

• .

.....

----

i .........

"

: .........

. . . .

:

10

20

30 Frequency 40 (Hz)50

~

--

~

7"

"

. . . .

-4° [ .......... ................ ............ :............. : ............ i............ :........

0

--

:. . . . .

:

60

70

80

Figure 7.30 Maximum open-loopgain for aircraft system aflerfiltering modes. Applying these filters to the m a x i m u m open-loop gain as shown in Figure 7.29 results in the m a x i m u m open-loop gain for the filtered system as shown in Figure 7.30. Figure 7.30 demonstrates that the required level of attenuation has been achieved resulting in the m a x i m u m open-loop gain of the system being less than - 1 dB. As a result, inclusion of such filters into the aircraft system will ensure that a limitcycling condition cannot arise. As a demonstration of the significant reduction in phase lag obtained by applying such filters, the phase lag of the - 1 dB filters at a frequency of 3 Hz is - 18.0 degrees. This compares very favourably with a phase lag of - 32.4 degrees for - 9 dB filters at the same frequency. It can be seen that there is a significant advantage to be gained in applying a clearance r e q u i r e m e n t of - 1 dB for the structural modes. Such an advantage has however been achieved at the expense of system robustness to modelling errors. T h e ability of the - 1 dB filters to prevent a limit-cycle condition relies on the actual aircraft response being accurately modelled. Any increase in the system gain above that represented in Figure 7.29 may result in the open-loop gain o f the filtered system exceeding 0 dB. This could in turn result in a limitcycling condition. It is important therefore to assess what impact such a situation would have on rigid-body control. T h e ability to predict the possible outcome of an error in the modelling of the system is crucial to this alternative clearance procedure. For the linear system, it must be assumed that a structural m o d e for which the open-loop gain is greater than 0 dB, would result in an u n b o u n d e d structural oscillation in the closed loop. T h e nonlinear nature of the system allows the prediction

Aeroservoelasticity

281

100

~:::~::~:~:~:~:~::::::~:~::::~:!::::~i~:::i~ ~::: ~: ~:~:~:~ ...........

: .......

P

:"7

........

~ ............

: ............

~

~

....

: ............

:............

-~

.•10

"::

::::::::::::::::::::::::::::::::::::::::::::::::::::::::

======================

:::::1' : : : : : : : :

:::::~...: .... I..,....:./... ~.. ~.~ ~. fl . . . . . . . . . : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : .......

i ..... [

(i,

...........

*~' ........

~i~ ...........

'.~ ..........

i ............

........

......

'~

...........

~:..........

~' ...........

i ............

i ............

i

~ ...... ; .... I ......

~ 1 0 -= :

10"

0

Figure 7.31

!!i!

~

I

I

i

10

20

30

:::::::

===================== ..........

!.

i

I

I

I

40

50

60

70

Frequency (Hz)

.!'!~/

80

Maximum limit-cycle amplitude at error signal for nominal model (broken line) and with - 1 dB filter (solid line)

o f any resulting limit cycle and its effects, allowing a confident reduction in the structural-mode clearance requirements. It should be noted that even if the gain of the open-loop system were to exceed 0 dB, the existence of a limit cycle is by no means certain. As has been discussed earlier, the existence of a limit cycle is governed by consideration o f both gain and phase. The consequence of this is that, if the gain is greater than 0 dB, a limit cycle will only occur if the phase response of the system is appropriate. In terms of a Nyquist diagram, even though the response of the linear elements may exceed the unit circle, it may still not cross the locus o f the describing function of the rate limiter at a compatible frequency.

Limit-cycle prediction in the presence of system modelling errors T h e results of earlier sections have shown how it is possible to predict the maximum amplitude of any possible limit cycles within a system. In this case, provided that the system gain is as modelled, then no limit cycles will occur owing to the presence of correctly designed structural-mode filters. In the presence of modelling errors, however, the amplitude of any limit cycle can be obtained and its effect on the rigid-body control assessed. Consider the nominal system model, with no structural-mode filters in the feedback path. The resulting maximum amplitude of any limit-cycle oscillation can be predicted as in Section 7.3. This results in the maximum amplitude envelope as shown in Figure 7.25. If the - 1 dB structural filters were now incorporated into the system, then the maximum amplitude of any resultant limit cycle could be predicted as shown in Figure 7.31.

282

Flight control systems 10°

:![[i!!!iii~'!i!i!i!!!!!!}!!!!!![!i!{!!!!!!!!!!'?i!i

!i!!! ':!!!! !!!!!!!'.!?!!!!ii!!i)!??!??!!??!

21112112111211112112552i2111121211227111111211112i121212122212;211211 ..........

i ............

? ...........

i

...........

21221i221122212111; ) ............

?

...........

) ...........

....

2111221:

- ............

g lO-1 ~ 1 0 -=

~ 1 0 -~

10"

0

Figure 7.32

10

20

30

40

Frequency (Hz)

50

60

70

80

Maximum limit-cycle amplitude at error signal - 2* nominal model, - I dBfilters

Production of such an envelope in the case of the nominal model is purely an academic exercise. In reality, provided that the system gain is as modelled, then the - 1 dB filters will prevent limit cycling. Production of the maximumamplitude envelope for the nominal model does allow the effect of modelling errors to be quickly assessed, however. Suppose for example that the open-loop gain of the system was in e r r o r by a factor of two. From Figure 7.31, the amplitude of any possible limit cycle can easily be obtained. The resulting amplitude envelope is as shown in Figure 7.32. Although the system model is in error to such a degree, it is still only possible for limit cycles to occur where the open-loop gain of the system exceeds 0 dB. The open-loop gain response of such a system is as shown in Figure 7.33 where it is possible to identify those frequencies at which a limit cycle may occur as those at which the open-loop gain is greater than 0 dB. Incorporating these results on to the specification of the maximum limit-cycle amplitude results in a prediction of the possible limit-cycle frequencies and amplitudes when the system gain is twice that of the nominal model. Such a prediction is shown in Figure 7.34. It can be seen, therefore, that it is possible to predict both the frequency and amplitude of limit cycles which may exist within the system given a particular level of error in the modelling of the system. In this case, this e r r o r was chosen as being a twofold increase in the open-loop gain o f the structural modes. It is important to be able to assess the effect, if any, of such limit-cycling

Aeroservoelasticity lO

,

o --lo

!

20

_~I

i . . . . .

!

.

cycles may ~cur.(i

1

i

-. ........ i....

~

i

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.....

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'o

-5%

Figure 7.33

i

-i ......

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283

20

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.

.

.

.

40

30

.

.

.

.

.

50

.

.

.

.

60

.

.

.

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70

.

80

Frequency (Hz)

Maximum open-loop gain for system with 2* nominal gain and - 1 dB filters in place

10 °

:::::::::::::::::::::::::::::::::::::::::::::an:::::::::::::::::::::::: ,o-' ...... i ............ i............ tiossiblelimit;ey61es::(*) ...... :.............

1

~

10 -2

} ~

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........................

1

0-40

Figure 7.34

10 ~

). . . . . . . . . . . . .

i 20

............

i 30

i. . . . . . . . . . . .

; ............

i i 40 50 Frequency (Hz)

i ............

i 60

i. . . . . . . . . . . .

i 70

80

Predicted limit-cycle frequencies and amplitudes for system with 2* nominal gain and - 1 dB filters

284


conditions on the satisfactory rigid-body control of the aircraft. If it can be shown that satisfactory rigid-body control is maintained, then the - 1 dB filters can be applied as designed. In this way, the condition where the system model is significantly in error can be explored and the safety of the system ensured.

7. 4.2 Active control for rigid body and structural-mode stabilisation As was explained earlier in this chapter, fundamental interaction exists between the rigid-body FCS, unsteady aerodynamics and the airframe structural dynamics through the FCS motion sensors, control laws and aerodynamic control surfaces. This aeroservoelastic phenomenon presents the possibility for closed-loop instability, which is traditionally prevented by incorporating notch filters into the FCS; forming a passive structural-mode control system. This passive approach attenuates the modal feedback contribution of the control-surface actuation demands, but of course the additional FCS filters can be expected to degrade rigid-body stability through the phase lag introduced. Although this approach continues to be applied successfully, increasing difficulty and cost is now encountered with the trend in modern aircraft designs towards higher instability, higher FCS gains and more complex weapon systems. One alternative solution is to extend the use of the existing aerodynamic control surfaces to suppress the structural vibration, forming an active structural mode control. A recent study [17] has investigated the use of an asymptotic pseudoderivative feedback (PDF) structure for simultaneous control of the rigid-body dynamics and the structural vibration. In single-input single-output (SISO) PDF control [Phelan 26], a pseudoderivative term replaces the erroractuated proportional action of the well-known proportional-plus-integral (P+I) structure, leaving only integral action in the forward path. Through analysis and comparative studies with P+I control, Phelan demonstrated that PDF control reduces the peak demands to the actuating elements driving the plant, and is more readily conditioned in the event of nonlinear saturations. Multi-input, multi-output (MIMO) generalisations of the SISO PDF philosophy have been developed based on robust inverse dynamics estimate (RIDE) inner-loop compensation [26]. However, RIDE control has been shown to be incompatible with the active structural-vibration control system, leading to the development of asymptotic PDF [17] to provide an intuitive and multivariable design procedure which satisfies a demanding set of criteria for both the rigid-body and the structural modes.

7. 4.2.1 The agile combat aircraft (A CA)--case study design criteria The case study presented to illustrate the effectiveness of the controller design procedure is an open-loop unstable, generic agile combat aircraft (ACA), typical of the developing structural-control problem. The ACA is a canard--delta configuration with trailing-edge inboard and outboard elevons

Aeroservoelasticity 285 and with fuselage-mounted foreplanes for symmetric axis control. A set of design criteria in the time and frequency domains for simultaneous rigid-body and active structural-vibration control was proposed together with established requirements for rigid-body stability and handling qualities [27] and conservative aeroelastic stability margins [10]. These are: (i)

Rigid-body stability is assessed against a 6 dB/35 ° exclusion boundary on a Nichols plot. (ii) A pitch-rate command be tracked to produce an integrating pitchattitude response [27] in the time domain. (iii) Manoeuvre trimming must be achieved through the inboard and outboard flaps only. In order to reduce trim drag at the chosen flight condition, the steady-state foreplane deflection should be zero. The performance of the active-control strategy is to be measured by the increase in structural damping to reduce airframe fatigue [28,29]. The Nichols stability criterion is extended to the controlled structural modes, and the conventional aeroelastic gain margin applies for frequencies beyond these modes.

7. 4.2. 2 Plant and control law description Without loss of generality, if the open-loop plant dynamics and input, output and extra measurement vectors can always be decomposed into the set of firstorder modes [30] respectively:

Jc2(t) x3(t)

=

A21 A2z A23 LA31 A32 A33

y(t)=[C 1 0

C3][xl(t )

/x2(t)/ + Lx3(t)J

x2(t )

m(t) = [M 1 M 2 M3] [il (t)

u(t) B3

x3(t)] T

i2(/)

(7.36)

x3(/) ] T

(7.37)

(7.38)

and w(t)=[F l

F 2 F3][x](t)

x2(t)

x3(t)] T

(7.39)

where xa(t ) E~m, x2(t ) E~n-2m, X3(/) E~m, A22E~f~(n-2m)×(n-Zm), A23E~)](n-2m)×m' A31Eg] raxm,

A21E£(~(n-2m) xm, A 32 ~)~m×(n-2m), A33~f~m×m, B3E~ m×m, rank B~=m (i.e. invertible), C l e ~ m×'~, C 3 E ~ mXm M 1 E ~ mxm, Mz~)~mx(n-2m), M 3 ~ mxm, F1E~f~mxm, F2~)~mx(n-2m), F3E,~f~mXm, u ( t ) E~'~ m is the input vector, y(t) e,~ m is the output vector, m(t) E~f~m is the extra-measurement vector, w(t)E~)~ m is the feedback vector and rank F~B~= m. Defining the asymptotic PDF control law as: u(t) = g(Ki.ze(t ) -Kpw(t)) +K~(t)

(7.40)

where ge ~ +, K i e ~m× m, Kp E ~m× m, and with the feed-forward term defined

286


by,

[.f1(t)l = [ O I m ][f,(t)]+[O ] v(t) [f2(t)_ ] &2 -2(I)l-I [_f2(t)J ~-~2

(7.41)

f(t) = [Im 0m][fl(t )

(7.42)

fz(t)] T

and introducing the extra integral-of-error action state relationship: Ze(t) =v(t) -w(t)

(7.43)

Furthermore, if the vector of extra plant measurements, re(t), is arranged such that:

[M1 M2 M3] =

R[ 0 0 Im] A21 A22 A2~

(7.44)

where R+ [diag~rl, r2. . . . . rm} Om×(n_2m)

(7.45)

then it follows from eqns 7.37 to 7.38 and eqn 7.44 that: [F l F 2 F3]=[C 1 0

(C~+diag~rlr2. . . . .

rm})]

(7.46)

Moreover, using eqn 7.36 under the necessary and sufficient condition that the closed-loop system is stable such that the steady-state relationship:

lirn

0 0 Im / x2(t) A21 A22 A2~ mxs(t)

=

(7.47)

is approached asymptotically, then from eqns 7.38, 7.44 and 7.47 it is clear that the extra measurements satisfy the necessary condition: lim (w(t)) = lim (y(t) +re(t)) =y(t)

(7.48)

and combining eqns 7.43 and 7.48, steady-state tracking in the sense of: lim (v(t) -y(t)) = 0

t~

(7.49)

will be satisfied using the control law governed by eqn 7.40. 7. 4.2.3 Asymptotic analysis of the closed-loop system

The set of closed-loop equations obtained by combining eqns 7.36 to 7.43 is not in a block-diagonal form. Thus decoupling of the multivariable system,

Aeroservoelasticity 287 required for the general control problem, would not be achieved and it would be difficult to generalise the characteristics of the system. Neglecting the feedforward term's contribution in eqn 7.40 to the closed-loop eigenvalues, the closed-loop system can be partitioned into distinct infinite and finite eigenvalue sets being amenable to fast and slow-mode block diagonalisation [31]. Thus, as the scalar gain parameter, g, tends to infinity and neglecting higher-order terms, the asymptotic closed-loop structure assumes the blockdiagonal form: I

[7"n~(/) ] Lz.i(t )

=

- Kp 1Ki F 3 1 g ; 1gi A23F~-.1K-1Ki 0

0

0

~

0

- F~-IF1 0 I 0 A21-A23F~_lF1 A22- _.l _ _ 0_ _ 0

0

O0

_

* - gB 3KpF~

(7.50)

v(t)

[Z,f(t)

- F~- 1Kp 1Ki

and,

y(t) = [CaF~-~Kp1Ki

C I-CaF~-IF,

0 C a]

Z,,] kzvJ

(7.51)

where the closed-loop states, Zn, and Z n . are associated with the asymptotic slow and fast modes respectively [17,31]~ It is immediately obvious from eqn 7.50 that the set of slow modes, Pl, is given by Pl = Zl U z2 U z3 , where:

Z1 = {Se C: SIm+Ki~ 1Ki=0 }

(7.52)

7.2 = {SE C: sI m+ F 31F 1=0}

(7.53)

z3 ={sE C: sI,_2m-A22 = 0}

(7.54)

and,

together with the set of 'fast' modes, P2, given by P2 = z4, where:

Z4 = {$E C: slm+ gB3KpF s = 0}

(7.55)

It should be apparent from the above system definitions that the closed-loop poles, z2, will always be stable and decoupled and the poles z~ will approach the set of transmission zeros relating the control input vector, u(t), to plant output, y(t). Thus, stability of the asymptotic closed-loop system is guaranteed if Pl U P2 C C-, where C- represents the open left-half complex plane, and provided that the open-loop plant is minimum phase. Therefore, using eqns 7.52 and 7.55, closed-loop stability and non-interacting multivariable control

288


can be arranged by defining: Kp = (F~B3)- 1 •

(7.56)

Ki=Kp~

(7.57)

where = diag~o-1, O-2. . . . .

O'm}, O - i ~ +

(7.58)

= diagtpl, P2. . . . .

Pm}, Pi ~'~+

(7.59)

The feedback gain definitions given by eqns 7.56 and 7.57 are in agreement with previous decoupling methodologies [33], high-gain control [33-35] and RIDE control [26], each of which established the conditions for excellent command tracking and disturbance rejection. The separation of the fast and slow modes as g--* ~, and the resultant blockdiagonal structure of eqns 7.50 and 7.51, gives rise to the asymptotic transfer function described by: (7.60)

FT(S ) = Fn~(S ) + Fn/(s )

where, Fns(S) = C3F~- 1Kp- 1Ki(sI m+ Kp- lKi) - 1 + (C 1 - C~F3-1F1) (sI," + F~-1Fl) -1F~-lKp- 1Ki-(sI m+ Kp- lKi.) -1 (7.61) and Fnf(S) = _ C3F31 ($I," + gF3m3gp)- 1Kp- 1Ki.

(7.62)

It is of some significance that the slow modes corresponding to z~ become asymptotically unobservable and uncontrollable and consequently do not appear in the tracking modes, eqns 7.61 and 7.62). Moreover, as g--* o0, the fast modes become increasingly negligible and eqns 7.60, will approach the asymptotic form: FT(S) -----F~ (s),

as g---, oo

(7.63)

7. 4.2. 4 Deterministic controller parameter selection

Previous work [36] has highlighted the link between singular perturbation analysis of high-gain control systems and the sliding modes of variable structure control [37] (VSC). A review of this work and other literature [38] has recently been done to emphasise the role of the equivalent control [39] with application to multivariable servomechanisms including integral-of-error action. It can be shown that for a controllable state-space plant governed by eqn 7.35 and defining m regulating switching planes: s(t) = [S 1 S 2 S3] [Xl (t)

x2(t )

x3(t) ] T

(7.64)

where S 1~ fil m× m, $2 ~ film× (n- 2,.) and S~ ~ ,q~,. m, then from the sliding-mode

Aeroservoelasticity

289

condition, s(t).~(t)~<0, in the neighbourhood of the switching plane, si(t) = si(t) = 0 i={1, 2 . . . . . m}, the equivalent control, maintaining the sliding mode, is given by: Ueq(t ) = -- (S3B3) - 1{(S2A21 + S3A~l)Xl(t) + (S2A22 + S 3 A 3 2 ) x 2 ( / )

+ (S 1 + SzA23 + S3A3~)x3(t)}

(7.65)

and the sliding mode is described by: 0

0

Im

-1

(7.66)

That is, the poles of the sliding mode of the switching regulator given by eqn 7.64 are the transmission zeros of the system matrix formed by the triple (A, B, S). The sliding-mode condition can be extended to asymptotic PDF by inspection of the high-gain control law. It follows from eqns 7.40 and 7.43, and assuming that the feedback and tracking conditions, eqns 7.48 and 7.49), are satisfied, that since the slow mode, eqn 7.51, of the asymptotic PDF controller is the same as the sliding mode, eqn 7.66, the steady-state control input vector is:

u ( t ) t _ = = gK: i f0 = ( v ( t ) - y ( t ) ) d t - gK:vv(t)+ K:vv(t) =ueq(t) t_~

(7.67)

Unfortunately, it is not possible to determine the infinite horizon solution to the equivalent control in eqns 7.65 and 7.67. However, neglecting this contribution, the pitch-attitude tracking criterion is satisfied by estimating the decoupling feedforward compensation with: ~[:v = g(FsB3) - 1~,

(7.68)

where, additionally, the feedforward natural frequency and damping diagonal tuning matrices are given by [18]: 1)= diagttol, oJ2. . . . . .

win}, w i ~

+

(7.69)

and = diag{~l, ~2. . . . . .

%},

~i E ~ +

(7.70)

Consequently, from eqns 7.67 and 7.68 the integrator state will estimate the ideal equivalent control and the pitch-attitude error is given by: 0~ v(t) - y(t) dt= g - IK: i- l U e q ( t ) t= ~ which will become increasingly negligible as g--.00.

