Research on the Controller of the Digital Cabin Pressure Regulating System Based on FIMF
Zhu Lei Fu Yongling
Zhao Jingquan
School of Automation Science and Electrical Engineering
School of Aeronautic Science and Technology
Beijing University of Aeronautics and Astronautics
Beijing University of Aeronautics and Astronautics
Beijing, China
Beijing, China
Email:
[email protected] experiences [3][4][5][6][7].The organization of this paper is as follows: In Section 2, working principle of digital cabin pressure regulating system system was introduced. The mathematical model was built in Section Section 3. In Section 4, the control strategy strategy of FIMF was proposed. pr oposed. Simulations Simulations are provided in Section 5, followed followe d by the conclusions in Section 6.
Abstract – Based Based on the cabin pressure regulating system characters of the nonlinear, larger inertia and time varying parameter, the arithmetic of fuzzy immune feedback (FIMF) was proposed to adjust PID control parameters real time and increase response and control capability of pressure loop, and using immune algorithm adjusting pressure loop control parameters real time which has optimizing performance and using fuzzy algorithm as operator function. The simulation results show that cabin pressure and pressure change rate satisfy the rule of environment control system, and the effectiveness of the new control strategy proposed in this paper was proved.
II. WORKING PRINCIPLE
Keywords – cabin cabin pressure control system, fuzzy immune feedback, environmentt control system. environmen
I. INTRODU INTRODUCTION CTION Cabin pressure regulating system is an important part of the air management system of aircraft, the performance of which effects the safety of the aircraft structure and the lives of crew directly. Cabin pressure regulating system should ensure that the cabin pressure and its rate of change to satisfy the specification requirement throughout the flight envelope. From Fro m now on, the cab cabin in pre pressu ssure re reg regula ulatin ting g sy syste stem m has undergo und ergone ne th three ree dev develo elopme pment nt st stage ages: s: pne pneuma umatic tic ty type, pe, electronic- pneumatic type and digital type. In our country, there the re are ma many ny pure pne pneuma umatic tic airc aircraf raftt cab cabin in pre pressu ssure re regula reg ulati ting ng sy syste stems ms sti still ll use used d in the airc aircraf raft, t, and rel relate ated d rese re searc arch h ma main inly ly co conce ncent ntra rate ted d on the im impr prov ovem ement ent of pneumatic structure, less on the digital control [1]. As an advanced cabin pressure regulating system for its strong stro ng adapta adaptabil bility ity,, the digit digital al cabi cabin n pres pressure sure regulating regulating system has been been widely widely used in many many kinds of aircraft, and and its core is the digital controlle controllerr [2]. With the rapid development of intelligent control, such a s the fuzzy control, control, n eur eural al netw network ork and expe expert rt sy systems stems were used in many systems. The fuzzy control and expert syste systems ms were we re wi widely dely used in many fields fields be becau cause se it nee needn dn’t the precis pre cisee mat mathem hematic atic mo model del and ca can n sim simula ulate te the huma human n 978-1-4244-5848-6/10/$26.00
©2010
IEEE
The digit digital al cabi cabin n pres pressure sure regulating regulating sy systems stems mainly includes inclu des cabi cabin n pres pressure sure cont controlle roller, r, sele selecto ctorr pane panel, l, ele electric ctric exhaust valve, cabin, etc (as shown in Figure 1). The cabin pressure press ure controller controller cont control rol the pres pressure sure and its cha change nge rate inside the cabin through outputting signal to drive th e electric exhaust valve. The outflow of cabin air flow is controlled because of the changing of the exhaust valve opening. The electric exhaust valve is butterfly structure. The actuators were we re ins instal talled led on the fr frame amewo work, rk, co consis nsists ts of thre threee DC brushless motor, drive control circuit and gear institutions.
Fig.1. Digital cabin pressure regulating system
III. MATHEMA MATHEMATICAL TICAL MODEL
A.
Cabin
The control object of cabin pressure regulating system is the cabin pressure and its change rate. Before setting up the
454
cabin pressure differential equations, the following assumptions were used [10]: 1) The cabin temperature keep constant while pressure was adjusted; 2) The cabin volume keep constant; 3) The air in the cabin can be looked as ideal gas, and its pressure, temperature and volume satisfy the state equation of ideal gas; 4) The leakage area of the cabin is constant; 5) The leakage flow of the cabin is zero. Based on the assumption, the cabin pressure differential equations expressed as follows: VC dpc (1) = GK − GB RTc d τ Where, R is the ideal gas constant, V C is the cabin volume,
T c is the cabin temperature, GK is the gas flow of cabin, GB is the flow of the exhaust valve, adiabatic process flow formula can be used to calculate flow, for example : GB = μ B F B
0.156 pc
T c
1.43
⎛ ph ⎞ ⎜ ⎟ ⎝ pc ⎠
1.71
⎛p ⎞ −⎜ h ⎟ ⎝ pc ⎠
(2)
Where, μ B is flow coefficient, F B is exhaust valve flow area, pc is cabin pressure, T c is cabin temperature, ph is atmospheric pressure.
