Essential Process Control for Chemical Engineers.pdf

Essential Process Control for for Chemical Engineers Dr. Bruce Postlethwaite

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DR. BRUCE POSTLETHWAITE

ESSENTIAL PROCESS CONTROL FOR CHEMICAL ENGINEERS

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Essential Process Control for Chemical Engineers 1st edition © 2017 Dr. Bruce Postlethwaite & bookboon.com ISBN 978-87-403-1655-1 978-87-403-1655-1 Peer reviewed by Dr. Iain Burns, Senior Lecturer, Director of Teaching, University of Strathclyde



CONTENTS

CONTENTS Foreword

8

Introduction

9

Main Learning points

9

1.1

Why do we need control?

9

2

Instrumentation

12

Main learning points

12

2.1

What is an instrument?

12

2.2

Factors to be considered in selecting an instrument

13

2.3

Instruments for temperature measurement

17

2.4

Pressure measurement

20

2.5

Flow measurement

23

2.6

Level measurement

27

2.7

Chemical composition

30

1

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3

CONTENTS

Communication signals

32


32

3.1

Types of communication signal

32

4

Final control elements

39

Main Learning points

39

4.1

Control valves

39

4.2

Control valve sizing

41

5

Diagrams for process control systems

48


48

5.1

Process flow diagrams (PFDs)

48

5.2

Piping and instrumentation diagrams (P&IDs)

49

6

Inputs and outputs in control systems

55


55

6.1

Process inputs

55

6.2

Process outputs

56

6.3

Processes in control engineering

57

6.4

An example of variables and processes

58

7

Introduction to feedback control

59


59

7.1

Feedback control and block diagrams

59

7.2

Positive and negative feedback

61

7.3

Control loop problems

61

7.4

Direction of control action

64

7.5

Controller hardware

66

8

Introduction to steady-state and dynamic response

70


70

8.1

Steady-state gain

70

8.2

Dynamic response

73



9

CONTENTS

Dynamic modelling

87


87

9.1

Laplace transforms

88

9.2

Derivation of basic transforms

88

9.3

Solution of differential equations using Laplace transforms

91

9.4

Transfer functions

93

9.5

Block Diagrams

94

9.6

Block diagram algebra

95

9.7

Solutions of responses for high-order systems

95

9.8

Forming dynamic models

100

10

Analytical solution of real world models

106


106

10.1

Types of non-linearity

106

10.2

Linearisation of non-linear equations

107

10.3

Simplifying expressions through deviation variables

110

10.4

Procedure for simplifying and solving a non-linear model

112

10.5

Putting it all together – a reactant balance for a CSTR

112

11

PID Controller algorithm

117


117

11.1

Really simple feedback controller – on-off

118

11.2

Proportional-integral-derivative (PID) control

119

11.3

Proportional only control

121

11.4

Integral only control

126

11.5

Derivative action

127

11.6

Proportional-Intergral (PI) control

130

11.7

PID control response

131

11.8

Other forms of PID algorithm

133

12

Control system analysis

137


137

12.1

Analysis of a typical feedback control system

137

12.2

The PID algorithm as a transfer function

139

12.3

Analysis of proportional control of a first-order process

140

12.4

Example of a first order process under proportional control

142

12.5

Example of a second-order process under proportional control

145

12.6

Analysis of integral control of a first-order process

148



CONTENTS

13

Controller tuning

149


149

13.1

What needs to be done to tune a PID Controller?

149

13.2

How do you decide what is a good controller performance?