(7.71)

290


7. 4.2.5 Aeroelastic-model description It is well known that airframe structural dynamics and unsteady aerodynamic effects can be represented in the form of the flutter equation: .~l(t) + (1) + o'Vl])~l(t ) + (E + o-VZC)q(t) = Fu(t)

(7.72)

and, defining the output measurements as a function of the rates and displacements of state variables: y(/) = 1VII~I(t) + l~I2q(t)

(7.73)

where q(t) ~ ~n is the generalised structural mode and rigid-body state vector, u(t) E ~f~mis the vector of control-surface rotations, o-is the relative air density (P/Psl), Vr is the true air speed in ms- l, ii, ~ ~ " × ", I) ~ ,9l"×" and E ~ ~R"×" are the structural inertia, damping and stiffness matrices respectively, B~,~n×" and C~9~ "×n are the aerodynamic damping and stiffness matrices respectively, F~92 "×m is the input matrix, and 1~11~,~m×, and lVI2~,~m×n are the output matrices. Elementary matrix algebra converts eqns 7.72 and 7.73 into the state-space form of eqns 7.36 and 7.37 where it can be arranged that the kinematic relationship of the plant dynamics results in x~(t) representing displacements only and x3(t) representing rate of displacements only. It is appropriate to select the structural rates of displacement for feedback control to increase the structural damping. Consequently, first-order asymptotic behaviour is produced from the rates-only rigid-body and structural-mode outputs, and this gives the freedom to dispense with the extra measurements. Under these conditions, and combining the controller definitions, eqns 7.56 to 7.59, the asymptotic decoupled tracking transfer function becomes:

(7.74)

7. 4.2. 6 Controller parameter tuning effects It has been found that the most intuitive procedure for selecting appropriate tuning parameters o"i, Pi, tzi, wi and ¢i(i= 1, 2 . . . . . m) to match a reference rigid-body response of a closed-loop system with dominant eigenvalues is given by the third-order set: Pl = - xl

(7.75)

P2 -- - x2 +-jy2

and to satisfy the active structural vibration requirements with physically realisable control-surface demands requires consideration of the following: (i)

The closed-loop fast modes do not appear in the asymptotic tracking

A eroservoelasticity 291 transfer function, but must be defined to be sufficiently separated from the slow modes to satisfy the conditions for block diagonalisation. However, high bandwidth fast modes cause significant excitation of the structural dynamics and result in large transient decoupling controlsurface demands. Furthermore, a comparison with variable structure control revealed that a high bandwidth fast mode regulator will 'rapidly estimate' [36] the decoupling equivalent control vector, which will cause violations of the high frequency margin. (ii) The closed-loop slow modes form the basis of the asymptotic transfer function and it is appropriate to define the rigid-body slow mode according to the desired closed-loop pole, Pl, in eqn 7.75. The damping design criterion for the structural modes will be satisfied for any firstorder asymptotic closed-loop controlled mode and this introduces the freedom to select the structural slow modes. However, it should be noted that the integrator state, eqn 7.71, will apply equally to the structural integral-of-demand and for the rigid-body term for which it was derived. Since the structural rate commands are always identically zero, it follows that under relatively high integral gain conditions the structural displacements will be constrained. This can be considered as effectively controlling the structural stiffness, or decoupling from rigid-body manoeuvres, and is known to produce large control-surface demands. (iii) The feed-forward compensation has been included to satisfy the integrating pitch-attitude design criterion, and to shape the closed-loop rigid-body transient response. Accordingly, the feed-forward steady-state gain is defined by eqn 7.68, together with the diagonal second-order dynamics defined to match the dominant complex poles, P2, in eqn 7.75. Note that the structural feed-forward terms are not required because no corresponding tracking commands exist.

7. 4.2. 7 Dual rigid-body and structural-mode control Previous results for multivariable asymptotic PDF active structural-mode control applied to the model highlighted features which are incompatible with the current design assumptions and criteria: (i) Large increases in the control-surfaces rate and position demands were required compared to the passive structural-mode control and, more significantly, inappropriate steady-state control-surface trimming deflections. (ii) Unacceptable high frequency loop gains were computed causing severe violations in the high frequency gain margin. The increased control-surface demands and the high frequency aeroelastic gain-margin violations are a direct consequence of high-bandwidth fast modes providing rapid estimation of the multivariable decoupling equivalent control vector. More generally, the complete elimination of static structural deflec-

292


+. I1,,+ l vr(t)]j,~Yr

Yr

~

,21 - 1_2_1

~

l g Kir ~f~)~l ,

X

[X

plant

Ix(t)

,,B

demand

~

- O/B flap) demand

I

demand Iyr(t) =iF,Pflap,

wr(t)~ Figure 7.35 Dual rigid-body and structural-mode control asymptotic PDF FCS block diagram tion, caused by high g manoeuvring, can be regarded as effectively increased structural stiffness through the aerodynamic control surfaces; requiring unacceptable control-surface deflections for manoeuvre trim. Thus, active control of structural stiffness is not a practical objective of the control system considered here; perfect decoupling of the rigid-body manoeuvre loads from the structural response should not be attempted using multivariable controlsurface demands. It should be noted, however, that for improved ride comfort and handling qualities, it remains desirable to sufficiently decouple the rigidbody response from the structural response. Decoupling of the rigid-body response from the structural response can be controlled by the addition of two independent PDF control systems, rather than full multivariable control, utilising the rigid-body and structural-mode frequency separation to minimise the cross-coupling effects of the superposition. A block diagram of the dual controller structure is shown in Figure 7.35 where the subscripts s or r correspond to structural or rigid-body elements, respectively. Both sections of the dual PDF FCS are described by the previous theoretical derivations, and a complete set of controller tuning parameters is defined by the rigid-body scalar quantities, gr, ~Z, "~ ~r and dOr, the structural scalar gain, gs, and the structural m× m matrix quantities, ~s and The dual-control system can give rise to conflicting or dominating controlsurface demands from either the rigid-body or structural-mode components

Aeroservoelasticity 293 o f the superposition. In the extremes, the former would yield good tracking and decoupling of the rigid-body modes at the expense of ineffective structural control, and the latter would r e n d e r improved structural control at the expense of rejecting the pilot's commands. In combination with the earlier requirement to limit structural-mode decoupling, the structural controller gains are strictly limited, thus preventing the formation of the asymptotic controller structure and ensuring that the asymptotic estimation of the structural equivalent-control vector is not achieved. The multiple control surfaces in the aircraft and the dual structure of the FCS shown in Figure 7.35 allow for the simultaneous control, but not decoupling, of three rigid-body and three structural modes. Since only one rigid-body manoeuvre axis is d e m a n d e d at the flight condition considered, it is necessary to gear that feedback signal to the three available aircraft control surfaces. In this example, unity gearing has been selected for simplicity. For the general case, selection of the gearing ratio can be made with regard to the control-surface authorities and the effect on the system transmission zeros. Therefore, the rigid-body output is defined as:

yr(t) = 0(t)

(7.76)

To form a square system, that is one with the same n u m b e r of inputs as outputs, three actively controlled structural modes should be chosen. Practical considerations for the selection of structural-mode measurements [ 17] concluded that only the lower-frequency structural modes are amenable to active control. However, the first three structural modes form a nonm i n i m u m phase system and are thus not compatible with asymptotic PDF control. Excellent multivariable decoupling can be achieved through the controller feedback definition for the first two structural modes augmented with the rigid-body tracking mode. Therefore, it is appropriate to this definition for the structural element of the dual-control system to facilitate the decoupling of the structural motion from the rigid-body response. It follows that the augmented structural output vector is defined as: ys(t) =

[WBI(t)

FuBl(t)

0(t)]

(7.77)

When using the combined structural mode and rigid-body feedback vector it is necessary to define zero values for the elements of the tuning parameters, E s and Es, corresponding to the output for the rigid-body dynamics in order to minimise the impact of the structural control loops on the established rigid-body stabilising function. Thus, assuming that the rigid-body m o d e has been augmented in place of the j t h (j~< m) structural feedback loop, then it is apparent from eqns 7.55 to 7.58, that the jth column of the structuralcontroller gains, Kp~ and Ka, will become null; control-surface demands will not originate from the augmented rigid-body feedback. Consequently, since the augmented rigid-body feedback will not affect the control-surface demands it can be substituted with foreplane deflection feedback to satisfy the control surface trimming requirement described in Section 7.4.2.1, but

294


without changing the structural-gains definition using eqn 7.77. Therefore, assuming that the foreplane is the ith (i~< m) plant input, control-surface trimming is achieved by directly assigning positive, non-zero values to Kps(i, ]) and I~(i, ]). This will now be demonstrated.

7. 4.2. 8 Initial controller parameters and tuning At the chosen flight condition, the closed-loop rigid-body poles of the passive notch-filter structural-mode control system are known to be: Pl = - 2.71 Pz = - 4.1441 +j6.5980, (9= 0.53, w, = 2rrx 1.24)

(7.78)

Taking into account the design considerations of Sections 7.4.2.6 and 7.4.2.7 above, it follows directly that the initial rigid-body controller tuning parameters are: gr= 100.0,

Zr=l.0,

l)r=2~'X 1.24,

~r =2.71

0r=0.53

(7.79)

Through the previous intuitive controller-tuning mechanisms (Section 7.4.2.6) and examination of the resultant closed-loop structure, it was possible to define the tuning parameters for the structural damping to completely remove the lightly-damped structural oscillations; with only the required low frequency coupling from the rigid-body manoeuvre remaining. The final structural-tuning parameters, limited by considerations for the high frequency gain margin, were obtained as:

gs = 1.0, Z s = diag~60.O, 50.0, 0} ~s = diag~O.O01, 0.001, 0}

(7.80)

With the addition of the foreplane control-surface trimming feedback, the final rigid-body and structural-controller gains are: l I~r = 0.048, I~,s = 10- ix

5.93 9.36 -5.64

Kir=0"090'I~=10-5x / 9.36 L-5"64

- 2.20 -4.40 -52.0

-4.40 -52.0

0 0 0.5

0 10.0

(7.81)

(7.82)

it should be noted that the structural-stiffness parameters, ~ , are strictly limited in accordance with the above design guidelines.

7. 4.2. 9 Transient response analysis The rigid-body and structural-mode transient responses with the final tuned parameters are shown in Figure 7.36. These results demonstrate that not only

Aeroservoelasticity

295

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has a deterministic procedure been established to match the desired closedloop rigid-body eigenvalues, but that this also tracks the demanded pitch-rate response. It is of some importance that the rigid-body response for relatively small scalar gains, gr, is indistinguishable from the fully asymptotic results, illustrating that the PDF fast mode rapidly becomes insignificant and that the tracking transfer function is dominated by the slow mode, as given by eqn 7.63. It can also be stated that the addition of the structural feedback has not degraded the rigid-body tracking response, and that the frequency separation of the combined structural and rigid-body controllers remains sufficient given an appropriate selection of tuning parameters. The effectiveness of the active structural control is visible from a comparison with the results for passive notch filtering, included in Figure 7.36. Although an increase in the closed-loop performance for the second structural mode, FuB1, is achieved, the results for the first structural mode, WB1, are more significant [26,27]. In comparison with the reference WB1 response, there is a 33% reduction in the positive peak amplitude, and 28% for the negative peak. More importantly, the modal damping is increased from 2.1% to 44.9%, which could lead to significantly reduced airframe fatigue. The linear control-surface demands for the tuned system are shown in Figure 7.37, together with the corresponding results for passive notch filtering. The importance of restricting active control of the structural


296

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Figure 7.37 Linear control-surfacedemands stiffness is proven in Figure 7.37, showing that the steady-state control-surface deflections are identical to the reference results, including a zero deflection for the foreplane for manoeuvre trimming.

7. 4.2.10 Stability-margin analysis Using the separated low and high frequency regions for stability analysis [17] the low frequency gain-phase margins, calculated at YrYr (Figure 7.35), are shown in Figure 7.38, and the high frequency gain-only margins, calculated at point XX, are shown in Figure 7.39. One consequence of the relatively small scalar gain, gr, is that the low frequency margins deviate from the ideal asymptotic first-order frequency response but, clearly, generous margins are nevertheless produced. The influence of the nonasymptotic high frequency structural modes on the low frequency stability margins is not considered to be significant since the more conservative high frequency stability criterion ensures that the exclusion boundary is not approached. The high frequency margins satisfy the requirement for dBs of attenuation at all frequencies. This demonstrates that the high-bandwidth equivalent control is not estimated as a result of sensible (i.e. do not use high structural-tuning gains) limitations on the controller tuning parameters. The minimum gain margins at approximately 15 and 57 Hz were tuned using a combination of the rigid-body scalar gain and the structural parameters, and ultimately determined the

Aeroservoelasticity 297 41D

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Figure 7.39 High frequency stability margins

structural damping. Further improvements in the structural damping would require higher gains, but these values would lead to a violation of the gain margins at high frequencies.

7. 4.2.11 Summary Singular perturbation and block diagonalisation analysis of a multivariable generalisation of the pseudoderivative feedback control system design methodology has been performed and applied to the task of simultaneous rigid-body and structural-mode control. It has been shown under the conditions of negligible actuation dynamics, for a certain class of open-loop plant dynamics, that asymptotic closed-loop stability is guaranteed even in the presence of closely coupled structural modes. The asymptotic PDF structure has been used to define decoupling controller-gain matrices, and a deterministic means for controller definition with intuitive tuning mechanisms has been developed to satisfy a pr/or/design criteria. Increases in structural mode-damping have been demonstrated through an application to the agile combat aircraft, with acceptable practical values for control-surface demands and satisfing the high frequency stability margins. However, the effects of the active control strategy on other aircraft systems, for example, actuator fatigue, have not been investigated.

7. 4.3 Flexible aircraft modelling The strong relationship between angle-of-attack and modal response has been demonstrated in flight on both the experimental aircraft programme and Eurofighter 2000, and a link between the rigid and the flexible control-power

298


effects has been proposed in explanation. Although theoretical and wind tunnel studies have been carried out on the variation of the overall unsteady forces with incidence [19,20], this needs to be extended to examine the control-power terms which are of particular interest in the structural coupling problem. Experimental work at Bath University [21], sponsored by British Aerospace, has focused on reproducing the steady and unsteady effects observed in wind tunnel tests for the experimental aircraft programme, and the identifying features of the flow field which are responsible. On the basis of this data, further work will aim first of all to confirm the link between steady and unsteady control-power variation with incidence and, further, to understand its basis, so that steady data, which will inevitably be available from the early stages of a project, can be interpreted for SC analysis. The eventual goal is to achieve a structural-coupling clearance process which does not involve flight testing. The perceived inadequacy of current modelling and model-matching techniques has been shown to be a major influence on the SC design and clearance methodology. The ideal model will be able to reproduce actual modal frequency-response characteristics for all the modes of interest and for all the combinations of excitation and response. Approaching this ideal will require advances in modelling, particularly for the fuselage, in understanding what influence effects local to the sensors have on overall SC characteristics, and in understanding how actual and test-measured characteristics compare. Achievement of these advances will require still greater integration of structural and FCS (SC) design teams, motivated by the broader implications of the phase stabilisation and the further developments in structural coupling which were noted above.

7.5 Conclusions This chapter has demonstrated the interdependencies from aerodynamic configuration design, through the characteristics of the flight control system to the magnitude of the structural-coupling problem together with the methodology employed, emphasising how the need for closer integration of engineering design teams in each area for successful achievement of overall programme objectives has developed in parallel with more demanding applications of active-control technology. Adoption of phase stabilisation has been described as a major development in the design and clearance process for structural coupling as applied to EF2000, but the associated costs, in terms of additional and more exacting analysis, the requirement for additional flight test measurements and the implications for other, perhaps previously only loosely-related disciplines, have been shown to be high. Finally, an overview has been given of ongoing development work which includes examination of some of the fundamental issues, with the aim of reversing the trend of increasing costs.

Aeroservoelasticity

299

7.6 References [1] WEYMEYER, W.K, and SPORING, R.W.: 'An industry survey on aeroelastic control system instabilities in aerospace vehicles.' 1AS paper. 62-47, January 1962 [2] HOFMANN, L.G, and KEZER, A.: 'Simplified analysis of flexible booster FCS.' MITE-1210,June 1962 [3] 'Notes on some problems of high speed aircraft programmes.' Royal Aircraft Establishment TMIAP-649, March 1957 [4] FELT, L.R., HUTTSELL, L.J., NOLL, T.E, and COOLEY, D.E.: 'Aeroservoelastic encounters',J. Air~,July 1979, 16, (7), article 78-1289 [5] NORRIS, G.: 'Amraam block placed on Lockheed F-16s.'Flight International, 20 October 1993 [6] KEHOE, M.W., LAURIE, E.J., and BJARKE, L.J.: 'An inflight interaction of the X29A canard and FCS.'AIAA-90-1240-CP, 1990 [7] THOMPSON, M.O.: 'At The Edge of S p a c e - - T h e X-15 Flight Programme.' Airlife, 1990 [8] EVANS, G.J., and BEELE, B.J.: 'Auto aeroelastic mode coupling, a comparison of predicted and actual characteristics.'AGARD FMP S&C, September 1968 [9] TAYLOR, R., PRATT, R.W. and CALDWELL, B.D.: 'The effect of actuator nonlinearities on ASE.'J. Guid. Contr. Dynam, March 1996, 19, (2) [10] FCS--'design installation and test of piloted aircraft, general specification for.' MIL-F-9490D [ 11 ] TRETTER S.A.: 'DiscreteTime Signal Processing.' (john Wiley and Sons, 1976) [12] TAYLOR, R., PRATT, R.W., and CALDWELL, B.D.: 'The effects of sampled signals on the FCS of an agile combat aircraft with a flexible structure.' Proc. American Control conference, Seattle, 1, June 1995, pp. 505-509. Also, Trans. Inst. Meas. Contro~ March 1996.,18, 3, pp. 160-164 [13] NANSON, K.M., and RAMSEY, R.B.: 'The development and use of inflight analysis at B.Ae. Warton.' AGARD FVIP meeting, Lisbon, paper 18, September 1996 [14] YOUNG, P. and PATTON, R.: 'Comparison of test signals for aircraft frequency domain identification.'J. Guid. Contr. Dynam., 1988, 13, (3) [ 15] PRIESTLEY: 'Spectral analysis and time series--Vol. 1.' (Academic, 1981) [16] TAYLOR, R., PRATT, R.W., and CALDWELL, B.D.:. 'An alternative approach to aeroservoelastic design and clearance.' R.Ae.S. conference, on Aeroelasticity and structural dynamics, Manchester, June 1995, pp. 21.1-21.9. Also,/EE Proc. Control Theory Appl., 1996, 143, 1, pp. 1-8 [17] HEEG, J., McGOWAN, A., CRAWLEY, E., and LIN, C.: 'The piezoelectric response tailoring investigation.' Proceedings of. RAeS international forum on Aeroelasticity and structural dynamics, 1,June 1995 [18] FELTON, R.D.: 'Controller design methodologies for rigid body and structural mode control of an agile combat aircraft.' Ph.D. thesis, Lancaster University, 1996 [19] FORSCHING, H.W.: 'Unsteady aerodynamic forces on an oscillating wing at high incidences and flow separation.' AGARD CP 483, paper 7, April 1990 , [20] BECKER, J.: 'Aeroservoelastic stability of aircraft at high incidence. 68th AGARD Fluid dynamics panel specialist meeting, May 1991 [21] PILKINGTON, D.J., and WOOD, N.J.: 'Unsteady aerodynamic effects of trailing edge controls on delta wings.' Aeronaut.J, March 1995, 99, (983), pp. 99-108 [22] NAGRATH, I.J. and GOPAL, M.: 'Control systems engineering', (John Wiley and Sons, 1982) [23] TAYLOR, R., PRATT, R.W., and CALDWELL, B.D.: 'An alternative approach to aeroservoelastic design and clearance', CEAS Aeroelasticity and StructuralDynamics Forum, Manchester, June 1995 [24] TAYLOR, R., PRATt, R.W., and CALDWELL, B.D.: 'The application of actuator performance limits to aeroservoelastic compensation', AIAA-95-1195, AIAA/ ASME/ASCE/AHS/ASC structures, Structural dynamics and materials conference, New Orleans, April 1995 [25] PHELAN, R.M.: 'Automatic control systems'. (Cornell University Press, 1977)

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[26] COUNSELL, J.M.: 'Autopilot Design for Wingless Missiles'. Trans. Inst Meas Control, 1991, 13, (3), pp. 160-168 [27] JORDAN, C.: 'FCS Design Study for an Advanced Combat Aircraft'. BAe (Defence) Ltd. Warton Aerodrome, Preston, Lancashire, PR4 lAX. Report. BAe-WAE-RP-GEN-FCS-000709 [28] BURRIS, P.M. and BENDER M.A.: 'Aircraft load alleviation and mode stabilization (LAMS). B-52 system analysis, synthesis, and design'. Air Force Flight Dynamics Laboratory. Air Force Systems Command., Wright Patterson Air Force Base, Ohio, technical report AFFDL-TR-68--161. November 1969 [29] BENDIXEN, G.E., O'CONNELL, R.F, and SIEGERT, C.D.: Digital Active Control System for Load Alleviation for the Lockheed L-1011'. Rockwell International, Cedar Rapids., AeronauticalJ. Royal Aeronautical Soc., 1981, 85, pp. 430-436 [30] KOKOTOVIC, P.V., O'MALLEY, R.E., and SANNUTI, P.: ~Singular perturbation and order reduction in control theory--an overview.'. Automatica., 1976 12 [31] KOKOTOVIC, P.V.: 'A Riccati equation for block diagonalisation of illconditioned systems' /EFF. Trans. Autom. Control, 1975, Ac20, pp. 812-814 [32] FALB, P.L. and WOLOVICH, W.A.: 'Decoupling the design and synthesis of multivariable control systems.' IF..EETrans. Autom. Contro~1967, AC12,.(6) [33] PORTER, B. and BRADSHAW, A.: 'Design of linear multivariable continuoustime tracking systems incorporating high-gain error-actuated controllers' Int. J. Sys. Sci. pp, 461-469. 1979, 10,.(4.) [34] BURGE, S.E.: 'Design of multi-functional flight controllers for structural load alleviation.' Ph.D. thesis, University of Salford, 1985 [35] HOPPER, D.: 'Active control for VSTOL aircraft.' Ph.D. thesis, Lancaster University, 1990 [36] YOUNG, K.D., KOKOTOVIC, P.V., and UTKIN, V.I.: 'A singular perturbation analysis of high-gain feedback systems'. IbTEE Trans. Autom. Control, 1977 22, pp. 385-400 (931-938). [37] ZINOBER, A.S.I.: 'Deterministic control of uncertain systems' (Peter Pereguens Ltd, 1990) [38] BRADSHAW,A.: 'Report on equivalent control.'. Lancaster University, Lancaster, UK, January 1994 [39] UTKIN, V.I.: 'Equations of the slipping regime in discontinuous systems.' Automation and Remote Control, 1971 32, pp. 1897-1907