1.43 1.71 ⎤ ⎡ ⎢1.43 ⎛⎜ ph ⎞⎟ − 1.71⎛⎜ ph ⎞⎟ ⎥ ∂GB 0.156 pc ⎢ ⎝ pc ⎠ ⎝ pc ⎠ ⎥ = μ B F B ⎢ ⎥ 1.43 1.71 ∂ph T c ph ⎢ ⎥ ⎛ ph ⎞ ⎛ ph ⎞ ⎢ 2 ⎜ ⎟ −⎜ ⎟ ⎥ ⎝ pc ⎠ ⎝ pc ⎠ ⎣⎢ ⎦⎥
(6) This shows that the coefficient of the cabin pressure dynamic equations, with different flight, it is desirable to different values.
B.
Brushless DC motor
The dynamic equations of Brushless DC motor are expressed as follows: di (7) u = e + ia Ra + La a dt d Ω (8) Tem = TL + RΩ Ω + J dt Where, u ia e T em are input voltage, armature current, inductive electromotive force and electromagnetic torque respectively, La is armature inductance, Ra is armature resistance, T L is load torque, RΩ is drag coefficient,
Ω is rotor mechanical angular velocity, J is moment of inertia.
After equation (1) was linearized at the equilibrium point (with subscript 0), the available cabin pressure linearization
C. Gear deceleration machine
equation can be obtained as follows:
⎡⎛ ∂G ⎞ ⎛ ∂Gy ⎞ ⎛ ∂GK + ⎢⎜ B ⎟ + ⎜ ⎟ −⎜ dτ ⎣⎢⎝ ∂PC ⎠ 0 ⎝ ∂PC ⎠ 0 ⎝ ∂Pc
VC dδ pc RTc
⎞ ⎤ ⎟ ⎥ δ pc ⎠ 0 ⎦⎥
Ω1 =
Ω
(9) K Where, Ω is the mechanical angular velocity of rotor, Ω1 is the mechanical angular velocity of gear deceleration machine output, and K is the reduction ratio of reduction machine.
⎛ ∂G ⎞ ⎛ ∂G ⎞ ⎛ ∂G ⎞ = ⎜ K ⎟ δ pK + ⎜ K ⎟ ΔTK + ⎜ K ⎟ ΔF K ⎝ ∂PK ⎠0 ⎝ ∂TK ⎠ 0 ⎝ ∂F K ⎠ 0 ⎡⎛ ∂G ⎞ ⎛ ∂G ⎞ ⎤ ⎛ ∂G ⎞ − ⎜ B ⎟ ΔFB − ⎢⎜ B ⎟ + ⎜ y ⎟ ⎥ δ ph ⎝ ∂FB ⎠0 ⎣⎢⎝ ∂Ph ⎠ 0 ⎝ ∂P h ⎠ 0 ⎦⎥
D.
Butterfly structure exhaust valve
(3) t
Where: 1.43
0.156 pc ⎛ ph ⎞ ∂GB = μ B ⎜ ⎟ ∂FB T c ⎝ pc ⎠
α = α 0 + ∫ Ω1dt
1.71
⎛p ⎞ −⎜ h ⎟ ⎝ pc ⎠
1.43 1.71 ⎤ ⎡ ⎢ 0.57 ⎛⎜ ph ⎞⎟ − 0.29 ⎛⎜ ph ⎞⎟ ⎥ ∂GB 0.156 ⎢ ⎝ pc ⎠ ⎝ pc ⎠ ⎥ = μ B F B ⎢ ⎥ 1.43 1.71 ∂pc T c ⎢ ⎥ ⎛ ph ⎞ ⎛ ph ⎞ ⎢ 2 ⎜ ⎟ −⎜ ⎟ ⎥ ⎝ pc ⎠ ⎝ pc ⎠ ⎣⎢ ⎦⎥
(4)
0
(10) FB = F B max (1 − cos α )
(11)
Where, F B is exhaust valve flow area, F B max is exhaust valve maximum flow area, α is exhaust valve opening, α 0 is exhaust valve initial position.
E. Supplement equation
(5) According to the standard definition of atmosphere, the relationships between atmospheric pressure changes and height are [10]:
455
PH = P 0 (1 −
h 44330 (
)(
/ aR )
11000 − h
P H = 22613exp
6340
)
, h < 11000
Where K 2 is restrain gene, the sign is positive. f (⋅) is non-linear function, it introduces reaction function of kill and wound T cells and era ( k − d ) exterior matter.