150

13.3

Some methods of controller tuning

154

13.4

Control loop health monitoring

161

13.5

Control loop diagnostics

162

14

More advanced single-loop control arrangements

163


163

14.1

Cascade control

163

14.2

Selective or autioneering control

167

14.3

Override control

169

14.4

Ratio control

172

14.5

Feedforward control

173

15

Design of control systems

181


181

15.1

Control envelope

181

15.2

Multivariable processes

184

15.3

How to determine the number of controlled variables

185

15.4

Plantwide mass balance control

191

16

Control system architecture

194


194

16.1

The effect of technology on process plant control rooms

194

16.2

Human factors in control room displays

197

16.3

Distributed control systems

200

16.4

Safety Instrumented Systems

201

17

Bibliography

202

Acknowledgements

203

Appendix

204

The use of software for teaching process control at Strathclyde University

204



FOREWORD

FOREWORD Tis book is based on the course notes from the introductory process control class at Strathclyde University in Glasgow, Scotland. Tis course is itself based on the IChemE model-curriculum for chemical engineers and covers the material that ALL chemical engineers are supposed know. Te IChemE curriculum was drawn up by a team of industrialists and academics, led by Professor Jon Love, in response to a recognised need for ch emical engineers to be taught a more industrially relevant course. Tis book isn’t a traditional academic textbook in that there are no references anywhere in the text. Te main reason for this is that the material has been gathered from many different sources after a working lifetime of teaching in the area and trying to identify an original source is impossible. I have included a bibliography for readers who wish to look further into the subject. I hope students and teachers find this book useful. A major new part of the course at Strathclyde University (where I teach) has been the introduction of new process control learning software called PISim, and this is described in the appendix. PISim will be commercially released in late Autum 2017.



1

INTRODUCTION

INTRODUCTION

MAIN LEARNING POINTS • Why process control is necessary Process control is concerned with making sure that processes do what they are supposed to in a safe and economical way. Tis isn’t an easy task as most processes are subject to many inputs called disturbances that constantly cause the controlled variables to move away from their desired values (or setpoints ). o prevent this other process inputs called manipulations have to be moved to restore the process to the desired state. Process control is concerned with the overall system. A control engineer has to know about the instruments used to measure process quantities, the valves and other final control elements that allow control systems to adjust the process, communications to transmit information around, the control algorithms that decide how to respond to the information coming from the process, and finally the control engineer needs to understand how the process itself behaves: not just its steady-state behaviour but more importantly its dynamic response. Control engineering is now an area which offers big career opportunities for chemical engineers. Te area used to be dominated by electrical/electronic engineers as the major challenges were in the hardware. Tis has changed. Sophisticated modern control systems allow much more complicated, process related, control schemes and now a major requirement for a control engineer is that they have a good understanding of the process.

1.1

WHY DO WE NEED CONTROL?

Figure 1 – a pressure trace from a SCADA system



INTRODUCTION

• In real chemical plants, steady-state doesn’t exist. Tings are always changing. emperatures move up and down, levels get lower and higher, etc (see figure 1). • All processes are subject to disturbances . Tese are inputs to the process that change in a way that is beyond the reach of the local control system. A rainstorm on the outside of a distillation column will cool the column and require action to be taken to increase the heat input. Raw material variations are another common disturbance. Actions of other control systems can also cause disturbances to the process of interest – if a control system upstream or downstream of a process reduces a flowrate its effects will cascade throughout the rest of the process. • Te control system needs to actively regulate against the effects of these disturbances. It does this by either measuring the disturbances directly (where this is possible and economic) or by measuring their effects on the controlled variables of the process. It then makes adjustments to other inputs to the process called manipulated variables to try to reduce or eliminate the effects of the disturbances. When controllers are holding controlled variables at fixed setpoints they are said to be in regulator or disturbance rejection mode. • Process don’t suddenly start at their flowsheet conditions, they don’t shut down on their own and don’t change production rate, etc without active intervention from control systems. When these major changes are being made to a process, the controllers will be acting in a setpoint tracking or servo mode. In servo mode, a controller will be trying to make the controlled variable track a moving setpoint. • Control systems also have a major part to play in process safety. Te basic control system will usually ensure that the process stays within acceptable limits and will be equipped with alarms to warn operators of any problems. Interlocks may also be present in the basic system. Tese are used to lock particular inputs when other conditions are in existence. For example, the access doors to a kiln may be locked by a control system if the internal temperature is dangerously high. In extreme circumstances, special control systems (called safety instrumented systems or SIS ) that are separate from the normal process control system may come into play. Tese may be local to a particular piece of equipment, for example a high-temperature trip on a pump motor; or may have a process or plant-wide focus, for example an emergency shutdown system.