Chapter 8

Eigenstrueture assignment applied to the design of an autopilot function for a civil aircraft L.E Faleiro and R.W. Pratt

8.1 Introduction One of the earliest stages in the design of a flight control system (FCS) for a civil aircraft is based on the use of linear aircraft models to produce an initial controller structure. This is because linear models, usually based on small perturbations of the full nonlinear aircraft model at a point in the aircraft flight envelope, are easier and quicker to analyse mathematically. Both traditional single-input single-output (SISO) methods and most m o d e r n methods d e p e n d on this linear-synthesis stage to produce the basis for a controller. For this reason, much effort has been put into developing linearcontrol system design techniques which serve to produce a better controller for these linear aircraft models. It is often found, however, that the resulting controller does not p e r f o r m well when tested in a more realistic aircraft environment, where considerations such as a much wider flight envelope, varying aircraft configuration, system nonlinearities and model uncertainties come into being. The traditional industrial approach to solving this problem is to adjust the controller iteratively until the system is satisfactory. This process results in an e n o r m o u s a m o u n t of time and money being spent on tuning the controller using nonanalytical procedures. Because of the time involved in adjusting the controller in this way, linear synthesis may constitute very little of the total design effort. In the finished software, this is further diluted by the fact that the original linear-model-based control algorithms may constitute as little as five to ten per cent of the whole controller. It follows that it would be advantageous to be able to improve the initial linear synthesis to the point where much less tuning is required during subsequent design stages. This in turn would lead to a quicker and cheaper, and possibly better, design process. Naturally, this would require the development of more flexible and intuitive design tools. Modern methods have attempted to address this by

302


providing two things. First, they make use of the full multi-input multi-output (MIMO) representation of the linear system, thus implicitly accounting for all the interactions between the various states of the aircraft at the same time. Secondly, they attempt to produce controller designs that are robust e n o u g h to withstand the transition to the nonlinear aircraft model without a corresponding loss in performance or stability. However, a major criticism has been that these methods lack a physical insight, and aircraft FCS designers often have difficulties in being able to relate changes in the parameters of the resulting controller to potential changes in the closed-loop aircraft dynamics during the design process. The Group for Aeronautical Research and Technology in Europe (GARTEUR) action group on robust flight control produced a 'Robust flight control design challenge '1, involving the aeronautical industry, research organisations and universities across Europe, which worked towards addressing this deficiency. Eigenstructure assignment (EA) was one of the m o d e r n methods which were used during the challenge, and it showed promise in being able to bridge the gap between theoretical pursuit and physical interpretation. This chapter is a description of the way in which the potential, and the failings, of EA as a robust FCS design m e t h o d were exposed during its application to the robust civil aircraft model (RCAM) problem within this design challenge. The design problem will first be described. The methodology used to solve it through linear synthesis of a controller will be explained briefly, and then demonstrated for the aircraft problem. The resulting controller will be examined using a nonlinear model to show whether or not the m e t h o d was able to provide the necessary results, design speed and insight into aircraft dynamics to be helpful in improving the final controller.

8.2 The RCAM control problem The RCAM is a six-degree-of-freedom nonlinear model of a medium-sized twin jet engine civil transport aircraft with actuator nonlinearities, which is available in Matlab and Simulink. A detailed description of the aircraft and of the control problem can be found in reference [1]. As shown in Table 8.1, it has four inputs, nine states and 21 measured outputs. The nomenclature used in this table will be used throughout this chapter. Software is provided with the model which facilitates the extraction of linear models at specific points in the flight envelope. The designer has to specify aircraft mass, centre-of-gravity location, aircraft altitude and airspeed, and the model is trimmed and linearised at the corresponding flight condition. The linear models so produced are in a state-space format which can be used for subsequent controller design. 1At the time of writing the full RCAMmodel and information on the RCAMdesign challenge were available at the followingwebsite: http://~acw.nlr.nl/public/hosted-sites/garteur/rfc.html

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The desired trajectory of the controlledRCAM

T h e RCAM design challenge was attempted by 12 universities and research organisations, involving the use of nine different methods of linear synthesis. The use of these methods was examined by engineers from the aeronautical industry to evaluate their applicability to realistic flight control problems. The RCAM problem definition itself is based on the design of a flightcontrol system to fulfil a set of design specifications categorised by performance, robustness, safety, ride-quality and control-activity results for standard inputs to the aircraft controller. The purpose of these is to introduce a broad range of requirements for the finished controller.

8. 2.1 A landing-approach simulation The main focus of the controlled aircraft is that it should be able to complete a given landing-approach path m i s s i o n - - t h e controller must therefore be an autopilot. Reference commands based on aircraft geodetic position are generated by a simulation environment which is provided and these commands have to be used by the controller to hold the aircraft on a given trajectory. This desired trajectory for the design challenge is shown in Figure 8.1. More details of this approach simulation are given in Section 8.5. The simulation software provided the designed controller with required commands in the following variables: (i) Longitudinal dynamics--geographical distance from the runway centreline (x and z), airspeed, Va, forward velocity, u, vertical velocity, w. (ii) Lateral dynamics--geographical distance from the runway (y) and from the desired flight path (ylat), lateral velocity, v and heading rate ~0. The approach-path simulation included an engine failure and restart, a 90 ° banking turn and the capture of a glideslope. The designer had to construct a controller so as to make use of as many of these commands as required to provide an aircraft which followed the approach path while retaining the

Eigenstructure assignment to the design of an autopilotfunction

305

1.2

0.9

.................................................

--

i O.6 ~

O.4

0

3'5

r~se ==

4c

Time(s)

time

Figure 8.2 Characteristics of the response to a step command performance, robustness, ride-quality, safety and control-activity specifications described below.

8. 2.2 Performance specifications Performance specifications describe the desired transient response of the controlled aircraft to commands in variables of the aircraft. For the RCAM, these were specified in terms of minimum rise times and m a x i m u m overshoots of the responses to step commands. These characteristics of a response are shown in Figure 8.2 for a unity step command. The RCAM p e r f o r m a n c e specifications can be divided into two sets; those for the longitudinal dynamics and those for the lateral dynamics.

8.2.2.1 Longitudinal dynamics Altitude response--The controller has to track step c o m m a n d s in altitude with a rise time of less than 12 s. Overshoot to such a c o m m a n d should not exceed 5 per cent at an altitude of greater than 305 m (1000 ft). (ii) Airspeed responsewThe controlled system should track step changes in airspeed with a rise time of less than 12 s. There should be less than 5 per cent overshoot to these commands at an altitude of greater than 305 m (1000 ft). In the presence of a longitudinal wind step of 13 m s-~, airspeed should not deviate by more than 2.6 m s - 1 for more than 15 s. (iii) Crosscouplingbetween airspeed and altitude--for a 30 m step c o m m a n d in altitude, deviation in airspeed should be less than 0.5 m s - 1 and for a 13 m s - 1 step c o m m a n d in airspeed, deviation in altitude should be less than 10 m. (iv) Flight-path angle response--flight-path angle response to a step c o m m a n d should be tracked with a rise time of less than five seconds. Overshoot should be limited to less than five per cent at above 305 m (1000 ft).

(i)

306


8. 2.2. 2 Lateral dynamics Lateral-deviation response--the lateral-deviation tracking requirements stipulate that at an altitude of over 305 m (1000 ft), the lateral deviation should reduce to less than ten per cent of its c o m m a n d e d step value or initial disturbance within 30 s. Overshoot to a c o m m a n d should not exceed five per cent. (ii) Roll angle and sideslip during engine failure--the roll-angle specification limits the deviation of roll angle during engine failure in still air to 5 ° with a peak of 10 °. Any steady-state roll angle should be less than 5 ° and on engine restart, roll-angle overshoot should not exceed 50 per cent of this steady-state value. Sideslip should be minimised during engine failure. U n d e r m o d e r a t e turbulence (see reference [1] for a definition of this term) roll angle should remain smaller than 5 ° . (iii) Heading rate--in case of engine failure, heading rate should be limited to 3 deg.s-1.

(i)

8. 2.3 Robustness specifications T h e criteria for robustness are specified as a r e q u i r e m e n t that the system retains sufficient stability (i.e. the system should not b e c o m e unstable) and p e r f o r m a n c e (i.e. the system should respond to c o m m a n d s and disturbances in the same way) over the full aircraft configuration envelope of: • horizontal (15 to 23 per cent of mean aerodynamic chord, MAC) and vertical (0 to 21 per cent of MAC) variations of the aircraft centre of gravity; • aircraft mass variations of 100 to 150 tonnes; • controller time-delay variations of 50 to 100 ms.

8. 2. 4 Ride-quality specifications T h e ride-quality criteria are designed to ensure that the controlled aircraft will provide passenger comfort to an acceptable degree, during n o r m a l manoeuvres. Vertical acceleration should be limited to +_0.05 g and lateral acceleration should be limited to +_0.02 g. Unless otherwise mentioned, there should be no overshoot in c o m m a n d e d variables at an altitude of over 305 m (1000 ft).

8. 2.5 Safety specifications Safety criteria define boundaries which ensure passenger safety t h r o u g h o u t the flight envelope, and they stipulate limitations of: • • • •

51.8 m s - l for m i n i m u m airspeed; 18 ° for m a x i m u m angle-of-attack; 30 ° for m a x i m u m roll angle; minimised sideslip angle at all times;

Eigenstructure assignment to the design of an autopilot function

307

• less root-mean-squared (RMS)intensity to lateral Dryden gusts for closedloop sideslip response than for open-loop response.

8.2. 6 Control-activity specifications Keeping control activity as low as possible is desirable, as it consumes less fuel and leaves m o r e margin of control for the pilot if required. It also reduces wear in the actuators and increases the fatigue life of the structure of any moving c o m p o n e n t s involved. The control-activity specifications stipulate that, u n d e r m o d e r a t e turbulence conditions, m e a n actuation rates: • for the control surfaces should be limited to 33 per cent of their m a x i m u m rates; • for the throttle should be limited to 15 per cent of its m a x i m u m rate.

8.3 E i g e n s t r u c t u r e analysis

and assignment

Eigenstructure assignment (EA) has previously been used to develop flight control systems in theoretical exercises such as an F-16 [2], a VSTOL aircraft [3] and the RCAM itself [4], and has also b e e n i m p l e m e n t e d in the lateral control systems of the NASA high alpha research vehicle [5] and of some Airbus aircraft [6]. T h e somewhat simpler methodology that was used for the RCAM design described in this chapter is primarily c o n c e r n e d with controller design for controllable and observable linear, time-invariant MIMO aircraft systems o f the form: ic=Ax+ Bu

(8.1)

y--Cx

(8.2)

where x~ ~ " is the vector of aircraft states, y~ ~P is the vector of outputs and u ~ 3l" is the vector of inputs.

8.3.1

Eigenstructure analysis

T h e n eigenvalues and eigenvectors of the open-loop aircraft are defined by:

A=

[Al

" " "

'~i " " " An]

and V= [v, • •

•

Yi

" " "

Yn]

where

AV= VA

(8.3)

T h e left, or dual-basis, eigenvectors of the same system are given by W, where

WA= A W and

308


WT= [ W l

• • •

wi

. ..

Wn]

(8.4)

Solving the equations given in (8.1) and (8.2) yields an expression which provides a direct link between the eigenvalues and eigenvectors of the aircraft and its time behaviour:

y( t) = E CuiwTeAitXo+E CUiW i=1 .

e'~(t- ~')Bu( 7")dr

i=1 .

.

w

homogeneous component

.

~

v

(8.5)

forced component

This shows that there are four components in this equation which can affect aircraft dynamic behaviour: (i) (ii) (iii) (iv)

the the the the

eigenvalues of the system, Ai; eigenvectors of the system, v i and wi; initial conditions of the system, x0; inputs to the system, u.

8.3.1.1 Real-time modes of behaviour The index i in eqn 8.5 refers to each of the n dynamic modes of the aircraft. In conventional longitudinal aircraft dynamics, for instance, these are the short-period pitching oscillation (SPPO) mode and the phugoid mode. T h e discussion here will initially be limited to talking about the h o m o g e n e o u s c o m p o n e n t (no effects from an input to the system) of aircraft dynamics. The dynamic behaviour of all systems can be considered as a collection of first-order and second-order modes. Each mode is composed of two elements. The first is one that describes the transient (time-decay and frequency) behaviour of the mode. In classical control engineering, this is the pole of the mode; in eigenstructural terms, this is the eigenvalue of the mode. The second c o m p o n e n t of each mode is a magnitude which it has at any time step; this is the residue of the mode. More specifically, what matters are the relative residues of the modes. These directly influence the prevalence of the modes in each of the states in the state vector, x, and each of the measured outputs in the output vector, y. In classical control engineering, the residue of a m o d e is d e p e n d e n t on two things, the poles and the zeros of the system. In eigenstructure assignment, the residue of each mode is proportionally related to the magnitude of the eigenvector of that mode. Together, the eigenvalues and eigenvectors form the eigenstructure of the system. These concepts can be examined by considering the longitudinal dynamics of a fourth-order linear RCAM model. The eigenstructure o f the modes of this example system is shown in Table 8.2. Each of the modes in the table can be attributed to aircraft dynamic characteristics by an examination of the eigenvalues and the magnitudes of


309

Table 8.2 Eigenstructure of the RCAM longitudinal dynamics Modes: Eigenvalues:

SPPO - 0.83 + 1.11 i

0

F o.o14 q l 0.010

w

L 01999

J

Phugoid - 0.011 ± 0.13i 0.002 0.013 1 0.989 0.142

Table 8.3 Mode-output coupling vectors of the RCAM longitudinal dynamics Modes: Eigenvalues:

SPPO - 0.83 + 1.11 i

Phugoid - 0.011 + O.13i

q

0.014 0.010 0.015 0.999 0.487

0.002 ] 0.013 0.989 0.142 1.026

0 U W WE

the eigenvectors of the system. Taking the phugoid m o d e as an example, analysis of its eigenvalue shows that this m o d e has a d a m p i n g ratio of a b o u t 0.08 and frequency of 0.13 rad s-1. Its column eigenvector shows that, if this m o d e is excited, it will cause a large deviation in forward velocity, u. It will also cause a deviation in vertical velocity, r~ but the peak deviation o f w will only be a b o u t 14 per cent of the value of the peak deviation of u in the same cycle. It can also be d e t e r m i n e d that for every 1 m s - 1 in the peak deviation of u, the peak in 0 will deviate by 0.013 rad in the same cycle. Information can also be gleaned from the magnitudes of the rows along the eigenvectors. For instance, Table 8.2 shows that the time response of forward velocity u has a m u c h larger c o m p o n e n t in the phugoid m o d e (0.989) than of the SPPO (0.015). This means that a perturbation in both aircraft dynamic modes will cause u to describe similar motion to the phugoid mode. Interactions between modes and aircraft outputs can be inspected by using the m o d e - o u t p u t coupling vectors, CE, in exactly the same way as the eigenvectors, V, can be examined to d e t e r m i n e interactions between aircraft modes and aircraft states. Table 8.3 shows a selection of m o d e - o u t p u t coupling vectors for this example aircraft. In this case, the chosen outputs include the four states of the aircraft, and vertical velocity of the aircraft in the

310


Figure

8.3 Basic output feedback regulator configuration

earth axis, wE We can now see that although the SPPO is m u c h m o r e evident in the body-axis vertical velocity w, the phugoid m o d e is d o m i n a n t in wE. Physically, this is because the phugoid m o d e involves changes in 0 and u. w~: is a function of b o t h of these, and, as they alter m o r e than w in p h u g o i d motion, so will wE . So far, the discussion has centred on the h o m o g e n e o u s motion in aircraft dynamics. When the relationship between system inputs and system m o d e s needs to be considered, the input-mode coupling vectors, WB, can be e x a m i n e d in a similar way to the eigenvectors or m o d e - o u t p u t coupling vectors. I n p u t - m o d e coupling is demonstrated later, during controller design, and will not be e x p a n d e d u p o n here. Eigenstructure analysis is thus a tool that can be used to: * examine the nature of the modes of an aircraft; • provide information on the a m o u n t of each dynamic m o d e present in an aircraft state; • provide information on the a m o u n t of each dynamic m o d e present in an aircraft output; • provide information on how an input might affect the dynamic m o d e s of the aircraft. This technique of analysis was invaluable during the RCAM EA design process, as the information obtained was then used to focus on removing any undesirable interaction between aircraft inputs and modes, and between aircraft modes and states/outputs.

8. 3. 2 Eigenstructure assignment A simple output feedback controller K can be used to effect control by altering the inputs of the aircraft system given in eqns 8.1 and 8.2: u = Ky

(8.6)

T h e regulator design that results is shown in Figure 8.3. If c o m m a n d tracking is also required, it is c o m m o n practice with EA to a u g m e n t the aircraft-system matrices with the equations for the outputs which need to be tracked. T h e EA p r o c e d u r e is then followed for the a u g m e n t e d system and, once a controller


311

is designed, it is separated into its tracking and regulation components. Equation 8.5 shows that, given a set of initial conditions and inputs to an aircraft system, the time response of the outputs y(t) can be manipulated by altering the eigenstructure of the system. All that is required to do this is a method of specifying the eigenvalues and eigenvectors of the closed-loop system direcdy. There is sufficient design freedom to allow the assignment of a set of max(m,p) desired eigenvalues to the closed-loop system [7]. For most aircraft, the number of measured outputs, p, exceeds the number of inputs, m. Poleplacement design methods can be used to assign a set of p eigenvalues to the closed-loop aircraft. However, for this set of p completely assigned eigenvalues, EA offers the use of the additional freedom to choose the p closed-loop system eigenvectors which can be assigned. Let these p desired eigenvalues and eigenvectors of the aircraft closed-loop system be defined by:

Ad=[A 1 . . . Ai . . .

Ap] a n d V a = [ v I . . .

vi . . .

vp]

(8.7)

where

(A + BKC) Vd = VdAa

(8.8)

In the following development, the Moore-Penrose pseudoinverse is used instead of the standard matrix inverse where the matrices concerned are not square. When B, C and Va are non-singular, rearranging eqn 8.8 gives:

K= B - l (VaAd- ava) ( CVa) -1

(8.9)

However, we cannot assign arbitrary vectors into the set of desired closed-loop eigenvectors Va in eqn 8.9 that will produce a controller K to satisfy eqn 8.8, as the closed-loop system possesses limited freedom of assignment depending on the desired eigenvalues, A a. Various forms of EA methodology to determine the possible Va given A d exist, ranging from the first tentative steps in output feedback by Kimura [7] to their further development by Andry, Shapiro and Chung [8] to recent work such as that done by Sobel, Lallman and Shapiro [9-11]. All these methods require the control system designer to specify a set of desired eigenvalues (A a) and eigenvectors (Vd) for the closedloop system, and they all produce a proportional gain matrix feedback controller (K) using a mathematical algorithm. The most basic of these algorithms is as follows: From eqn 8.8: (A + BKC) vi = Aiv~

(8.10)

Vi 1 = 0 [ A - A//~ B] KCvi

(8.11)

312


z A

desired vector

achievable vector ,,

,#" X

Y

;pace, defined by ;, describes the )ver which the Je can be realised

%

Figure 8. 4

Diagrammatic rq~resentation of a two-dimensional achievable space in a three-dimensional state-space

And for a nontrivial solution to this equation:

KCv i

(8.]2)

Any combination of the vectors (and only these vectors) in the null space (N) of [A - AI~ B] will provide a vector v i which, when used as an eigenvector, will produce a closed-loop system with the desired eigenvalue Ai. This null space is therefore known as the achievable vector space. This leads to the limitation that only min(m,p) elements at most can be specified in each desired eigenvector and can subsequently be achieved exactly. If m o r e than min(m,p) elements are specified, the ith desired vector v i can be projected onto the achievable space to obtain an achievable eigenvector vai. This is illustrated diagrammatically in Figure 8.4 for one of the modes of a simple threedimensional system. I f a three-dimensional vector v i is desired, as shown in the Figure, it is projected onto the achievable space (Reference [8] shows how this can be done), and the resultant is the nearest achievable vector vai which can be obtained to give the required eigenvalue, Ai. All of the p achievable eigenvectors are then assembled into an eigenvector matrix which can be substituted as the desired eigenvectors Va together with the desired eigenvalues Aa into eqn 8.9 to give a static feedback matrix K f o r the closed-loop system. All that remains is to decide on how to specify a desired eigenstructure in the first place. It is extremely difficult to do this. T h e difficulty does not come from choosing desired eigenvalues, which can be d e t e r m i n e d in the same way as closed-loop system poles are chosen in traditional synthesis methods, but rather in the specification of desired


313

Table 8.4 Example of desired closed-loop vectors

0

x] X

x]

U

0

X

W

X

0

States q

SPPO

Phugoid

X

eigenvectors. These can be defined to reflect different requirements. From the RCAM design specifications, decoupling and robustness were the most i m p o r t a n t of them.