(12)
, h ≥ 11000
(13)
The total stimulation of B cells acceptant is S ( k ) =T h(k ) −T s(k )
Where, h is the calculated atmospheric height from the sea level, a is the average temperature lapse rate, g is
(17)
The function of B cells come from the integral of S (k ) and
gravity acceleration.
the quantity of kill and wound T cells come from u kill ( k ) .
u kill ( k ) = K {1 − ηf [ Δu kill (k )]}ε ( k )
IV.DESIGN OF IMMUNE CONTROL
(18)
Where, K = K 1 and η = K 2 / K 1 , parameter K control the Biological immune system is necessary defense system for biology, especially for vertebrate and human. It can protect the body to resist invasion of pathogens, harmful foreign body and cancer cells etc. Lymphocytes are the most important immune system cells which include B cells and T cells mainly. The adjusting process of T cells can be defined as immune adjusting process of positive feedback and negative feedback respectively to identify and remove antigens and microbial cells as such an external substance, it is a h ighly evolved process of biological ad justment process, and the immune system possess the capability of learning, memory and pattern recognition by these process [8].
speed of responsion, parameter η has the function of stabilization. The performance of immune system is mainly depending on the selection of these p arameters.
B. Design of fuzzy immune PID controller Conventional PID controller includes the message of past, present and future of error. The integration of immune controller and conventional PID controller can improve system performance effective [9,10]. Considering k as the hits of discrete dynamic system and exterior matter quantity as control error, the e(k ) defined as
e( k ) = yd (k ) − y( k )
A. Immune feedback mechanism The exterior matter quantity of era k is defined as ε (k ) = γε (k ) − ukill (k − d )
Where yd ( k ) is the anticipant output, y( k ) is the object system output. The IM controller is a variable gain P type non-linear controller getting by using quantity of u kill ( k ) of kill and
(14)
Where γ is the increase gene of exterior matter, u kill ( k ) is the kill and wound quantity of T cells, d is the death time. After stimulated by exterior matter T h (k ) , the output come from T cells is defined as (15) T h( k ) = K 1ε ( k )
wound T cells as control input. The IM controller of PID type K z − 1 can be get by replacing K p using K p (1 + i + K d , z − 1 z the function is
Where K 1 is stimulation gene, the sign is positive. Consider the restrain T cells forbid the action of other cells is used to feedback control, the suppose function of restrain T cells to T s (k ) of B cells is
T s(k ) = K 2f [Δukill ( k )]ε ( k )
+
u pid (k ) = K p {1ηf [ Δu (k )](1 +
+
K i z 1
+
+ K d
z − 1
K d is differential coefficient, η is restrain coefficient. The structure of IM controller is shown in figure 2. +
K p
_
+
K i
(20) e(k ) z − 1 z Where K p is gain coefficient, K i is integral coefficient,
(16) _
yd (k )
(19)
u (k )
z
K d ( z 1)
d
z +
z f ( )
1
_
u( k )
Fig. 2. Structure of IM controller
The choice of non-linear function f (⋅) has a tremendous impact to the form and effect of controller. The appropriate function description can not be given by conventional non-linear function because of time-varying, non-linear
characters of pressure loop. Fuzzy control is one of the most commonly used method in intelligent control, it does not depend on the mathematical model of control system and not sensitive to the changing of system parameters, and has the
456
characters of rapidity and strong robust, so it is suitable for the requirements of the pressure loop. The immune controller change to FIM (fuzzy immune) controller which has the self-tuning function after introduce fuzzy algorithm as non-linear function after introduce fuzzy controller to f (⋅) [9]. Since the fuzzy control is built based on rules and logic, the calculation will be increased caused by excessive amount of rules, fewer rules for the control of the controller will cause
rough description. Because immune algorithm has better optimizing capacity, therefore the simple and effective FIM controller can be got through establishing appropriate rules of the fuzzy controller. According to the character of pressure loop, the control rules has 49 items is shown in table 1.
Table 1. fuzzy rules
e(k)
NB
NM
NS
ZERO
PS
PM
PB
NB
NB
NB
NM
ZERO
ZERO
PS
PM
NM NS
NB NB
NM NM
NS NS
ZERO ZERO
PS PS
PM PM
PM PB
ZERO
NB
NS
NS
ZERO
PM
PB
PB
PS PM
NB NM
NS ZERO
ZERO PS
PS PM
PM PB
PB PB
PB PB
PB
NM
PS
PS
PB
PB
PB
PB
Δe(k)
Supply flow 6000kg/h Cabin leakage area 38cm2 Diameter of exhaust valve 353mm Resolution of pressure sensor 10Pa Resolution of position 0.1degree Gear reduction ratio 1/300 Maximum speed of motor 5000r/min Control period 100ms Exhaust valve flow coefficient 0.8 PID simulation results, see r eference [11]. The simulation results of cabin pressure and cabin pressure change rate using the FIMF controller are shown in figure 4 to figure 8.