8.3.2.1 Decoupling requirements It has been shown that the eigenvectors can be related to the contribution which each m o d e makes to the state vector, x. Hence, if we want to remove the influence of a m o d e in a state, we can set the corresponding eigenvector e l e m e n t to zero. This can be illustrated by the set of eigenvectors shown in Table 8.4. We would perhaps like to remove the effect of the SPPO m o d e on forward velocity, u. We therefore specify the relevant e l e m e n t in the desired closedloop eigenstructure to be zero. A similar situation occurs with a r e q u i r e m e n t to remove the effect of the phugoid on body-axis vertical velocity, m An extension of the EA algorithm to decouple modes from outputs rather than just states exists [12] but was not used for the RCAM design as mode-state decoupling was sufficient. In relation to how EA can provide a solution to this desired decoupling, examine Figure 8.5. The figure shows the same generic m o d e in a threedimensional system as that in Figure 8.4. However, the r e q u i r e m e n t here is that as well as having the desired closed-loop eigenvalue, we want this m o d e to be decoupled from dimension y. Thus, for this system, the only possible achievable eigenvector is given by the intersection between the achievable vector space (which is the only place where the desired eigenvalue will be produced) and the x-z plane (the locus of points which does not contain any c o m p o n e n t of y). Since the desired eigenvector contains desired decoupling information (i.e. a zero in the dimension y row), it will lie on the x-z plane. Unfortunately, one e l e m e n t of each desired eigenvector must be set to a non-zero value to avoid a null result during vector projection in the mathematical algorithm. As there is only sufficient f r e e d o m available to assign m elements in each of the p desired eigenvectors of an aircraft system, this limitation gives us the f r e e d o m to decouple (i.e. set to zero) only ( m - 1 ) elements in each one. If m o r e than this are specified, a least-squares

314


Z

,.a^~;,~

....

+. . . . . . .

achievable vector 'a/

X

defined by .scrioes tt'ie which the an be realised

%

Figure 8.5

Diagrammatic representation of decoupling in a three-dimensional statespace

projection of the desired vector onto the achievable vector space is used to achieve the best possible fit.

8.3.2. 2 Robustness requirements Although an i m p r o v e m e n t in p e r f o r m a n c e can be p r o d u c e d by the use of this basic EA method, there is no scope to improve the robustness (as defined in Section 8.2.5) of the closedqoop system. Variations in the parameters of the aircraft translate into variations in the A, B and C matrices. These then manifest themselves as changes in the eigenvalues and eigenvectors o f the closed-loop system, hence altering the behaviour of the aircraft. As this alteration is undesirable, the effect of p a r a m e t e r changes on the eigenstructure of the aircraft system should be minimised using a modified eigenstructure technique. T h e m e t h o d of improving robustness that was considered for the RCAM design is based on 'Method 0', as detailed in Kautsky et al. [13]. The objective of the original m e t h o d is to choose desired eigenvectors, vi, such that each one is as orthogonal as possible to the space spanned by the remaining vectors, resulting in minimal interaction between the system modes. In most cases, this leads to an i m p r o v e m e n t in robustness, as the effect of an alteration in an aircraft p a r a m e t e r will only perpetuate through a limited n u m b e r of system modes and will translate into a variation in the transient response of fewer aircraft states. The ability to achieve this can be examined in Figure 8.4. Here, we have a limitless choice of achievable closed-loop eigenvectors from the twodimensional achievable vector space. If, instead of defining a desired eigenvector, we now choose the vector from this space that is as o r t h o g o n a l as possible to the remaining eigenvectors of the system, we can designate this


315

Table 8.5 Degreesoffreedom available with EA (Specified for an aircraft with n states, which conventionally has more outputs (p) than inputs (m); k is the number of specified elements in each desired eigenvector) Number of eigenvalues that can be assigned Number of eigenvectors than can be assigned Number of outputs that can be used in feedback Number of outputs that can be tracked Number of specified elements in each eigenvector than can be assigned exactly Number of specified elements in each eigenvector than can be decoupled Degrees of freedom available for robustness improvement

p p p m m m-1 m - k (k~ < m)

vector as an eigenvector of the closed-loop system v i. The system will have the desired closed-loop eigenvalue, and will at the same time be as robust to parameter variation as possible.

8. 3.2.3 Robustness with decoupling considerations Unfortunately, a focus on solely achieving robustness will usually lead to a loss in performance. What is required is a compromise between achieving robustness and being able to assign vectors to achieve decoupling requirements. In Reference [12], a complete EA methodology to achieve this is described. The method described in Reference [12] obtains an achievable vector space which is preformed based on decoupling requirements. An aircraft system with n states and m inputs has a resulting achievable vector space of dimension (nx ( m - k)), or (nx 1) when k > ~ m, where kis the n u m b e r o f specified elements in each desired eigenvector. 'Method 0' [13] is then used to find system eigenvectors from this vector space which are as orthogonal to each other as possible, thus producing improved system robustness. However, 'Method 0' can only utilise freedom which remains in the system once decoupling has already been performed. A list of the degrees of freedom available with EA is given in Table 8.5. If k is greater than or equal to m, there is no freedom to improve robustness as all the dimensions of the achievable vector space have been used up. In Figure 8.5, for instance, m---2 and k= 1, so there is only one possible location for ui. Nevertheless, this was the methodology that was used to produce a design for the RCAM, as it is the most flexible and provides the best compromise in the achievement of both p e r f o r m a n c e and robustness specifications. Other aspects of EA include parametric eigenstructure assignment [14], [15], polynomial eigenstructure assignment [16], multimodel aircraft applications [17] and the utilisation of the left eigenvectors in synthesis [3], [18].

316


These are currently in less c o m m o n use, and only the simplest f o r m of EA has b e e n developed here for use with the RCAM linear synthesis.

8.4 The eigenstructure assignment design cycle T h e following solution to the RCAM design challenge p r o b l e m has been d o c u m e n t e d in greater detail in Reference [4]; the design specifications have been described in Section 8.2. As part of the overall controller design process, these must be transformed into a controller structure and a controller synthesis. For the RCAM linear synthesis, the nonlinear RCAM model was t r i m m e d at the design point to produce a nominal model which was used t h r o u g h o u t the design process. This design point was taken as the condition on a p p r o a c h with the aircraft in its standard configuration: aircraft airspeed of 80 m s - 1., aircraft altitude of 305 m (1000 ft); aircraft mass of 120 tonnes; aircraft centre of gravity at 23 per cent horizontal MAC and 0 per cent vertical MAC; • flight path angle of 0 ° (level); • still air (no wind effects).

• • • •

8. 4.1 Controller structure An examination o f the RCAM model showed that the longitudinal and lateral dynamics of the aircraft were decoupled. Thus, it was decided that two controllers would be used; one for the longitudinal dynamics and one for the lateral dynamics.

8. 4.1. I Longitudinal controller T h e open-loop seventh-order longitudinal nominal condition are given by: -

/~

0.980

0

0

0

0

0

0

0

0

6.670

0

0

0

-0.016

0

-2.440

1.000

0

0

0

0

0

2.190

-9.780

-0.028

0.074

0

0.180

19.620

u

77.360

-0.770

-0.220

-0.670

0

-6.480

0

w

0

- 79.870

- 0.030

0.990

0

0

0

z

0

0

0

0

0

- 6.670

0

6t

0

0

0

0

0

0

- 0.670

6t,'

0

0.67£

-

-

=

dynamics for RCAM at the

0.5800 ] -q0

+

o o1[:: hl

(8.13) For the sake of simplicity, the actuator dynamics for the tailplane and throttle (6 t and 6th) will be omitted from the following documentation, although the design process itself included them. The eigenstructure of the open-loop


317

Table 8.6 Eigenstructure of the longitudinal open-loop system

Mode Eigenvalue: ~':

SPPO -0.83+ 1.11i 0.600 1.38

Wn:

q0 u w z

Phugoid -0.011 ± 0.13i 0.089 0.13 I 0.001 0.002 0.120 0.017 0.990

I 0.014 0.009 0.014 0.943 0.332

Altitude 0 ---

o] 0 0 0 1

system is shown in Table 8.6. As with most conventional aircraft, the RCAM has SPPO and phugoid modes, but also an additional altitude m o d e which is neutrally stable. This latter m o d e was a result of a u g m e n t i n g the original aircraft linear m o d e l with z as a state. T h e r e are seven output m e a s u r e m e n t s directly available from the longitudinal RCAM model. T h e design specifications describe requirements for an autopilot and, as the modes shown in Table 8.6 are not well d a m p e d , some feedback-based stability augmentation was required, as well as c o m m a n d a u g m e n t a t i o n from the input signals to the actuators. As the advantages of using all the design freedom to improve the control system over classical m e t h o d s of design were being examined, five of the outputs were chosen as feedback signals, as given in eqn 8.14:

nz

0

q

7.880 0 0

-0.078 0 -79.870

-0.023 0.990 -0.028

-0.068 0.029 0.990

0 0 0

0 u w

0

0

0

0

1

z

li]i1°°° ° ° ° J[ VA =

(8.14)

It was chosen to regulate the changes in airspeed, Va, and altitude, z, as these were required to be kept at the trim condition, and the changes in pitch rate, q, vertical acceleration n z, and vertical velocity, w~:, to increase damping. In a classical controller, not all of these would be used, but with EA, they provide us with m o r e design freedom. We can now assign five desired closed-loop eigenvalues and closed-loop eigenvectors. This is sufficient to manipulate the closed-loop system SPPO and phugoid modes and the altitude m o d e successfully. T h e resulting longitudinal controller is depicted in a block diagram in Figure 8.6. T h e r e are two main c o m p o n e n t s to the structure: (i)

Five output feedback signals were used to regulate the aircraft. This is

318

Flight control systems Autopilot commands

St

~th

Longitudinal measurement feedback Trim conditions

Figure 8. 6 Longitudinal controller structure

done by multiplying the perturbations in the output signals by the static gains in the matrix Kton which produced tailplane and throttle signals to return the aircraft to the trim condition. This constitutes proportional control. (ii) The difference between the c o m m a n d reference signals in Va and z and their respective outputs are integrated and fed through a gain matrix, Lun. This compensates for the situation where the aircraft is flying offdesign point to ensure that the error between the reference signal and the output signal is always zero. This is effectively integral control. The structural simplicity of this controller was helpful in pinpointing problems that occurred during the design process. As the entire controller is a set of static gains and two integrators for steady-state error removal, it was easy to examine the gain matrices Kton and Lt0n in order to determine which elements were affecting which output-to-input relationships.

8. 4.1.2 Lateral controller T h e lateral linear open-loop dynamics for the nominal trim condition o f the RCAM are given by: -p-

o

o

r

0

0

0

0

0

0

2.038

o

0

0

0

0

0

0

0

0

- 6.670

0

~a

6.670

0

0

0

0

- 3.330

_ 6%

0

3.33(

0.550

0

0

- 0.024

0

- 0.840

0.052

- 0.520

0

0

0.005

0

-0.018

-0.330

1.000

0.028

0

0

0

0

0

~0

0

1

0

0

0

0

u

2.270

- 79.000

9.790

0

-0.170

flat

0

0

- 2.260

79.870

1.000

6.

0

0

0

0

-r

0

0

0

0

- - 1.270 r

0.290"

v

ylat

0

0

0

0

6,

(8.15) The actuator dynamics for the aileron and r u d d e r (8 a and 6) will be omitted from the following documentation, although the design process itself included them. The eigenstructure of this system is shown in Table 8.7. Again, the modes of the open-loop system are similar in nature to those of most conventional aircraft. As the regulation of lateral deviation, ylat, is a necessary part of the controller, the basic linear model is augmented with the ylat state.


319

Table 8. 7 Eigenvectors of the open-loop lateral dynamics ylat

Mode:

Roll

Spiral

Dutch roll

Heading

Eigenvalue:

- 1.30

- 0.18

- 0.24 + 0 . 6 0 i

0

0

~':

--

--

0.37

--

--

0.64

--

--

0.005

0

0

0.026

0

0

0.008

0

0

O)n:

-

--

-

i0.2]18

0.001

r

[00171ioI [o]

0.015

0.001

0.167

0.004

0.011

0.003

v

0.014

0.047

0.890

0

0

ylat

0.961

0.999

0.455

1

1

~b

~0

This results in the addition of a neutrally stable m o d e called the ylat mode. In the original model, which does not include ylat as a state, ~0is the d o m i n a n t e l e m e n t in the heading mode. However, as seen in Table 8.7, ylat now b e c o m e s the d o m i n a n t e l e m e n t of this mode. As heading is neutrally stable, any perturbation in aircraft motion will result in a heading being attained and this heading being maintained in the steady-state. However, if heading has a non-zero value, ylat will increase to infinity. Thus, the heading m o d e now affects ylat to a m u c h larger extent than it affects heading angle, as ylat now b e c o m e s a linear function of time. Six of the eight outputs available in the lateral dynamics of the RCAM are necessary to i m p l e m e n t sufficient control over the five modes described in the open-loop lateral dynamics; the six that were chosen are shown in eqn 8.16. For the autopilot function, it was necessary to regulate changes in heading rate ~/, and lateral displacement ylat. Hence, roll angle 4, (which is directly related to heading rate, an unavailable signal) and ylatwere chosen as two o f the feedback signals. Sideslip angle fl roll rate p, yaw rate r and track angle X were chosen as feedback signals in order to improve regulation during an engine failure.

P r

4, X ylat

0 1.000 0 0 0 0

0

0

0

0.013

0

P

0 1.000

0 0

0 0

0 0

0 0

r

4,

0 0 0

1.000 -0.028 0

0 1.000 0

0 0.013 0

0 0 1.OOC

ylat

(8.16)

As with the longitudinal controller, the errors between the two c o m m a n d signals (4, and ylat) and the respective outputs were integrated and fed into a

320

Flight control systems Autopilot commands

Lateral measu rement feedback Trim conditions

Figure 8. 7 Lateral controllerstructure

c o m m a n d augmentation system. The linear closed-loop lateral controller is shown in Figure 8.7. As with the longitudinal controller, there are two main components to the structure, K~t and Lt~t., which have similar functionality to Kto~ and L~. Small commands in ~ were converted into commands in ~ using the following function:

(8.17)

Any errors in roll angle owing to wind disturbance were automatically accounted for, as the resulting deviation of ylat was being corrected by the controller. This section has described the controller structure for the RCAM design with EA. A lot of this structure came from d e e p e r understanding o f the controlled aircraft which was only gained once the design process had begun. Thus, some aspects of the controller structure described here were added on during the design procedure itself. The gain matrices that constitute the core of the controller are simple gain relations between aircraft outputs and inputs. This structure was therefore f o u n d to be easy to follow during the design process, as each controller gain could be traced to specific aircraft behaviour.

8. 4.2 Construction of a desired eigenstructure T h e EA linear synthesis p e r f o r m e d for the RCAM design required two sets of inputs. The first were the system matrices A, B and C. The second were a set o f desired closed-loop eigenvalues, A a and eigenvectors, Vd. This desired eigenstructure was based on the design specifications for the control problem.

8. 4.2.1. Performance specifications As shown in Section 8.2.2, the first of these specifications consists of p e r f o r m a n c e specifications. These can be separated into two types:


321

This is the step response to modes of the form: 2 COn 2

2

s + 2~co~ + co~ ID -n

damping

The overshoot of the response is dependent on damping ratio. Once that has been established, the natural frequency of the desired mode can be approximated by

1+1.I~+1-4~ 2 (O n

~-

risetime

Time(s)

Figure 8.8

Relationship between modal damping and natural frequency

(i)

specifications for certain outputs to track step c o m m a n d s within a given rise time and with a m a x i m u m overshoot; (ii) specifications for the disturbance allowable in a variable due to step c o m m a n d s or changes in other variables. T h e first of these can be addressed by choosing desired eigenvalues that either have a m i n i m u m time constant (for first-order modes) or provide a m i n i m u m d a m p i n g and frequency (for second-order modes) in all the m o d e s o f the closed-loop aircraft. T h e r e are simple relationships between the rise times and overshoots of second-order modes and their d a m p i n g and frequency, as depicted in Figure 8.8. This knowledge was used to provide an initial set of desired eigenvalues, A d. In o r d e r to keep controller gains low (which reduces control activity), these were also chosen as close to the aircraft open-loop eigenvalues as possible. As described in Section 8.2, the variables of RCAM that n e e d e d to be tracked by the control system were:

• longitudinal dynamicy, altitude z and airspeed VA; • lateral dynami~ lateral deviation ylat and heading rate ~b. These specifications provided values for the desired eigenvalues as shown in Tables 8.8 and 8.9. Note that as the aircraft models have been a u g m e n t e d with the tracking variables, there are two extra states and modes in the desired eigenstructure. T h e desired eigenvalues were given a m i n i m u m corner frequency of 0.2 rad s - l in the case of first-order modes and a m i n i m u m d a m p i n g ratio of 0.7 and m i n i m u m natural frequency of 0.2 rad s - 1 in the case of second-order modes. T h e specifications to reduce the change in one variable affecting a n o t h e r were addressed by using decoupling in the desired eigenvectors Vd.

322


Table 8. 8 Desired eigenstructure of the longitudinal closed-loop system Mode:

SPPO

Eigenvalue:

-0.8±0.8i

Phugoid

Altitude

Vj track

- 0.15±0.15i

-0.3

-0.4

(:

0.71

0.71

~n:

1.13

0.21

q

x

X

O

x

u

0

w

I

z

VA track z track

L x

-

-

-

-

-

-

X

X

X

X

X

X

X

x

0

x

0

0

x

0

X

X

X

X

X

X

X

X

X

X

Lx

1

x

-

-

z track -0.5

X

_

X

_

Table 8. 9 Desired eigenstructure of the lateral closed-loop system Mode:

Roll

Spiral

Dutch roll

Heading

ylat

ylat track

Eigenvalue:

-4.40

-0.20

~':

--

--

-

-

O~n:

P

-

X

I"

X

--

0.21

--

0

X

-

- 1.50

-

X

X

X X

X

X

X

X

X

X

X

X

X

X

X

0

0 I x

X

0

ylat

X

X

X

I I I

X _X

-0.55

--

X

V

ylat track

-0.13

0.71

X

X

track

-

-0.182±0.157i

track - 0.50

~

.X

0

i x

I

0

0

X

X

I

X

X

X

o

I

X

X

LoJ

_

X

.

.X

X X

Lx

_X

Longitudinal dynamics, altitude should be decoupled from airspeed command and vice versa. This led to decoupling the altitude and altitude-tracking modes from forward speed, u, and decoupling the airspeed track mode from upwards velocity, m Based on knowledge of conventional aircraft dynamics, other modes were also decoupled from some states in order to lessen the interaction between aircraft horizontal and vertical variables. These are given in Table 8.8.

Lateral dynamic~ A command in roll should not result in a sideslip. This leads


323

to decoupling the roll, roll track and spiral modes from lateral velocity, ~,, proportional to sideslip angle, 13. Also, heading mode and lateral-deviation tracking mode were decoupled from l, as these modes were excited in response to roll commands, which was undesirable. It was decided that a c o m m a n d in lateral deviation would be effected through rolling motion, but to ensure that heading angle did not alter very much as a result, the ylat track m o d e was decoupled from heading angle ~0. Thus, heading angle will change during a lateral-deviation command, but not excessively. Lastly, the dutch roll was causing oscillatory motion during most lateral manoeuvres in the initial stages of the design. Because of this, it was later decoupled from some of the lateral states of the aircraft. The resulting desired eigenvectors are shown in Table 8.9.

8. 4.2.2 Robustness specifications It has been mentioned (see Section 8.2.3) that EA does not explicitly address robustness specifications. For the RCAM, the m e t h o d of EA used ensured that if any freedom remained in the assignment of eigenstructure, it was used to improve robustness as described in Section 8.3.

8. 4.2.3 Ride-quality specifications The ride-quality specifications (see Section 8.2.4) related to maximum accelerations and minimum damping. The maximum-acceleration criteria could not be addressed directly by EA, but the minimum-damping criteria have been accounted for by using a damping ratio of greater than 0.7 for all the assigned closed-loop modes.

8. 4.2. 4 Safety specifications T h e r e were five safety specifications for the RCAM problem (see Section 8.2.5). Only the minimisation o f sideslip could be addressed by ensuring that modes which affected sideslip were highly damped in order to return this variable to zero as quickly as possible.

8. 4.2.5 Control-activity specifications In order to minimise control activity (as described in Section 8.2.6), the desired closed-loop eigenvalues were placed as near the open-loop eigenvalues as possible. Once a desired eigenstructure had been constructed based on all the design specifications which could be converted into one, the EA itself was performed. The design algorithm for EA, as described in Section 8.3, is very simple. However, the linear synthesis process was a difficult one, consisting of controller synthesis and analysis. This was not to do with the EA tools themselves, but with interpreting the results of the analysis and with making

324


consequent decisions in specifying a refined eigenstructure. This is not a problem that is unique to EA. It is always important that the designer understands the aircraft system well enough to be able to relate the different aspects of the numerical m e t h o d (in this case consisting of eigenvalues and eigenvectors) to the dynamics of the aircraft.

8. 4.3 Initial synthesis The initial step in the design synthesis for the RCAM was a simple one. All that was required was the EA algorithm; this was implemented as a Matlab program. T h e r e are two basic inputs to this program; a set of linear system matrices, A, B, C, and the desired eigenstructure, A a and V~, given in Table 8.8 and Table 8.9. These were entered into the program to produce a gain matrix, which was then separated into its regulation and tracking components. Table 8.10 shows the initial controllers that were designed in this way. The controlled aircraft was then assessed to determine whether it met the required specifications or not. The RCAM controllers were assessed using a variety of techniques to determine measures for the performance (including decoupling) and robustness of the closed-loop system. This analysis of the controller took up most o f the time in the design process. It was done using a combination of simulation and eigenstructure analysis to ensure that performance goals were satisfied, and some sensitivity analysis to determine how robustness goals were being met.

8. 4. 4 Methods of controller analysis 8. 4.4.1 Performance analysis Time-response simulation: this m e t h o d of analysis provided an immediate impression of the capabilities and failures of the closed-loop system. It also provided direct assessment of the design specifications for RCAM, most of which were given in terms of step responses. Thus, the attainment of the majority of the design specifications was tested using linear simulation.

Eigenstructure analysis, if deficiencies in aircraft performance were found by the use of simulation, eigenstructure analysis, which has been described in Section 8.2, was p e r f o r m e d on the closed-loop system. Eigenstructure analysis was useful in determining which modes were coupled with which states of the system. If simulation showed that a particular state was exhibiting larger deviations than expected, the coupling of that state to the various modes was examined. If the mode causing the detrimental behaviour could be identified, it was decoupled from the state and EA was p e r f o r m e d again. Although a solution was not always easy to come by (when a mode was not controllable, for instance), eigenstructure analysis was a useful tool for providing an insight into the internal coupling of the RCAM system.

I

0 O

0

N ,.... (N

O

0 I'~

O 0 O9

d O'~

0 0 0 0

o

~4 O

0") e~l

I

I

O

P~ O

I

O

~

N q

O

¢5d

¢~

O I

cN

I

O I

o8

O

I

O

I

~

~-(D

I _ _

I

~

I

0

-.~dd

I

-~dd

I

I

d

I


"~.

O

325

326


8. 4.4.2 Stability analysis Although EA is able to guarantee the placement o f p closed-loop eigenvalues in the RCAM, where p is the n u m b e r of outputs, it is unable to guarantee the final position o f the other ( n - p ) eigenvalues where n is the n u m b e r of states. This means that in the analysis of the RCAM closed-loop system, it was necessary to check that the system was stable. This was easy enough, as a full set of eigenvalues with negative real parts implied stability.

8. 4. 4.3 Robustness analysis In the design specifications, the robustness of the system has been defined by its stability and performance in the face of changes in the time delay of the controller and the centre of gravity and mass of the aircraft. These can be separated into performance robustness, the ability of a nominal system to retain the performance specifications, and stability robustness, the ability of a system to retain adequate stability.

Performance robustnesy, one measure of the performance robustness of an aircraft system to these parameter variations is the sensitivity of its eigenvalues to changes in the matrix (A+BKC). A measure exists [19] for overall p e r f o r m a n c e robustness. Taking the closed-loop system, if ,~ is an eigenvalue of the perturbed system, (A + BKC) + E it can be shown that:

I ~ - Ail - <~K(V) IIEII

(8.18)

where K(V) is the spectral condition n u m b e r of the eigenvector matrix V. For an arbitrary system, the larger the condition n u m b e r of the eigenvector matrix, the larger the excursion in eigenvalues from their nominal values that may occur for a given perturbation, E. The mathematical p r o o f of this result can be found in Reference [13]. Thus, one goal of the EA design was to reduce the condition n u m b e r of the closed-loop eigenvector matrix.

Stability robustnes~ an assessment of the stability of the RCAM subject to unstructured perturbation calls for some measure of stability margin. Work d o n e by Lehtomaki et al. [20] provides a stability-margin formula for MIMO systems. If the minimum singular value of the return difference matrix (RDM) at the aircraft input is larger than some constant, i.e: _o-[I+ KG] >! c

(8.19)

then simultaneously in each loop of the feedback system there are guaranteed gain margins given by:

GM

1 1 l+c'l-c

(8.20)


327

Table 8.11 Eigenstructure of the longitudinal closed-loopsystem Mode: Eigenvalue: ~':

SPPO -0.8+0.8i 0.71

OJn:

1.13

q0 u w z VA track z track K(V

0.008 I 0.009 (0) 0.928 0.419 0.021 0.371

Phugoid - 0.15+0.15i 0.71 0.21

Altitude -0.3 --

0 0.001 0.046 (0) 0.202 0.215 0.954

0 0.001 (0) 0.043 0.287 0.004 _ 0.957 -J

_

-0.4 --

--

--

-

0.001 0.002 0.248 (0) 0.276 0.621 0.691 -

z track -0.5 ---

0 0.001 (0) 0.178 0.440 0.010 _ 0.880

30 400

)

Gain margin Phase margin

VA track

-4.3

dB, 9 dB

+38 °

and a guaranteed phase margin given by:

(8.21) All the system-loop gains a n d / o r phases (but not both at the same time in any one loop) may be altered within the limits prescribed by the GM and PM without destabilising the system. Similar considerations can be used to produce stability margins, given perturbations at the aircraft outputs. The measures of spectral condition number and stability margin that have been described here were used in the analysis of the robustness of the RCAM.

8. 4.5 Analysis of the longitudinal controller The closed-loop eigenstructure of the initial design shown in Table 8.10 is given in Table 8.11. It can be seen that the desired eigenvalues were attained and the bracketed elements show that the decoupling which was specified (see Table 8.8) in the desired eigenvectors was attained. The interaction of the tracking commands with the outputs can be followed by using the closed-loop input-mode and mode-output coupling vectors. The coupling between the commanded inputs and the modes of the longitudinal system is given by:

WtonBtonLton

(8.22)

328


Table 8.12

Input-mode coupling of the longitudinal closed-loop system Mode

Va

z

command

command

0.390 0.969 4.020 0.357 1.748

0.459 0.043 1.431 0.049 3.146

SPPO Phugoid Altitude VA track z track

15

VA 10;

5

WE E

o -5

-~0

-15

10

20

30

40

50

Time (seconds)

Figure 8. 9 Response of initial longitudinal system to a 13 m s- 1 step command in airspeed

These vectors are shown in Table 8.12. They demonstrate that: (i)

When there is a c o m m a n d in airspeed VA, all the system modes will be strongly excited. Looking back at Table 8.11, this will cause an excursion in both forward velocity, u, and in altitude, z. (ii) When a change in altitude, z, is commanded, the SPPO, the altitude and the z track modes are the most involved. These modes alter the z state, but as can be seen in Table 8.11, they are not d o m i n a n t in the forwardvelocity state. Thus, our cursory examination of the eigenstructure of the system indicates that it is likely that Va is decoupled from a c o m m a n d in z, but z does not appear to be decoupled from a c o m m a n d in Va.

This evaluation of the eigenstructure can be tested by using linear simulation o f step commands on these tracked variables. Figure 8.9 shows the time response of this system to a step-command increase of 13 m s - ~ in VA, Note that, as predicted by eigenstructure analysis, there was a large excursion in z. A step c o m m a n d of 30 m in z p r o d u c e d the results shown in Figure 8.10.


329

30 25

=~

2o

g 10 5 C

20

10

30

40

50

"time (seconds)

Figure 8.10 Response of initial longitudinal system to a 30 m step command in altitude

Table 8.13 Eigenstructure of the lateral closed-loop system Mode: Eigenvalue: ~': (On:

Roll -4.4 ---

p /~ 4, q, v

0.259 0 0.059 0 (0) 0.031

Spiral -0.2 ---

Dutch roll -0.18+0.15i 0.77 0.23

Heading -0.13

(0.004) 0.003 (0.015) 0.012 0.996 0.015 (0.050) (0.061)

0 0 0 0 (0) 0.129 0.002 0.992

.

ylat 4, track

ylattrack

0 0 0 0 (0) [ , 0.196 i 0.002 I I .0.007_ [_0.981 _[

-

K(V )

34 730

Gain margin Phase margin

- 1.8 dB, 2.3 dB

_

ylat

4,

ylat

-0.55

-1.5

-0.5

. . .

0.008 0.270 0.002 ! 0.015 0.015 0.180 0.003 0.010 (0) (0) 0.482 0.785 0.005 0.006 0.876 0.523

m B

0.004 0 0.009 (0) 0.200 0.438 0 0.876

+13 °

Again, as predicted, VA had been decoupled well enough from a command in z to satisfy the design specifications. These two simple tools (eigenstructure analysis and linear simulation) were enough to provide a preliminary analysis of the closed-loop longitudinal dynamics.

8. 4.6 Analysis o f the lateral controller The closed-loop eigenstructure of the initial lateral controller is given in Table 8.13. It can be seen that the desired eigenvalues were assigned and


330

o.Gj 0.5 0.4 "2

E

'0~

6

0.3

~o.2i

4

g

"0

2

0

?0.1 ?0.2 10

20

30

40

5O

Time (s) a. Velocities and distances

Figure 8.11

?0'31

10

20

30

40

Time (s) b. Angles and angular rates

Response of initial lateral system to a 10 m step command in lateral deviation

decoupling (required decoupling is given by the elements in brackets), in most cases, occurred where it was required it. Owing to the limited freedom to decouple, the specified decoupling asked for in the dutch-roll m o d e had not been met fully. Instead, the best possible decoupling had been provided, as described in Section 8.3.2. T h e lateral-dynamics performance specifications are for specific rise times and overshoots for a step command in lateral displacement. Figure 8.11a shows a linear simulation of the response to a 10 m c o m m a n d in lateral displacement. This response satisfied all the required criteria in the design specifications and Figure 8.11 b shows that, as required, heading change was kept low for these small changes in lateral displacement. As all the other lateral directional requirements required the use of nonlinear simulation, they will be discussed in Section 8.5.

8. 4. 7 0 p t i m i s a t i o n of the controllers Once the designer is able to understand the way in which the aircraft system can be manipulated by altering its eigenstructure, the process becomes one in which desired eigenvalues and eigenvectors are altered in an iterative m a n n e r until a satisfactory solution is obtained. Thus, there is no best solution, as the combinations of eigenvalues and eigenvectors which can be used is vast. With EA, any small alteration of the eigenvalues alters the vector space from which the achievable eigenvectors can be selected. This means that, although it is easy for the designer to choose arbitrary eigenvalues to produce desired responses, it is not possible to examine the effect of this choice on the eigenvectors of the resulting closed-loop system easily. The effects can only be

Eigenstructure assignment to the design of an autopilot function r-

q

r-

NO/H, ave~__ YES

Algorithm to ] compute L.~.~,/QOalS DeeR"lupdated parameters~ ~ ~ , a t t a i n e d ? ~

\/

d~dlni;alAdvd Eigenstructure Assignment Al~lor thm

I

331

v

K(final)

L "J~

Goals for performance and stability robustness Designer interactionj

K

~

btain performance~ and stability | measures /

Goal kttainment algorithm .

Figure 8.12 Schematic of the goal-attainment procedure indirectly assessed using metrics such as rise times, overshoot to commands, eigenvector matrix condition number and stability margins. To preserve the desirable qualities of a system designed using EA, a goal attainment optimisation algorithm was implemented with an internal EA algorithm. This procedure has been demonstrated with aircraft EA controllers before [21-23]. The design began with an arbitrary set of eigenvalues and produced an EA controller. This controller,/~ was then used to evaluate a set of objective functions based on improving performance and robustness. If the controller did not achieve the desired goals, the eigenvalues were altered slightly using a gradient-based method and the EA procedure was repeated using this new desired eigenstructure until a solution was obtained. This procedure is depicted schematically in Figure 8.12. This process of linear synthesis, linear-system analysis and linear-system optimisation using goal attainment was repeated until a system which met as many of the RCAM design specifications as possible was produced. The resulting controllers are shown in Table 8.14. Comparing the properties of these controllers with those given in Tables 8.11 and 8.13 for the initial design, it can be seen that using goal attainment with EA improved performance robustness of the longitudinal controller and both performance and stability robustness of the lateral controller.

8.5 N o n l i n e a r s i m u l a t i o n o f t h e c o n t r o l l e d a i r c r a f t Once the final controller had been designed, it was evaluated using nonlinear simulation to assess the extent to which achievement of the design

332

~

0

LO Le~

o6

I

I

I

I

0 0

I

0

I

I

0

I

O0

0

0

0

0

0

I 0

I

I

oc5 0

0

I

~O0 Oo

O0 o~.

0

~o

N O 0 0 0 I

I

cO 0 . ~ . oO 0

CO 0 0.":¢.0 o,I 0

O~ 0 0 0

.el.o

0

t 00°

I


o6

I

-~dd

I

I - -

I

"~ ,,,a~

I

o

~ o~ o o o~~

~

~ >

LU

~0

~

I

"~

C9~_

Eigenstructure assignment to the design of an autopilot function 3o

'

333

~

25

~:

20

5

0

5

10

15

20

2'5

30

35

40

Time (s)

Figure 8.13 Response to 30 m step command in altitude

specifications could be preserved from the linear synthesis. The results given here can be c o m p a r e d with the design specifications given in Section 8.2.

8.5.1 Performance speCifications These are the main criteria which had to be satisfied. Unless otherwise specified, the following results are for the closed-loop aircraft at the nominal condition.

8.5.1.1 Longitudinal dynamics Altitude response, the step response of the aircraft to a 30 m increase in altitude z is shown in Figure 8.13. This fulfilled the design specifications, as the response had a rise time of 8 s (desired at less than 12 s) and an overshoot of 1.7 per cent (desired at less than five per cent).

Airspeed response, the response of the aircraft to a step c o m m a n d in airspeed VA is shown in Figure 8.14. The output had an overshoot of seven per cent (desired at less than five per cent) and a rise time of 14 s (desired at less than 12 s). This puts the Va c o m m a n d system at just a little outside the desired boundaries. Figure 8.15 shows that when perturbed by a 13 m s -1 wind step, the airspeed deviation took 26 s to reach less than 2.6 m s - 1 (desired time is less than 15 s). However, this compromise was made during controller optimisation using goal attainment in order to give the system more robustness.

Cross coupling between airspeed and altitude, cross coupling was slightly larger than allowed by the specifications for a 30 m c o m m a n d in z. This p r o d u c e d a 1.4 m s -1 deviation (desired at less than 0.5 m s -1) in VA and is shown in Figure 8.16. The coupling of z for a c o m m a n d in Va of 13 m s - 1 was much less

334

Flight control systems 1.2

o.~

•

0.6

~

0.4

E

v

o,2

0

Figure 8.14

'o

2'0 3'0 ;o 5'o "time (s)

60

70

80

Response of airspeed to a unity step command

6 4

2 0 ,~

-2

E "

v

-10 -12

-14

10

20

30

40

50

60

70

80

"time (s)

Figure 8.15

Airspeed deviation during a wind step disturbance along the aircraft airspeed axis

than the allowable limit of 10 m, as shown in Figure 8.17.

Flight path angle response the response of the aircraft to a c o m m a n d e d flightpath angle y change of 3 ° is shown in Figure 8.18. Although this response had an overshoot of only 1.6 per cent, it had a rise time of 10 s (desired at less than 5 s), and so did not respond as well as desired. This situation could not be remedied easily using the EA controller, which had been designed to solve z c o m m a n d and Va c o m m a n d situations, whereas a flight-path-angle c o m m a n d implies a vertical speed (~) command.

8.5.1.2 Lateral dynamics Lateral deviation: the lateral deviation ylat of the aircraft from an initial 1 m off the desired trajectory, and the response to a command in lateral deviation o f


335

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Figure 8.16

Coupling for a 30 m step command in altitude

14 '=2

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Figure 8.17

Coupling for a 13 ms- ~ step command in airspeed

one metre, are shown in Figure 8.19. This plot shows that the lateral-deviation regulation system was u n d e r d a m p e d . It caused a reduction of lateral deviation to ten per cent of its original value in less than eight seconds (desired at less than 30 s), but also resulted in an undershoot of 25 per cent. This was not acceptable performance. However, it was allowed in order to ensure that the aircraft did not stray outside the allowable bounds in the event of an engine failure (see Section 8.5.6). The response to a c o m m a n d e d lateral deviation satisfies the step-command requirements.

Roll angle respons~ the response in roll attitude, ~b, and sideslip angle,/3, during an engine failure and restart is shown in Figure 8.20. The maximum roll-angle deviation that resulted was 6 ° (less than 10 ° was desired). The design was such that roll angle was minimised to zero after this to ensure passenger comfort.

336

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Time (s)

Figure 8.19 Lateral-deviation performance

As can be seen in the figure, this resulted in a steady sideslip o f about 3~ The roll behaviour of the system under moderate turbulence conditions (the definition o f this term in the context o f the RCAM challenge is c o m p l e x [1]) is shown in Figure 8.21. The roll angle was within the limit of five degrees, but this was at the expense of high aileron activity.

Heading rate. Figure 8.22 shows the heading rate which resulted from an engine failure. This was within the 3 ° s - l limit allowed. Restarting the engine did not cause a violation of this limit either.


337

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Roll angle under moderate turbulence

8.5.2 Robustness specifications It was f o u n d that for a controller time delay of 50 ms, the system had both p e r f o r m a n c e robustness and stability robustness over all other specified parameter variations, that were specified. With the maximum time delay of 100 ms, a small part o f the p a r a m e t e r envelope, namely at aircraft aft and high centre o f gravity and with a mass of greater than 145 tonnes, the system became unstable. Hence the system was not as robust as required.

8.5.3 Ride-quality specifications These criteria relate to passenger comfort u n d e r normal manoeuvres. Results for all the step c o m m a n d s showed that accelerations remained within the given bounds.

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1.5 1 0.5 0 -0.5

restart -1 -1J

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Figure 8. 22 Heading rate during an enginefailure and restart

Table 8.15 Satisfaction of the maximum rate requirements

Aileron Tailptane Rudder Throttle

Mean rate (deg s -1)

Maximum in design specs (deg s -1)

15.50 4.30 0.60 0.32

8.30 5.00 8.30 0.24

8.5.4 Safety specifications For an evaluation of roll-angle safety, see Section 8.5.6.2 All other variables were kept to within their limits.

8.5.5 Control-activity specifications The requirements were that mean actuator rates should be less than 33 per cent of the maximum rates. As shown in Table 8.15, these limits were violated, mainly by aileron activity, Figure 8.23 shows the actuator movements u n d e r moderate turbulence conditions. Note that here as well, the aileron exhibited excessive movement. This was due to the fact that it was trying to regulate lateral deviation too quickly, and was using very high gains to do so (about 3 ° of aileron were c o m m a n d e d for every metre off the desired trajectory).


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8.5.6 Evaluation using a landing-approach simulation Part of the analysis of controller strategies for the RCAM design challenge involved flying the controlled aircraft on a desired landing-approach path using nonlinear simulation. Both tracking performance and inner-loop regulation of the controlled system were evaluated by means of bounds on key o u t p u t variables. This simulation also came in useful for testing the EAcontrolled aircraft's ride quality and safety criteria. The entire simulation trajectory in three dimensions is shown in Figure 8.24. The numbers on the plot define four distinct flight segments of a landing approach. The controller was flown at four flight conditions to evaluate the robustness of the system. These involved flying at the nominal, the most forward and the most aft centre of gravity and with a long controller time delay, and the results of these flights were overlaid on the same graphs.

340

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Figure 8.25 Segment k the effect of enginefailure 8.5.6.1 Segment I: the effect of engine failure (0-I) T h e aircraft began at an altitude of 1000 m and with a track angle of - 9 0 ° relative to the runway centre line. All through the approach, a constant airspeed of 80 m s-1 was maintained. In this first segment, the left engine failed and fell back to idle (point a in Figure 8.25) and then restarted (point b). It can be seen in Figure 8.25 that the EA controller had high robustness (the four overlaid plots are not easily distinguished), and the aircraft was kept well within the p e r f o r m a n c e bounds shown in dotted lines.