V. SIMULATION The model of the digital cabin pressure control system was built in simulink(shown in fig3). The reference signal of the controller is the cabin pressure schedule AUTO which is computed under the flight profile BARO. FIMF is realized through S function of Matlab software. Position Controller is the model of brushless DC motor, motor driver control circuit and gear deceleration machine. Cabin_Press is the model of cabin. Pressure_Sensor is the model of the pressure sensor. The main simulation parameters are shown in table 2.
Fig.4. Flight profile
Fig.3. Control system model in Simulink Table 2. Simulation parameters
parameter Cabin volume Cabin temperature
Value 500m3 20
457
Fig.5. Cabin pressure altitude
VI.CONCLUSION Simulation results show that the cabin pressure regulating system performance was greatly improved by using FIMF controller than simple PID controller in the entire flight profile, and the steady-state error of cabin pressure less then 30 meters, the cabin pressurization rate less then 20Pa/s, the decompression rate less then 30.4Pa / s, the electric exhaust valve motion smoothly. Test results meet the specification requirement of the environmental control system. The effectiveness of that the FIMF control of cabin pressure regulator was proved.
Fig.6. Stable error
ACKNOWLEDGMENT The author wishes to thank the IEEE for providing this template and all colleagues who previously provided technical support. REFERENCES [1]
Wang Z. L.,Qiu L. H, Yu L. M., “Major Development Trends of Aircraft Hydraulic System”.Proceedings of the International Conference on Recent Advances in Aerospace Actuation Systems and Tang Jian, Zhang Xing-juan, Yuan Xiu-gan. Study of dynamic characteristics of new type of cabin pressure regulator [J].Aircraft Engineering, 2005, (4):45-49 [2] Furlong O D. Fluidic cabin pressure control system for military and civil aircraft [J].Aeronautical Journal 1971 (725)361-374 [3] KwongWA, PassinoKM, YurkovichS. Fuzzy learning systems for aircraft control law reconfiguration[A].Proceedings of the 1994 IEEE International Symposium on Intelligent Control[C].Colum bus:IEEE,1994.333-338 [4] VascakJ, KovacikP, Hirotak. Performance based adaptive fuzzy control of aircrafts[A].10th IEEE International Conference on Fuzzy Systems[C].Melboume:Insitute of Electrical and Electronics Engineers Inc,2002.761-764 [5] Chen G R. Conventional and fuzzy PID controllers: An overview. Int J Intelligent Control and Systems, 1996, 1(2):235-246 [6] Zhang Huaguang, Quan Yongling. Modeling Identification and control of a class of nonlinear system. IEEE Trans on Fuzzy Systems, 2001, 9(2):349-354 [7] Kawafuku M., “ Adaptive learning method of neural network controller using an immune feedback law ”. Advanced Intelligent Mechatronics, 1999. Proceedings. 1999 IEEE/ASME International Conference, pp. 641 – 646, Dec.1999. [8] Dong Hwa Kim, “Intelligent tuning of a PID controller for multivariable process using immune network model based on fuzzy set” Fuzzy Systems, 2001. The 10th IEEE International Conference pp.93-98, 2001. [9] Dong Hwa Kim, “ Auto-Tuning of Reference Model based PID Controller Using Immune Algorithm” Proceedings of the 2002 Congresspp. 483-488, 2002. [10] A. B ergman, W. Burgard, S. Hemker, “ Adjusting parameters of genetical gorithms by fuzzy control rules”. New Computing Techniques in Physics Research , World Scientific,Singapore, pp.354-358, Sep. 2002. [11] Lei ZhuYongling FuJingquan ZhaoDong Guo. Research on the Controller of the Digital Cabin Pressure Regulating System Based on the Fuzzy Gain Scheduling[C]. Proceedings of the 9th International Conference on Electronic Measurement and Instruments, 2009, V3: 494-498
Fig.7. Rate of cabin pressure change
Fig.8. Exhaust valve opening
The simulation performance comparison between the FIMF control and PID control is shown in Table 3. From table4, we can see the system performance has greatly improved by using FIMF controller in the flight profile. Table 3. Performance comparison of FIMF and PID control
Parameter Pr essurization r ate (Pa/s) Decompression rate (Pa/s) Stable error(m)
PID <40 <60 <30
FIMF <20 <30 <20
458