8.5.6.2 Segment II: the 3 deg s -1 turn (1-2) The turn was initiated by c o m m a n d i n g a step 3 deg s - x heading rate (at point cin Figure 8.26) which ceased after 30 s (point d). However, this EA controller had also been designed to keep lateral deviation down, and as soon as the aircraft began to deviate from the required course at point c, a bank angle was c o m m a n d e d to reduce this deviation. Lateral deviations off the desired track show that this system overshot the p e r f o r m a n c e boundary. Thus, although a c o m m a n d e d 3 deg s-1 turn would normally have posed no problem, the instantaneous deviation from the desired trajectory which occurred as the aircraft overshot the start of the turn caused excessive aileron commands, and p r o d u c e d high lateral aircraft acceleration. M a x i m u m lateral acceleration was desired at less than +0.02 g~ As shown in Figure 8.27, this r e q u i r e m e n t was violated twice. The first time was during the engine failure, where lateral acceleration deviated to ten times the allowable value. This was to be expected, and was considered allowable for this e m e r g e n c y situation. However, undesirable p e r f o r m a n c e during the steady turn sticks out again, where accelerations of +0.08 goccur. M a x i m u m vertical acceleration was desired to be less than + 0.05 g. Figure


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8.28 shows that this value was violated twice. The less harsh violation was during the wind shear, where we would have expected an uncomfortable ride. However, the worst violation, at - 0.4 g, came during the steady turn, which would be considered a n o r m a l manoeuvre. This response was caused by the quick response to the lateral deviation from the desired path that occurred. T h e consequent roll response resulted in an excessively large longitudinal response, as the two systems are highly coupled during a steady turn. This inadequate p e r f o r m a n c e was a direct result of catering for engine failure in the EA design process. This conflict was also responsible for bad roll-angle response in the turn. T h e roll angle over the evaluation simulation for the nominal system and the

342


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Figure 8. 28 Vertical acceleration during approach nominal system with a 21 per cent m e a n aerodynamic chord vertical centre of gravity are shown in Figure 8.29. T h e desired roll-angle limit is 30 ° . This was m e t by the nominal system, but exceeded (at a peak of 38 °) by the aircraft with a high centre of gravity. This p r o b l e m would be solved by a m o r e realistic d e m a n d profile in the turn simulation.

8.5.6.3 Segment III: the capture of the glideslope (2-3) This glideslope began with a c o m m a n d e d - 6 ° change in flight-path angle (point e in Figure 8.30) and then moved to a - 3 ° slope (pointJ). This plot shows that both p e r f o r m a n c e and robustness characteristics in this segment were g o o d for the closed-loop aircraft.


343

35 3C 2E 2C

0 -5 -10 - 15

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1O0

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Time (s)

Figure 8.29 Roll angle during approach 8.5.6.4 Segment IV.: the final approach with windshear (3-4) While on final a p p r o a c h with a glideslope of - 3 °, a windshear was introduced (point g in Figure 8.31). T h e vertical deviations from the desired path are shown in the Figure. For the controlled aircraft, p e r f o r m a n c e was within the bounds, and robustness was good. Thus, the EA design showed that it was able to fulfil its mission, but it exhibited excessive roll m o v e m e n t in response to a large step deviation in the aircraft position from the desired lateral flight trajectory.

8.6 Conclusions T h e aims of the eigenstructure assignment (EA) design for the robust civil aircraft model (RCAM) that have been described in this chapter were concurrently: • to demonstrate that linear design could be made robust so that less nonlinear tuning would be required to produce a satisfactory system, resulting in m o r e rapid design iteration; • to show that a m o d e r n m e t h o d could be as visible and as flexible as m o r e traditional methods. T h e RCAM design-challenge experience p r o d u c e d mixed conclusions, and this is a s u m m a r y of the opinions of both the designers and of the industrial evaluation of the controller that was carried out. Importantly, the controllers p r o d u c e d by EA were seen to be of a simple structure, and easy to understand. In implementation, this will lead to quick certification, as a lack of unconventional implicit dynamics in the controller makes it structurally transparent to most designers. Problems in functionality

344

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SegmentIII: capturing the desired glideslope

can be related to direct gains, leading to easy access to the controller by simulation engineers, flight control computer implementation engineers and flight-certification engineers. Although EA was able to produce good performance and robustness with a highly automated procedure, controller structure is limited by the method when used for aircraft flight control. If more complex classical elements, such as command prefilters or wash-out filters, are used, EA is unable to facilitate the accurate analysis or suitable design of a robust controller if these components cannot be integrated into the aircraft linear state-space matrices. In terms of the design process, the RCAM exercise demonstrated that

Eigenstructure assignment to the design of an autopilot function 600

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Segment I~."Aircraft performance during a windshear

eigenstructure analysis provides a tool which ultimately assists in controller synthesis. The aircraft dynamics were broken down into simple relationships between dynamic modes and their interaction with the states and outputs of the aircraft. Then, adverse interactions between aircraft dynamic modes and its states or outputs were identified and focused on in the next design stage. This multi-input, multi-output analysis showed potential as a way in which modern methods can be developed to visualise aircraft dynamics. Although this improvement in analysis was utilised, it was found that not all the specifications of the RCAM control problem could be satisfied. The designer must still have experience with both the method and the aircraft in order to understand the way in which the desired eigenstructure must be

346


manipulated. Guidelines for the systemisation of EA design are in the process of development, but it will take some time before a mature EA methodology can be applied to the design of complete aircraft flight control systems. T h e RCAM design challenge application demonstrated that eigenstructure analysis and assignment provided a m e t h o d of producing a robust autopilot system and a useful tool for the simplification of the examination of flightcontrol systems.

8.7 References [1] MAGNI,J-E, BENNANI, S., and TERLOUW, J. (Eds): 'Robust flight control--a design challenge' (Lecture notes in Control and Information Sciences, Springer-Verlag, March 1997) [2] STEVENS, B.L., and LEWIS, EL.: 'Aircraft control and simulation' 0ohn Wiley & Sons, Inc, 1992) [3] SMITH, P.R.: 'Application of eigenstructure assignment to the control of powered lift combat aircraft'. RAe Bedford Tech. memo FS 1009, February 1991 [4] FALEIRO, L.E, and PRATT, R.W.: 'An eigenstructure assignment approach', MAGNI,J.E, BENNANI, S., and TERLOUW, J. (Ed.) in Robust flight control--a design challenge' (Lecture notes in Control and Information Sciences, Springer-Verlag, March 1997) [5] PAHLE, J.W., WICHMAN, K.D., FOSTER, J.V., and BUNDICK, W.T.: 'An overview of the controls and flying qualities technology on the F/A-18 high alpha research vehicle'. NASA Dryden technical report NASA-H-2123, September 1996 [6] FARINEAU, J.: 'Lateral electric flight control laws of a civil aircraft based upon eigenstructure assignment techniques'. Proceedings of the AIAA Guidance, navigation and control conference, August 14-16, 1989, Boston MA [7] KIMURA, H.: 'Pole assignment by gain output feedback', IEEE Trans. Autom. Control, August 1975, pp. 509-518 [8] ANDRY,A.N., SHAPIRO, E.Y., and CHUNG, J.C.: 'Eigenstructure assignment of linear systems',/EEE Trans. Aerosp. and Electro. Syst., 1983, 19, pp. 711-72 [9] SOBEL, K.M., YU, W., and LALLMAN, EJ.: 'Eigenstructure assignment with gain suppression using eigenvalue and eigenvector derivatives', J. Guid. Control Dyn. 1990, 13, (6) [10] SOBEL, K.M. and LALLMAN, F.J.: 'Eigenstructure assignment for the control of highly augmented aircraft', J Guid. Control Dyn. 1989, 12, (3), pp. 318--324 [11] SOBEL, K.M. and SHAPIRO, E.Y.: 'Application of eigenstructure assignment to flight control design: some extensions', J. Guid. Control Dyn. 1987, 10, (1), pp. 73-81 [12] CHOUAIB, I. and PRADIN, B.: 'On mode decoupling and minimum sensitivity by eigenstructure assignment'. Mediterranean electrotechnical conference, MELECON '94, Antalya, Turkey, April 1994 [13] KAUTSKY,J., NICHOLS, N.K., and VAN DOOREN, P.: 'Robust pole assignment in linear state feedback', lnt.J. Control, 1985, 41, (5), pp. 1129-1155 [14] FAHMY, M.M. and O'REILLY, J.: 'Parametric eigenstructure assignment by output feedback control', Int. J. Contro~ 1988, 48, (1), pp. 97-116 [15] FAHMY, M.M. and O'REILLY, J.: 'Parametric eigenstructure assignment by output feedback control: the case of multiple eigenvalues', Int. J. Control, 1988, 48, (4), pp.1519-1535 [16] WHITE, B.A.: 'Robust polynomial eigenstructure assignment using dynamic feedback controllers', Proc. Inst. Mech. Eng. Part 1, 1997, 211, (1), pp. 35-51 [17] MAGNI,J.-E: 'RCAM design challenge presentation document: a modal multimodel control approach'. GARTEUR report TP-088-12, April 1997 (summary available in Reference [1])


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[18] LITTLEBOY, D.: 'Numerical techniques for eigenstructure assignment by output feedback in aircraft applications'. PhD thesis, Department of Mathematics, Reading University, UK, December 1994 [19] HORN, R.A. andJOHNSON, C.A.: 'Matrix analysis' (Cambridge University Press, 1985) [20] LEHTOMAKI, N.A., SANDELL, N.S., and ATHANS, M.: 'Robustness results in linear quadratic gaussian based multivariable control designs', /EEE Trans. Autom. Control 1981, AC-26, (3), pp. 75-92 [21] GARG, S.: 'Robust eigenspace assignment using singular value sensitivities', J. Guid. ControlDyn. 1991,14, (2), pp. 416-424 [22] FALEIRO, L.F. and PRATT, R.W.: 'Multi-objective eigenstructure assignment with dynamic flight control augmentation systems.' Proceedings of the AIAA Guidance, navigation and controlconference, San Diego, USA, July 1996 [23] FALEIRO, L.E and PRATT, R.W.: 'Multi-objective eigenstructure assignment in the design of flight control systems.' International Federation of Automatic Control (IFAC) 13th triennial world congress, San Francisco, 1996, P, pp. 201-206


Chapter 9

An H00 loop-shaping design for the VAAC Harrier R.A. Hyde

9.1 Introduction This chapter describes how multvariable control has been applied to the Defence Evaluation and Research Agency (DERA) Bedford Harrier and flight tested. 1 The work was carried out as a research study at Cambridge University Engineering Department [1-3] between 1988 and 1993. At that time there were significant advances in the so-called H~ ( p r o n o u n c e d H-infinity) control design m e t h o d [4]. The advent of numerically well-conditioned solutions to the H~ optimisation problem such as Reference [4], and the increase in computing power made the design technique a very viable alternative to more classical methods. However, there was a huge gap between the elegant theory and producing a control law suitable for implementation on an aircraft. In particular, the linear controllers produced were high order, and it was not clear how to gain schedule them with flight condition. The aim of the research p r o g r a m m e was to narrow this theory-practice gap. The first phase investigated the design and implementation issues associated with multivariable optimal controllers, and resulted in a control law for the DERA generic VSTOL aircraft model (GVAM). Based on the success of this, DERA and the Science and Engineering Research Council(SERC) funded a two-year follow-on phase at Cambridge University to develop a control law suitable for flight testing on the DERA research Harrier u n d e r the vectored thrust aircraft advanced flight control (VAAC) programme. The H~ m e t h o d is what is known as a robust multivarible design method. The term multivarible means that it is suited to systems with several inputs and outputs where each input strongly affects more than one output. The longitudinal control of the Harrier is such a system, the three primary motivators being nozzle angle, engine thrust and blended tailplane/reaction 1Cambridge Control is currently tasked by DERABedford to look at implementation and flight clearance of mnltivariable control laws. Some of the ideas presented in this chapter have come out of this programme and are the subject of ongoing research. Control law 005 was originally funded by the Science and Engineering Research Council (now EPSRC) when R.A. Hyde was a post-graduate student.

An H= loop-shaping design for the VAA C Harrier

349

control system (RCS). Moving any of these three inputs will affect forward, normal and pitching motions. The collaborative programme set up between DERA and Bedford and Cambridge University had two objectives, namely: • to show how H~ methods could be used in a practical application; • to demonstrate implementation of multivarible control on an aircraft. The resulting control law, designated control law 005 by DERA, is one o f a n u m b e r of control laws being evaluated on the VAAC Harrier but it is unique in being multivariable. Multivarible control (MVC) has been heavily sold by universities to industry over the last ten years or so, but the industrial jury is still out as to whether they want to make the move away from so-called classical design. Control law 005 is important in that it is one of the few multivarible aerospace studies where all of the implementation issues have been addressed and flight testing carried out. To date, 005 has been used to demonstrate the practicality of the method. Assessment of benefits and flight clearance issues for multivarible control are on-going topics of research. The possible benefits of a multivarible approach are not just better performance a n d / o r robustness. MVC may also produce cost reductions through a more systematic design process. For the Harrier the benefits are going to be for transition and hover flight modes. At these speeds all three longitudinal motivators are used. The bandwidths at which the nozzles, engine and RCS are used are very close (between 2 and 5 rad/s), and this with the cross-coupling, makes conventional successive loop closing difficult. In practice it means that the three design loops are iterated on, and hence there is a time penalty. Furthermore, a modification to one loop later on in the design process is likely to affect other loops, and so the iteration penalty arises each time a change is made. Also, the structure o f the controller is limited compared to a multivarible controller, and hence performance a n d / o r robustness may be compromised. T h e benefits of MVC are likely to be much greater for the next generation of advanced short take-off and vertical landing (ASTOVL) aircraft which will have many more ways of generating and applying forces and moments. Such forces and moments will be generated by a combination of aerodynamic surfaces and by a complex power plant. The control law will need to integrate the flight and propulsion control systems giving rise to the concept of IFPCS (integrated flight and propulsion control systems), cross-coupling is likely to be high owing to physical design constraints. In particular, it is unlikely that the engine will act as closely to the centre of gravity as is the case with the Harrier. However, the Harrier does provide an ideal platform on which to demonstrate and evaluate the different design processes and controller architectures which will be appropriate to the next generation of aircraft. The next section introduces the VAAC Harrier and its longitudinal-control requirements.

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9.2 T h e V A A C H a r r i e r The DERA vectored thrust aircraft advanced flight control (VAAC) Harrier is a research aircraft sponsored by MOD which is being used to research control concepts in handling and control. The goal is to demonstrate that through the application of new approaches and design methods, a major reduction in pilot workload can be assured. More background information can be found in Reference [5]. The aircraft is a modified two-seater training aircraft; a safety pilot flies from the front cockpit and the test pilot flies from the rear cockpit. The test pilot flies the experimental flight control system (FCS) implemented on a hardware system which is monitored independently by a separate system. The monitor provides an envelope of flight parameters within which the aircraft is permitted to fly with the experimental FCS selected. The monitor follows the control law demands and returns control to the safety pilot if any predetermined parameter which makes up the flight envelope is violated or potentially dangerous situations arise. In this m a n n e r the experimental control law is not required to be safety-critical, and hence new ideas can be tried out without going through rigorous flight-clearance procedures. Figure 9.1 shows a schematic diagram of the aircraft. On a typical approach to landing the pilot will attempt to maintain a steady flight path (GAMMAD) while decelerating to the hover alongside the ship. To do this he has to alternately move the nozzle and throttle levers with his left hand while stabilising the aircraft in pitch with his right hand. Movements to nozzle and throttle couple into pitch requiring compensation from the stick. The objective of the experimental control law is to take care of this coupling and give the pilot two primary commands, namely speed demand and flight-path demand. A control law with this strategy is called a two-inceptor law. From Figure 9.1 it can be seen that the control law has three primary surfaces with which to control the longitudinal motion, namely throttle, nozzle and tailplane. The tailplane back drives the reation control system when the nozzles are down. The three degrees of freedom are used to control pitch attitude, forward speed and vertical speed.

9.3 Hoo Loop shaping For 005 a particular type of H~0 control called H~ loop shaping is used which was originally developed by Glover and McFarlane [6]. This design approach is particularly attractive in that the designer specifies the main loop shapes in the same way as for the classical design. The optimisation part (H0~) then synthesises the crossterms automatically as well as making any necessary changes to the diagonal terms. The structure of the control law for a threeinput three-output system is shown in Figure 9.2. The WI(1,1), W1(2,2), W1 (3,3), W2(1,1), W2(2,2), W2(3,3) are designed as if designing a classical

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An H~ loop-shaping design for the VAAC Harrier

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353

Alternative implementation for loop-shaping controllers

controller, but without regard to cross-coupling. K~ is the H~-synthesised multivariable compensator. O f course, a good classical design relies on appropriate matching of i n p u t o u t p u t pairs, which is not always straightforward. For the VAAC this presents no p r o b l e m once nozzle and throttle are resolved into normal ( T z) and forward (T~) thrust demands. Once input--output pairs are matched, the Bode plot for each loop is examined and the required low frequency gain, roll-off rate at crossover and high frequency roll-off rate are set by choosing a p p r o p r i a t e dynamic pre- and postcompensator terms. T h e designer is not restricted to diagonal weights (i.e. weighting terms which do not crosslink different loops), and in general the structure for the closed loop is shown in Figure 9.3. Note the DC gain correction in the forward path for the references, r. This is required to ensure that the y tracks r in the steady-state. In practice it may not be clear how to design off-diagonal terms in W 1 and W 2, although there is some recent research which suggest ways in which this can be d o n e [7,8]. For most designs, the loop-shaping exercise can proceed in the same m a n n e r as for a classical design. Once the plant is shaped, the robust multivarible compensator, K:~, is synthesised. This c o m p e n s a t o r makes the closed loop robust to uncertainty in the shaped plant. To do this the weighted plant is expressed in a particular mathematical f o r m referred to as normalised coprime factorisation (NCF), WzGW1 = M-1N. T h e factors M and N are stable rational transfer functions satisfying the normalisation constraint MM* + NAt* =/. The synthesised controller maximises the robustness to additive uncertainty on the factors as illustrated in Figure 9.4. The optimisation minimises the H~ n o r m of the transfer function from u to eI and e2, the H a n o r m being defined by:

I[PI[~: = sup 6-[P(jto)] i.e. it is the maximum-singular value over frequency. T h e small-gain t h e o r e m says that, to destabilise the closed loop, the total loop gain through the A blocks and closed loop must be greater than one. By making the transfer function from u to e1 and e2 as small as possible, the size o f AM and A N required to destabilise the loop is increased. By writing out the transfer function from d 1 to e1 and e2 it can be shown that the optimisation minimises the cost function:

354


e2

et

N(s)

Figure 9. 4

M(s)-'

Coprime factor uncertainty

1/ema x =

inf [/]

stab sing K

K

(I+ GK)

T h e value of emax is thus the H a n o r m b o u n d on the size of A M and AN which can be tolerated. It is used as a design indicator, m u c h in the same way as gain and phase margin are for classical single-loop design. A small ema× indicates that the specified loop shapes are inconsistent with the r e q u i r e m e n t of good robustness. For the purposes of design it is not necessary to have a detailed knowledge of the mathematics behind the method. The optimisation can be solved using standard functions available in the Matlab toolbox Mutools [9] which uses the state-space solution of Reference [4]. T h e designer's efforts are thus primarily directed towards selecting appropriate weights to make the trade-off between system p e r f o r m a n c e and robustness as indicated by the value of e.

9.4 Linear design for the VAAC In this section the linear design for the hover is described. In total, to cover the flight envelope between 0 and 250 knots, four linear designs were carried out. Full details of these can be found in Reference [2]. To reduce the d e p e n d e n c y o f linearisations for a given airspeed on nozzle angle, instead of working with inputs of thrust magnitude and thrust direction, resolved thrust d e m a n d s are used, i.e. if Taem and 0n represent thrust d e m a n d and nozzle angle d e m a n d , then the resolved thrust d e m a n d s are: 7~ = Ta~× cos(O.)

T~ = Ta~ x sin (0.)


355

Given the three p r i m a r y inputs (throttle, nozzle and tailplane), three outputs can be controlled. In the hover the pilot wishes to control pitch and forward and vertical velocities. H e n c e the output feedback variables selected are: Yl = q + A00 y2=~+Axxx Y3 = £+ A~x £ Each has the structure of stabilisation variable+ A × hold variable. The stabilisation variable sets the loop shape at the open-loop crossover, and is a high-integrity measurement. T h e hold variable sets the low frequency (longterm) response, and is not critical to the stabilisation and dynamic response o f the aircraft. With the inputs and outputs thus defined, the p r o c e d u r e of Reference [1] is followed for the design: (i)

Scale the inputs. T h e throttle d e m a n d limits are: 0.26< Tdem< 1.0 H e n c e both T x and Tz vary roughly in the range 0 to 1. T h e tailplane d e m a n d (r/) can vary in the range: - 11.75 < r/< 12.75

(ii)

(iii)

and is scaled times ten so that the d e m a n d is now expected to vary roughly in the range - 1 to 1. Note that this scaling is only necessary when interpreting closed-loop transfer functions at the plant i n p u t the scaling is lost in the weight W 1 in stage (vi). Scale the outputs. T h e outputs are scaled so that one unit of coupling into any of the scaled outputs is as equally undesirable. T h e horizontal and vertical acceleration outputs are scaled in units of g, the acceleration due to gravity. T h e pitch rate, QD, is scaled x0.1. T h e interpretation of this is that a coupling of 0.1 g (ten per cent of the m a x i m u m achievable in any direction due to powered lift) is as equally undesirable as the pitch attitude wandering off at 1 ° per second. Bandwidth requirements and restrictions. T h e m a x i m u m frequency up to which each actuator can be used may be d e t e r m i n e d by a n u m b e r of factors including the speed of the dynamics, rate limits and modelling uncertainty. From such considerations the following limitations can be derived: • throttle/engine: up to 2 rad/s, the limiting factor being the severe nonlinear nature of the fuel-to-thrust characteristic, and the rate limit when spooling up from low engine power; • nozzle: up to 2 rad/s, the limitting factor being the nozzle a i r - m o t o r backlash. • tail/reaction jets: up to 5 rad/s. The limiting factor here is the high

356

(iv)

(v)

Flight control systems phase roll-off rate above this frequency owing to the combined effect of the computational delay, the anti-aliasing filters, the actuation dynamics and the sensor dynamics. Attempting to put in significant phase advance above 5 rad/s would lead to a control system with very poor robustness in that the combined modelling uncertainty from all these effects would be very large. There is also a lightly d a m p e d mechanical control run which back-drives the front reaction jet from the tailplane setting. This also makes it difficult to use bandwidths much above 5 to 10 r a d / s when in the hover. Note that if different bandwidths are used for the throttle and nozzle, then the bandwidths at which the resolved thrust demands are used will be d e p e n d e n t on nozzle angle. This would thus necessitate making the controller a function of nozzle angle as well as airspeed. Sensor models and second-order Pad6 approximations to represent computational delays and anti-aliasing filters are added to the linear model. For the purposes of design, the sensors, Pad6 approximations and actuators are cascaded together and approximated with equivalent low-order actuator models using balanced truncation. The sensor models can be pulled through to the input like this because all three sensors are modelled with the same dynamics. Extra first-order sensor filters with poles at - 20 r a d / s are added to all three outputs. These were also included within the model reduction. The model reduction keeps the order of the controller down without unduly compromising the robustness of the final closed-loop system. Conventionally, model reduction is p e r f o r m e d on the complete weighted design plant. Here we cannot do this as the structure of the weighted plant A matrix must be invariant between design points so that the gain-scheduling procedure can be carried out. In other words, we can only model reduce the dynamics that are invariant between design points when using balanced trunction. Plot the plant singular values and all plant i n p u t - o u t p u t pairs to determine which inputs affect which outputs and whether there are any output directions which are hard to control. Next, each of the loops is shaped in turn to have the required low frequency gain, high frequency roll-off and a roll-off rate in the region of 20 to 30 d B / d e c a d e at crossover. The weight: 7 3(s+ 0.5) 0 0 | S2

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Figure 9. 7 105 ft/s design: shaped pitch loop Aligning to achieve desired bandwidths. First a two by two c o n s t a n t align matrix is f o u n d to align the first two singular values at 2 r a d / s . Note that for a design in the hover this matrix is just the 2 x 2 identity matrix multiplied by a scalar. As airspeed increases, a step c h a n g e in horizontal thrust results in an ever-increasing vertical acceleration as well as a f o r w a r d acceleration due to increased lift at increased speed. T h e align matrix counters this, a n d h e n c e improves d e c o u p l i n g o f the final closed loop. T h e align matrix is filled out with a (3, 3) e n t r y to give the desired crossover for the pitch output. If this align matrix is d e n o t e d Wa, then the overall p r e c o m p e n s a t o r is given by W1 = WpWA. Figure 9.8 shows the singular values o f the s h a p e d p l a n t with the fullo r d e r actuator, sensor a n d c o m p u t a t i o n a l delay m o d e l s s u p e r i m p o s e d on the s h a p e d a p p r o x i m a t e d plant. It can be seen that the approxim a t e d p l a n t is close to the full-order plant a r o u n d crossover, a n d that the specified bandwidths have b e e n achieved. (vii) Calculate the o p t i m a l controller. T h e o p t i m a l Ymin=l/gmax is 2.54 indicating that the specified loop shapes are consistent with r o b u s t stability (y < 4 is usually taken to indicate an acceptable design). After setting y to ten p e r cent suboptimal, the achieved l o o p - s h a p i n g cost function when evaluated with the full-order p l a n t (i.e. not the design plant) is 3.34. (viii) T i m e - r e s p o n s e analysis. Figures 9.9-9.11 show responses to step d e m a n d s on the references. Clearly a high d e g r e e o f d e c o u p l i n g has b e e n achieved, a n d the t i m e - d o m a i n p r o p e r t i e s look good. T h e

(vi)

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references are fed into the loop using the a p p r o a c h p r o p o s e d in Reference [10]. This is essentially i m p l e m e n t i n g the controller as an observer which has an H-infinity filter plus LQR static feedback. References are then fed in on the output of the state feedback matrix. In Reference [10] it is shown that the closed-loop response in this case is equal to N and that the response is both desirable and robust to coprime factor plant uncertainty.

9.5 Implementation and flight testing 9.5.1 Gain scheduling In Reference [11] it was shown that the controller resulting from loopshaping a p p r o a c h can be written as an exact plant observer plus state feedback:

~ = A~ + H( C~- y) + Bu u=F~ where [A,B,C] is a state-space realisation of the weighted plant, H = - ZC*, and F = B' ( y - 21 + y - 2 X Z - I) - IX where X and Z are the associated control and filtering algebraic Riccati equation solutions [6]. In general, H~ controllers cannot be written as exact plant-state observers

360

Flight control systems Sic on horizontal g 1105feet/sec, 8 al }ha 1.2r

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Figure 9. 9 105 ft/s design: step demand on forward motion as there will be a worst disturbance term entering the observer state equation as shown in Reference [4]. However, for the loop-shaping controllers it is possible, and the clear structure lends itself to gain scheduling in that the F and H gains can be scheduled as a function of aircraft forward speed. Figure 9.12 shows a block-diagram implementation of this. In o r d e r to be able to interpolate between gains we must have: • the shaped plant matrices A,B,C varying smoothly with operating point; • the controller F a n d H g a i n s varying smoothly with operating point. Knowledge of the physical system to be controlled should be used to check that the first condition will not be violated. It can be seen that the second condition will be satisfied provided that the Riccati solutions X and Z and the y vary smoothly as A, B and C vary smoothly. Reference [12] shows that this is indeed the case.

9.5.2 Anti-windup T h e observer structure can also be used to ensure that controller states do not wind up when plant inputs (e.g. throttle) saturate. If, instead of using controller outputs, the actual plant inputs are used to drive the observer, then the controller states will remain consistent with the plant states. Figure 9.13 is a block diagram of the plant, weights and the controller in observer form.

An Ha loop-shaping design for the VAAC Harrier

361

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105 fl/s design: step demand on vertical motion

With the implementation shown, windup will still occur as the observer is driven by u rather than the actual limited plant inputs. If, however, we replace Gw (enclosed in the dotted lines) with the block diagram in Figure 9.14, then both W1 and the feedback controller will be protected against windup. To see that the feedback controller is desaturated is e a s y - - i t is driven directly from actual plant inputs via W- ] which is the same as driving it with ~2where ~2is the value of u which would have given plant input up had the system been completely linear. W1 has been replaced with a Hanus [13] self-conditioned form, Ws. If the state-space realisation of W1 is given by:

Then:

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362

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function from u to Up is W1. In the event of saturation, the i m p l e m e n t a t i o n of W s is equivalent to r u n n i n g W1 backwards on up, i.e. the states will always be consistent with current plant inputs. H e n c e the desaturation action. Control law 005 also has an align matrix, M. Taking this into account, the overall scheme can be i m p l e m e n t e d as:

Note that both M and M - 1 are required for the implementation, but the desaturation scheme does not increase the degree of the weighting function.

9 . 5 . 3 Flight modes So far only the feedback c o m p e n s a t o r has been discussed. C o m p e n s a t o r terms between the pilot inceptors and the control law closed loop are also needed. As these are c o m m o n to any design (not just multivariable and H~ designs), they are not described in detail here. Full details can be f o u n d in

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Figure 9.14 Self-conditionedform of the precompensator Reference [2]. Figure 9.15 gives overall plan of the flight modes. As this is a two-inceptor law, the left and right hands only have one function at any given flight condition. The extra degree of freedom, namely pitch attitude, when using, the powered lift is controlled via a trim switch on the stick. In normal operation the pilot would not need to use the trim switch. The left hand commands ground speed up to the first blend region, and airspeed beyond. The right hand commands vertical acceleration with a height rate or height hold. Above the blend region the stick commands qwith an attitude hold. This allows the pilot to make full use of available aerodynamic lift.

9.5.4 Flight testing The control law was first tested on the VAAC Harrier in 1993 and engaged first time without significant transients. For the control law to be engaged, it must be demanding actuator positions within ten per cent of their actual positions. The observer/Hanus off-line conditioning used ensured that the demands were close, and it was c o m m e n t e d that the control law engages very quickly. For the first part of the flight no inertial reference signals (IRS) were used by the control law, i.e. only aerodynamic plus signals derived from accelerometers and gyros were used. These signals are inherently more noisy than those generated by the IRS. The control law coped well with both sets of signals, but, as anticipated, performance was much smoother using IRS data. Flight-path changes were achieved accurately and with ease by the pilot, and flight-path wander after releasing the stick was approximately a quarter of a degree. T h e r e was no sign of the onset of instabilities during the flight. This is testament to the control law having sufficient robustness to differences between the design model and the aircraft. For first flight trials, the tests carried out went very smoothly. This may in part be seen as a result of the coprime factor uncertainty modelling being appropriate for the actual uncertainty e n c o u n t e r e d between the model and the aircraft.

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9.6 Flight clearance T h e aim of this Section is to discuss clearance issues which may specifically arise for multivariable controllers. T h e discussion has b e e n written for readers with no background in state-space and multivariable methods. To start with we n e e d to define precisely what we m e a n by multivariable. Figure 9.16 shows a representation of classical control structure for the longitudinal control of the Harrier in powered-lift mode. The elements Kll, K22 and K ~ are single-input single-output (SISO) compensators for the pitch loop, forward-speed loop and vertical-speed loop. Typically, they will contain integral action and phase-lead compensators. The e l e m e n t G contains everything else, i.e. the rest of the control law and the aircraft model. G will thus contain m e a s u r e m e n t filters and blending of feedback variables. A multivariable system is one in which there is significant cross-coupling through G, i.e. putting a disturbance on one of the inputs to G results in significant responses to m o r e than one output. This coupling occurs through the airframe a n d / o r power plant, e.g. a thrust change at 100 knots will affect airspeed, flight path and pitch attitude. Most systems are multivariable to some extent, but when the cross-couplings are small, the designer can ignore t h e m and design Kll , K22 and K33 individually. Consider the case where the cross-terms are significant. T h e n with the structure shown in Figure 9.16 we have a multivariable system with a set of single-input single-output compensators. This is sometimes referred to as a diagonal compensator, the reason for which can be seen from the way that the c o m p e n s a t o r terms are laid out in Figure 9.16. It is intuitive that if the plant G is multivariable and contains cross-terms, then the best c o m p e n s a t o r that


367

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Figure 9.17

SISO control law structure with a crossterm

,[ C(s) Figure 9.18

v D

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we can find should also have cross-terms, i.e. the compensator should have off-diagonal terms. Very often such terms are included in a classical design, and are added to mirror the cross-coupling structure within G. This is the case with most roll-yaw compensators which have the structure shown in Figure 9.17. A compensator that has these cross-terms is a multivariable compensator in terms of its i n p u t - o u t p u t response. For classical design methods, design of cross-terms is often an ad hoc process of iteration along with the design of the diagonal elements. The more coupled the system, the harder is the design problem and the more iteration required. A multivariable design m e t h o d is one in which the compensator crossterms are designed in a systematic way as part of the design process. Multivariable design methods do not usually produce the final controller in the form of separate SISO compensators as in Figure 9.17. Instead, they produce a single multivariable implementation o f the compensator. Figure 9.18 shows a block-diagram representation of a multivariable dynamic compensator. The input u and output y are vectors of input and output signals, respectively. The multivariable compensator can either be represented as a transfer function K(s) (or equivalently K(z) in the discrete time domain) which is made up of polynomials in s, or in state space. A discrete-time state-space description of K(z) is given by: Xn+1 = Ak Xn + BkUn

368


y.= Ckx. + Dku. T h e matrices Ak, Bk, Ck and D k contain real rational elements. T h e vector Xn is called the state vector, and its length is referred to as the o r d e r of the controller. T h e first equation is the state-update equation, and is executed once every sample period. The second equation is the output equation, and this too is u p d a t e d once every sample period. Clearly, i m p l e m e n t a t i o n requires no m o r e than standard addition and multiplication using indexed elements within arrays. Two-dimensional array handling is required to access the elements of Ak, Bk, Ck and D k. A short-hand notation for the state-space equations is:

L q I a~ Consider a two-input two-output multivariable state-space system with r states. T h e n B k can be partioned as:

[BklBk2] where Bkl and Bk2 are single-column vectors of length r. Similarly, Ck can be partitioned as:

% where Ckl and Ck2 are single-row vectors of length r. Finally, D k can be partitioned as:

DkllDkl2 ] Dk21Dk22 where Dkl 1, Okl2, Ok21and Dh22 are scaler numbers. Because of the principle of linear superposition, the two-input two-output multivariable system:

Ck]Ok is identical to the four SISO systems defined in Figure 9.19. C o m p a r i n g with Figure 9.17 it can be seen that Figure 9.19 has the same structure as that of a classical design with cross-terms. T h e discussion so far has had the objective of showing the relationship between a multivariable controller and a classical controller with cross-terms.

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Since a multivariable control law is equivalent to a classical control law with cross-terms, it can be seen that the clearance issue can be divided into the following two sub-issues: (i) stability and performance analysis of highly coupled feedback loops; (ii) implementation of the control law in multivariable state-space form. The first issue (which in the author's view is the harder and much more important one) is really a feature of multivariable systems as opposed to multivariable controllers. It is the large cross-coupling within the power plant and airframe which makes the design challenging, and this is what multivariable design methods are aimed at. A good design approach will provide a systematic approach to this cross-coupling that will reduce design iteration and give confidence that the design is not conservative in terms of achievable performance and robustness. For 005, the Ha optimisation step which finds the compensator returns the robustness indicator, ~ This indicator is used in the same way as gain and phrase margin are for classical control. In the single-input single-output case, e can be related to guaranteed levels of achieved gain and phase margin; the bounds are shown in Figure 9.20. Hence, one way forward might be to replace gain and phase requirements currently used in the clearance-requirements d o c u m e n t with bounds on e.

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An H= loop-shaping designfor the VAAC Harrier

371

The implementation issue is essentially that of whether (perhaps highorder) state-space compensators can be used. Flight control law 005 has 20 states, and compared to a classical control law this could be viewed as high. However, when it is considered that the compensator is three-input threeoutput, approximatly two states per input-output pair does not seem unreasonable if the crossterms are providing better robustness and possibly reduced design times. As well as relative complexity, numerical issues also need to be addressed. State-space implementations for a given input-output response are not unique, and appropriate scaling of the state variables is important. When scaled propely a state-space implementation should be just as numerically reliable as a set of SISO state-space descriptions. In conclusion, this section has tried to relate multivariable compensators to classical implementation structures. Hopefully it has been demonstrated that the idea of cross-terms is not new, but the way in which the compensator is designed and implemented is. With the advent of highly multivariable (i.e. crosscoupled) aircraft, it could be argued on stability grounds that multivariable stability measures should be required for clearance. At the very least, these measures will streamline the design process which will be important for keeping down development costs. The issue is thus clearance of multivariable aircraft as opposed to multivariable control laws.

9.7 T h e way ahead The Ha loop-shaping method used for flight control law 005 has been around now for some time, and it seems appropriate to say something about the more recent developments in control theory. A substantial amount of recent research has centered around two methods, namely the methods of nonlinear dynamic inverses (NDI) [14-15] and linear parameter varying (LPV) [16-19] plant descriptions. Both are still evolving, and may offer benefits to the flight control systems designer in terms of both performance and design time. In particular, both methods have the goal of designing for the complete flight envelope in one step without the need to carry out spot point designs followed by ad hoc gain scheduling. The NDI method appears attractive in that it is a very simple idea, and hence is easy to pick up and apply. It essentially involves differentiating the elements of the nonlinear output equation until a term containing the control input appears. The equations are then manipulated into the integrator decoupled form, and assigned to desired pole locations. The difficult part of the design is deciding how to assign the poles of the inverted system. Although it may be easy to get a design which works, gaining an understanding of how the pole assignment affects robustness and performance may be quite elusive. Thus the final design may require significant iteration, and may also be nonoptimal.

372


T h e LPV m e t h o d involves writing the aircraft model as a linear parameter varying plant description. For example, this LPV description might be a function of Mach n u m b e r and incidence. Performance is specified as with a standard H0~ design, and hence classical loop-shaping ideas can be used. An LPV controller is then synthesised which is d e p e n d e n t on the same parameters as the LPV plant. The synthesis of the controller requires the solution of a set of linear matrix inequalities (LMIs) [20,21] for which there are a n u m b e r of commercially available solvers. Currently finding the solution to moderately-sized problems requires significant computing effort. However, the control law complexity is the same as that of the original LPV plant. T h e theory behind the m e t h o d is somewhat involved, but as with standard Ha methods a full understanding is not needed to use the methods effectively. For flight-clearance purposes, the norm returned by the LPV m e t h o d should be sufficient to indicate an adequate robustness margin. Because a single test can be used for the whole flight envelope, the stability-analysis process is very straightforward. Furthermore, the framework allows analysis of rate of change of gain effects, e.g. the effect of rapid incidence changes is automatically captured by the approach [19]. Clearance of an NDI law would require additional testing, particularly when dealing with highly crosscoupled airframes. The LPV/LMI design approach has been applied in a design study to part of flight control law 005 with good success, and it is the subject of ongoing research with the control law.

9.8 R e f e r e n c e s [1] HYDE, R.A.: 'The application of robust control to VSTOL aircraft.' PhD thesis, University of Cambridge, August 1991 [2] HYDE, R.A.: 'H~ aerospace control design.' (Advances in industrial control series, Springer Verlag 1995) [3] HYDE,R.A., GLOVER, K and SHANKS, G.T.: VSTOL first flight of an H~ control law', Comput. Control. Eng.J.,1995 6 (1) pp. 11-16, [4] DOYLE,J., GLOVER, K., KHARGONEKAR, P., and FRANCIS, B.: 'State-space solutions to standard/-/,2 and H~ control problems,'/EEE Trans. Autom. Control, 1989, 34 (8) pp. 831-847 [5] SHANKS, G.T., GALE, S., FIELDING, C., and GRIFFITH, D.: 'Flight control and handling research with the VAAC Harrier aircraft' (Advances inflight control series, Taylor and Francis, 1996) [6] McFARLANE, D.C. and GLOVER, K.: 'Robust controller design using normalized coprime factor plant descriptions' (Springer-Verlag lecture notes in Control and information sciences, 1990) [7] GU, D.W., POSTLETHWAITE, I., GOH, S.J., and CARTER, P.: 'Rx: an expert enviroment for robust control systems design'. Technical report 97-3, Department of Engineering, Leicester University, January 1997 [8] PAPAGEORGIOU, G. and GLOVER, K.: 'A systematic procedure for designing non-diagonal weights to facilitate H~ loop-shaping'. 36th IEEE conference on Decision and control, San Diego, USA, December 1997 [9] BALAS, G.J., DOYLE, J.C., GLOVER, K., PACKARD, A., and SMITH, R.:'/~analysis and synthesis toolbox for Matlab.' The MathWorks Inc, April 1991 [10] VINNICOMBE, G.: 'Measuring robustness of feedback systems' PhD thesis, University of Cambridge, December 1992 [11] SEFTON, J.A. and GLOVER, K.: 'Pole/zero cancellations in the general H~


[12] [13] [14] [15] [16] [17] [18] [19] [20] [21]

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problem with reference to a two block design', Syst. Control. Lett, 1990, 14, pp. 295-306 RAN, A.C.M. and RODMAN, L.: 'On parameter dependence of solutions of algebraic Riccati equations', Math. Control, Signals Syst. 1998, (1), pp. 269-284, HANUS, R., KINNAERT, M. and HENROTTE, J.L.: 'Conditioning technique, a general anti-windup and bumpless transfer method', Automatica, 1987, 23 (6), pp. 729-739 LANE, S.H. and STENGEL, R.E: 'Flight control design using non-linear inverse dynamics', Automatica, 1988, 24 (4) pp. 471-483 ENNS, D., BUGAJSKI, D., HENDRICK, R., and STEIN, G.: 'Dynamic inversion: an evolving methodology for flight control design', Int. J. Control, 1994, 59 (1), pp. 71-97 BECKER, G.S.: 'Quadratic stability and performance of linear parameter dependent systems'. PhD dissertation, University of California at Berkeley, 1993 PACKARD, A.: 'Gain scheduling via linear fractional transformations', Syst. Control Lett., 1994, 22, pp. 79-92 BECKER, G. and PACKARD, A.: 'Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback', Syst. Control Lett., 1994, 23 WOOD, G.D.: 'Control of parameter-dependent mechanical systems', PhD dissertation, Cambridge University, 1995 GAHINET, P. and APKARIAN, P.: 'A linear matrix inequality approach to H~ control', Int. J. Robust Nonlinear Control, 1994, 4, pp. 421--448, BOYD, S., EL GHAOUI, L., FERON, E., and BALAKRISHNAN,V.: 'Linear matrix inequalities in system and control theory', SIAM Studies in Applied Mathematics, Philadelphia, 1994

© British Crown Copyright, 2000/DERA. R e p r o d u c e d with permission of the Controller of H e r Majesty's Stationery Office.

Index

achievable vector space 312-315, 330 ACT (active control technology) 10, 11, 18, 199, 226, 237 active structural mode control 284-297 transient response 294-296 tuning 290, 291,294 actuation system modelling 107-116 failure transients 112, 114-116 jump resonance 112-114 linear 109 nonlinear 109 saturation analysis 110-112, 114 actuation system performance requirements 96, 98-107 dynamic stiffness 104-106 failure transients 105, 107 frequency response 100, 102-104 maximum rate capability 99-101 stall load 98, 99 actuation systems 90-117 failure transients 112, 114-117 jump resonance 112-114 performance criteria 96, 98-107 modelling 107-116 nonlinear fi~equency response 109, 110 saturation analysis 110-112, 114 technology 90-96 actuator drive 195, 196 actuator operation 91-97 control loops 96, 97 direct-drive electric motors 92, 93, 95 electrohydraulic servo valves 92-94 linear variable differential transformers 92, 94, 95 aerodynamic excitation forces 230, 231 aerodynamic models 202 aerodynamic stability derivatives 68 aerodynamic transfer functions 57

aeroelastic model 290 gain 285, 291 instability 16 aeroplane-body fixed axes 60, 61 aeroservoelasticity see structural coupling agile combat aircraft (ACA) 284, 285 A'Harrah-Siewert P I t criteria 154, 155 air-data system 20, 21, 34 Airbus aircraft 3, 12, 13, 27, 34-43, 307 A320 3, 13, 34, 35 A330 35-42 A3XX 43 control surfaces 35 flight control law modes 37, 39--42 flight control system 36-38 aircraft flutter 25 aircraft ground testing 209-213 electromagnetic-compatibility testing 211-213 engine-running tests 213 FCS build tests 210 ground-resonance tests 210 structural-coupling tests 210, 211 aircraft in-service requirements 13--17 aircraft modelling 56-89 aircraft-motion sensor unit 228, 240, 246, 247, 250 aircraft-pilot coupling (see pilotinduced oscillations) aircraft-response transfer functions 72, 73 airstream direction detector 239, 240 airworthiness 7, 173 CoA (Certificate of Airworthiness) 7 FAR-25 7 JAR-25 7 algorithms 115, 116, 311,324, 331 altitude mode 317, 322, 328

376


anti-aliasing protection 240, 241,246, 247, 356 antiwindup 360-364 ARINC 429 digital databus 36 ARINC 629 databus standard 42 ASTOVL (advanced short take-off and vertical landing) aircraft 33, 34, 348 asymptotic closed-loop structure 286-288, 290, 291 ATA 100 numbering system 29 attitude 65, 66 automatic flight control system architecture 184-196 configurations 188-190 flight control computers 189-196 flying control interfaces 184, 186 inner-loop stabilisation 184, 185 system interfaces 184, 187, 188 automatic flight control system design 170-196 aircraft dynamics 178 architecture 184-196 configuration control 176 costs 183, 184 design and test methodology 174, 175 design considerations 178--184 development programme 170-174 environment 182 human interface 180, 181 maintainability 182 manufacturability 183 performance 181,182 physical constraints 182 reliability 182 requirements definition and verification 174-177 safety 176, 178, 180 testability 182 traceability 175, 176 automatic flight control system development programme 170-174 certification 173 critical design review 173, 174 final declaration of design and performance 173 hardware design 172 interface definition 172 preliminary declaration of design and performance 173 preliminary design review 173, 174 qualification testing 173 software design 172

study phase/vendor selection 170, 172 system definition 172 svstem integration and test 172, 173 automatic test equipment 210 autopilots 12, 27, 29, 33, 181,301-346 autostabilisers 198 autothrottle 27, 29 axes 59-67 aeroplane-body fixed 60, 61 body, 3, 4, 60, 61, 63-65 earth 59, 60, 65 transformations between systems 66, 67 wind 61, 63-65 bandwidth frequency 132, 134 bandwidth/pitch rate overshoot PIO criteria 156--158, 161-163 block diagonalisation analysis 287 Boeing aircraft 11-13, 27, 42, 151 Boeing 777 42, 151 built-in test 115, 116, 192, 205, 206, 209 continuous 115, 116 C-17 151 carefree handling 18, 218, 220, 221 supersonic 221 CCV (control configured vehicle) 10, 11 characteristic equation 76, 78, 84, 85 lateral 84, 85 longitudinal 76 characteristic polynomial 75, 84 civil aircraft 2, 6, 7, 12, 13, 15-20, 27-30, 34-44, 125, 301-346 automation levels 27-29 eigenstructure assignment 301-346 flight control system design 27-30 flight phases 17 fly-by-wire 19, 20, 34-43 handling qualities 17, 18 in-service requirements 15-17 closed-loop control systems 96, 108, 116 cockpit design 23, 24, 37, 39 command and stability augmentation system 199 Concorde 12, 13 confidence testing 209 control-anticipation parameter 126, 127 control-augmentation systems 142-147 control effectiveness 249 control laws: see flight control laws

Index control-response relationships 57, 58 control surfaces 7-9, 90, 91 primary 90, 91 secondary 90, 91 control wheel steering 12 controls fixed manoeuvre point 79 controls notation 67, 68 aerodynamic 67, 68 engine 67 Cooper-Harper scale 14, 119-121,132 coprime factor uncertainty modelling 353, 364 costs 6, 7, 46, 50, 51,183, 184 coupled-roll spiral 139 handling qualities 139 describing-function 261-265 dissimilar redundant components 30 dual-duplex architecture 29 dutch-roll mode 87-89, 139-142, 319, 323, 330 handling qualities 139-142 dynamic stick force per g, PIO criterion 154, 155 dynamic stiffness 104, 105 EAP (experimental aircraft programme) 10, 23--25, 200, 207, 208, 212, 217-223, 237-248 cockpit 23, 24 flight testing 217-223 structural coupling 237-248 systems architecture 208 EGPWS (enhanced ground-proximity warning system) 43 EH101 helicopter 180, 181,188, 189 eigenstructure analysis 307-310, 324, 328, 329, 345, 346 eigenstructure assignment 301,302, 307-346 algorithms 311,324, 331 available degrees of freedom 315 decoupling requirements 313-315 design cycle 316-331 output feedback regulator 310, 311 parametric 315 polynomial 315 RCAM 307-331 robustness requirements 314, 315 eigenvalues 308, 309, 311-315,317, 319-322, 326, 327, 329-331 eigenvectors 308-315, 317, 319, 320, 322, 326, 327, 330, 331 electromagnetic-compatibility testing 211-213

377

electromagnetic interference 211,212 engine failure 306, 335-338, 340 equations of motion 56, 57, 59-65, 68-77, 79, 80 angular relationships 63, 64 axes 59-67 decoupled small-perturbation 68, 69 lateral-directional asymmetric motion 69, 72 linearised small perturbation equations 59 longitudinal symmetric motion 68-72 perturbation variables 61-63 state-space form 69-72 equivalent control 288, 289, 296 equivalent systems 127, 130-133 mismatch 127, 131,133 equivalent time delay 131,132 Euler angles 65 Eurofighter Typhoon 3, 11, 30-33, 92, 178, 200, 220, 222, 223, 248-259 flight control system architecture 32, 33 flight tests 250, 251,254-257 primary flight-control actuators 92 structural coupling 248--259 F-16 307 F-18 127 F-104 G Starfighter 11 F-111 22 fail-op-fail-op philosophy 91, 92 fail-op-fail-safe 91 fail-safe 91 failure analysis 192 failure-detection algorithms 115, 116 failure-mode-effect criticality analysis 176 failure testing 206, 207 closed-loop 207 open-loop 206 failure transients 105, 107, 112, 114-117 FAR-25 17, 30, 40 fatigue life 235,246, 273 fault-tree analysis 176 flare mode 42 flexible-aircraft control surface excitation 226, 228-231 aerodynamic 230 inertial 226, 228-230 flexible-aircraft modal aerodynamics 230, 231,249

378


flexible aircraft modal dynamics 226-228 flexible aircraft modelling 275, 276, 279, 297, 298 flight clearance 366-371 gain 369, 370 phase margin 369, 370 robustness 369, 370 flight control computer data processing 189-196 actuator drive 195, 196 built-in test 192 control laws 194, 196 data latency 193 failure analysis 192 mode logic 193, 194 output routines 196 power-interrupt 190 sampling frequency 192, 193 sensor-data mixing 193 sensor failures 193 sensor management 192, 193 start-up 189, 190 flight control law development process 45--50 automatic code generators 47 costs 51 flight control law modes 37, 39-42 flare mode 42 flight mode 40-42 ground mode 39, 40 take-off mode 40 flight control law verification 204, 205 flight control laws 6, 17, 18, 23, 25, 26, 32, 33, 37-42, 202, 349, 350, 352, 362, 364-369, 371,372 multivariable 349, 366-369 flight control system build tests 210 flight control system design considerations 20-30 civil aircraft 27-30 military aircraft 20-27 flight control system development process 43-52: see also automatic flight control system development programme costs 46, 50, 51 digital 9 testing 197-223 V-model 44, 45 flight control system history 7-13 flight dynamics analysis 56, 59 flight envelope 3, 5, 6, 16-18 flight management systems 12, 27, 29

flight mode 40-42 flight-path angle 63 flight-path stability 136 flight-path time constant 124 flight-phase categories 119 flight simulators 202, 204, 205, 209 control law verification 204, 205 test flight rehearsal 209 flight test instrumentation system 209, 212 flight testing 197-209, 213-223, 250, 251,254-257, 364 EAP programme 217-223 Eurofighter 250, 251,254-257 facilities 213, 214 history 197, 198 in-flight analysis 200 Jaguar programme 21 4-217 VAAC Harrier 364 flutter-mode excitation equipment 214 flutter model 244, 245, 253, 258 fly-by-light 43 fly-by-wire 9-13, 17-20, 23, 24, 26, 30--43 benefits 17-20 mechanical parts 23 flying qualities: see handling qualities frequency-domain modelling 230 frequency response of actuation systems 100, 102-104, 109, 110 gain boundaries 102-104 nonlinear 109, 110, 112, 113 phase-lag boundaries 102-104 saturation analysis 110-112, 114 fuselage symmetric bending modeshape 228 gain 369, 370 gain scheduling 359, 360 gain stabilisation 258 generic faults 30 generic VSTOL aircraft model 349 Gibson's dropback criterion 134, 138 Gibson's PIO criteria 160-162, 163, 164 glideslope 342, 344, 345 ground mode 39, 40 ground-resonance tests 210 ground testing 201-213 aircraft 209-213 rig testing 203-209 guided-missile design 234, 235 H~ control design method 348-372 H~0 filter 359

Index H~ loop shaping 350, 352, 359, 363 handling qualities 119-167 control design concepts 147-150 coupled-roll spiral 139 dutch-roll mode 139-142 equivalent systems 127, 130-132 feedback 142-146 lateral-directional 136-142 longitudinal 121-136 multiple-input, multiple-output 146, 147 Neal-Smith method 132-138 phugoid 122, 123 pilot-induced oscillations 150-166 response types 147, 148 roll mode 136-139 short-period 123-127 spiral mode 139 Harrier aircraft 348-372 flight testing 364 longitudinal control 350, 351,366 heading mode 319, 323 helicopter modelling 73 helicopters 180, 181,184, 186, 188, 189 high-gain asymptote parameter for PIO prediction 152, 153 high-gain control 288 IFPCS (integrated flight and powerplant control systems) programme 33 impedance of actuation systems 104-106 in-flight analysis techniques 219, 221-223 air-data model validation 222, 223 structural mode excitation 222 industrial considerations 1-53 inertial excitation forces 226, 228, 230 inertial reference signals 364 input-mode coupling 327, 328 input-mode coupling vectors 310 integrated flight and propulsion control systems 349 programme 33 integration in the forward path 147, 149 integrity 26, 29, 30 internal measurement unit 250, 254 intersystem integration testing 207-209 iron bird 203 Jaguar programme 10, 11,199, 200, 203, 204, 207, 212-217, 220, 235,

379

236, 247 flight testing 214-217 structural coupling 235, 236, 247 JAR-25 17, 30, 40 jump resonance 112-114 landing-approach simulation for RCAM 339-343 capture of glideslope 342, 344 engine failure 340 final approach with windshear 343, 345 roll angle 341-343 turn 340-343 lateral-directional flying qualities 136-142

lift curve 78 lightning strike tests 212, 213 limit-cycle occurrence 277, 278 limit-cycle prediction 260-273, 281-284 aircraft system 265-269 amplitude 271-273, 281-283 frequency 282, 283 phase uncertainty 268--271 system modelling errors 281-284 limit-cycle prevention 273, 274 line-replaceable units 172, 173, 176, 188, 189 linear aircraft models 301,302 linear matrix inequalities 372 linear parameter varying 371,372 linear simulation 328-330 linear variable differential transformers 92, 94, 95 load factor limitation 40 load factors 16-18 loading limit 5, 6 Lockheed 12 longitudinal dynamics 124-127 longitudinal flying qualities 121-136 loop-shaping design 348--372 antiwindup 360-364 gain scheduling 359, 360 hold variable 355 loop shapes 356-358 stabilisation variable 355 low-pass filter 279 M2-F2 lifting body 152 Mach number 3, 5, 16, 17, 32, 41 McDonnell Douglas 11, 12 mean aerodynamic chord 306 mechanical flight control systems 7-9 MIL-F-9490D specification 242 MIL-STD-1797A 160

380


military aircraft 2, 6, 9-11, 13-15, 18-27, 30-34, 44, 90-117, 125, 127, 131,155, 199, 217, 223, 235-237, 248-259, 284, 285, 348-372 actuation system technology 90-117 classification 13 flight control system design 20-27 flight-phase categories 14 fly-by-wire 18, 19, 30-33 flying qualities 14 in-service requirements 13-15 operational states 15 modal damping 321 mode logic 193, 194 mode-output coupling vectors 309 model prefilters 150 Moore-Penrose pseudoinverse 311 multi-input multi-output methods 146, 147, 302, 307, 326, 345 multiplexing 92 multivariable compensator 353, 367 multivariable control 348, 349, 366-371 flight clearance 366-371 multivariable dynamic compensator 367 Mutools 354 NASA high alpha research vehicle 307 Neal-Smith method 132-138 Neal-Smith PIO criteria 157, 159 Nichols plot 230, 233, 243, 251,252, 258, 259, 285 nonlinear aerodynamic behaviour 22, 23, 34 nonlinear dynamic inverses 371,372 nonlinear frequency response 109, 110 nonlinear simulation of RCAM 331-343 landing-approach 339-343 nonlinear system theory 260-268 normalised coprime factorisation 353, 354 nose boom 214 notch filters 25, 149, 211,222, 231-234, 239, 241,244, 247-249, 279, 294-296 frequency response 232-234 Nyquist diagram 264, 265, 273, 274, 281 Nyquist stability criterion 230 open-loop gain 274, 278-283 operational states of flight control systems 15

Pl12 project aircraft 33, 34 Pad6 approximations 356 performance limit 5, 6 perturbation variables 61-63 phase advance filter 232, 234 phase delay 132, 134 phase lag 239, 241,247, 280 phase margin 369, 370 phase stabilisation 251-253, 258 phugoid mode 76, 79-81,121-123, 308-310, 313, 317 flying qualities 122, 123 pilot compensation 133, 1347 138 pilot control unit 180, 181 pilot-in-the-loop modes 6 pilot-in-the-loop simulation 49 pilot-induced oscillation criteria 151-165 A'Harrah-Siewert 154, 155 bandwidth/pitch-rate overshoot 156--158 category I 151,152 category II 164, 165 dynamic stick force per g 154, 155 Gibson phase rate 160, 161 high-gain asymptote parameter 152, 153 modal 152-155 Neal-Smith 157, 159 non-modal 155-164 Smith-Geddes 159, 160 pilot-induced oscillations 23, 150-166, 247 categories 150, 151 criteria 151-165 frequency prediction 162-164 rate limiting 164-166 susceptibility prediction 161,162 pilot workload 119 pitch angle 65 pitch normal law 40 pitching moment 4, 6 pitot static system 220 power-by-light 43 power-interrupt processing 190 proportional-plus-integral control 284 pseudoderivative feedback control 284-286, 289, 291,292, 295 control law 285, 286 sliding mode 289 quadruplex actuators 92 rate-limiting function 261-263 RCAM 302-346

Index control activity specifications 307, 338, 339 control problem 302-307 eigenstructure assignment 307-331 inputs 303 landing-approach simulation 339-343 nonlinear simulation 331-343 outputs 303 performance specifications 305, 306, 333-338 response characteristics 305 ride-quality specifications 306, 337 robustness specifications 306, 337 safety specifications 306, 307, 338, 340-342 states 303 trajectory 304 reaction control system 349, 350 real-time modes of behaviour 308--310 reduced-order models 76--80, 85, 87, 88 residue of mode 308 response to controls 74-89 dutch-roll mode 87-89 lateral 81-89 longitudinal 74-81 phugoid 79-81 roll-subsidence mode 85, 86 short-period pitching oscillation 76-79 spiral mode 86, 87 Riccati equation 359, 360 ride quality 306, 323, 337 rig testing 203-209 confidence testing 209 control law verification 204, 205 software validation testing 205-207 system-integration testing 207-209 test flight rehearsal 209 rigid-body aerodynamics 244 rigid-body control 284, 291-296 transient response 294-296 tuning 294 rigid-body dynamics 3 rigid-body stability 285 rigid flight control system design 239-250 feedback signal selection 239, 240 hardware 240 structural coupling 241-250 rip-stop ram design 92, 96 robust civil aircraft model: see RCAM robust flight control 302 robust inverse dynamics estimate

381

control 284, 288 robust multivariable design method 348-372 robustness 306, 314-316, 323, 326, 327, 337 robustness indicator 354, 369, 370 Rockwell/DASA X-31 experimental aircraft 11 roll angle 65 roll mode 136-139, 143, 319, 323 handling qualities 136-139, 143 roll normal law 41 roll-subsidence mode 85, 86 rolling moment, 4, 6 rudder lock 12 SAABJAS-39 Gripen 151 safety 6, 7, 15, 16, 30, 43, 176, 178, 180, 306, 307, 323, 338, 340-342 saturation analysis 110-112 sensor management 192, 193 SEPECAT Jaguar 198 servo-valve dynamics 108 short-period damping ratio 126, 128, 129 short-period mode 121,123--127 flying qualities 123-127 short-period pitching oscillation 76-79, 308-310, 313, 317, 328 sideslip 86 single-input single-output compensators 366-369 single-input single-output methods 301, 366-371 small-gain theorem 353 Smith-Geddes PIO criteria 159, 160, 162-164

software-development standards 30 software validation testing 205-207 spectral condition number 326 spiral mode 86, 87, 139, 319, 323 handling qualities 139 stability 2, 142-147, 242, 243, 249, 251, 252, 296, 297, 326, 327 stability axes 61 stability characteristics 73, 75, 84 stability margin 326, 327 stability modes 76 stall limit 3, 5 stall load 98, 99 start-up processing 189, 190 state-space formulation 56, 69-72, 361, 367-369, 371 stealthy aircraft 34

382


stick force 124-126, 131,142 stick prefilters 150 structural coupling 25, 210, 211, 222-298 active control 284-297 alternative clearance procedure 274-281 design examples 234-259 elements 226-234 future developments 260-298 structural-mode filters 275-281 open-loop gain 278-280 structural oscillations 24, 25 structural stiffness parameters 294 supersonic aircraft flight envelope 3, 5 supersonic performance 221,238 supersonic transport aircraft 43 T-38A aircraft 132 take-off mode 40 telemetry 213, 214, 219 temperature limit 5, 6 test rigs 203, 204 testing 197-223 aircraft 209-213 flight 197-209, 213-223 flight-control systems 197-223 ground 201-213 rig 203-209 Tornado aircraft 22, 199, 236, 237, 247 structural coupling 236, 237, 247 total vehicle management system 34 transfer-function matrix 73-75, 77, 81-84 lateral 81-84 longitudinal 74, 75, 77 transfer functions 57, 59, 72-75, 77, 78, 81-85, 121,122, 126, 142-144, 149, 156 aerodynamic 57 aircraft-response 72, 73 improper 73

lateral 81-85 longitudinal 74, 75, 77, 78, 121,122 transformations between systems of axes 66, 67 angular velocity 66, 67 linear quantities 66 transonic region 22 trimmed equilibrium 62 triplex redundant architectures 20, 92, 95 Tupolev 144 aircraft 12 turbojet engines 2 turbulence 41,306, 336, 337, 339 two-inceptor law 350, 364 two-input two-output multivariable system 368 unmanned air vehicles 34 VAAC (vectored thrust aircraft advanced flight control) programme 33, 348-372 flight testing 364 hover 354-356, 358 linear design 354-362 loop-shaping design 348-372 Vickers VC10 tanker aircraft 3 voter algorithms 115, 116 VSTOL aircraft 307 weather conditions 16 wind axes 61, 63-65 windshear 341,343, 345 windup 360, 361 X-15 number 4, 235 yaw angle 65 yaw normal law 41 yawing moment 4, 6 YF-16 152 YF-22 151 ylat mode 319, 323

FLIGHT CONTROL SYSTEMS practical issues In design and implementation

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