INTRODUCTION

• Finally, good control saves money. Plants are normally operated close to constraints (e.g. the acceptable product quality). Poor control means more variability and this means that the mean value of a controlled variable needs to be held further from the constraint than is necessary with good control. Figure 2 shows a simple example – the tops quality from a distillation column. Tis may have a limit on the lowest acceptable composition and it’s the responsibility of the control system to hold the composition about this limit. If the control is poor and there’s lots of variability, then it will be necessary to set an average value of composition much higher than if good control is used. Tis higher average composition will lead to increased reflux going down the column and hence more vapour having to be generated by the reboiler, which increases steam costs.

Figure 2 – The advantage of good control



2

INSTRUMENTATION

INSTRUMENTATION

MAIN LEARNING POINTS • Factors involved in selecting instrumentation • echniques for temperature, pressure, flow and level measurements Te instruments on a chemical plant are the devices used to monitor the important variables that allow the condition of the process to be determined.

2.1

WHAT IS AN INSTRUMENT?

ransducers or sensors are the primary sensing elements. Tey are devices that convert some physical quantity that we want to measure (e.g. temperature, pressure, etc). into some sort of signal that can be processed further. For example, a thermocouple converts a temperature difference into a voltage; a piezo resistive pressure sensor converts a pressure into a change in electrical resistance.

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INSTRUMENTATION

Signal conditioning is the signal processing that is applied to the output of the transducer. Sometimes this could simply be amplification, but often more complicated things like linearisation are required (ideally, the output of a device should change linearly with changes in the quantity being measured). Modern instruments such as Coriolis flowmeters have very complicated signal processing build into them to detect the phase shifts in the motion of the sensing elements. A transmitter is a device that converts the output from signal conditioning into a signal that is compatible with the communication system being used in the plant. Tere are many different standards in use ranging from 4-20mA analogue signals up to digital Fieldbus systems – these will be discussed later. An instrument is a device that contains at least one but usually more, and often all of the above (transducer, signal conditioning and transmitter). An instrument is a complete measurement package that senses the quantity to be measured and presents that measurement in a form suitable for use (e.g. a simple instrument might be a Bourdon gauge for pressure measurement – the transducer, a helical metal tube, distorts with pressure and drives the gauge needle directly; a more typical instrument for modern chemical plants might be a packaged RD (resistance temperature device) – it will include the RD, signal conditioning, and a transmitter).

2.2

FACTORS TO BE CONSIDERED IN SELECTING AN INSTRUMENT

2.2.1 RANGE

Te range of an instrument is range of the measured quantity over which the instrument will give a reliable output. Te range is always the same or bigger than the span of an instrument. While an instrument with a large range might seem to be always desirable this isn’t usually the case in practice. Te sensitivity (change in output vs change in measurement) of transducers drops significantly in large range devices leading to reduced accuracy. 2.2.2 SPAN

Te span of an instrument is an adjustable parameter (there will be a button, screw or software link on the instrument that will allow the adjustment). Te span is the distance the measured quantity has to move to drive the instrument output from its minimum value to its maximum (remember that instrument outputs match communication standards which have fixed maximum and minimum values). By adjusting the span, t he instrument’s sensitivity (output change vs. input change) can be altered – large spans will lead to lower sensitivities.



INSTRUMENTATION

2.2.3 ACCURACY AND PRECISION

All measurement instruments are subject to random error – if you take repeated measurements of a fixed quantity you will always get a scatter of values about a mean. An accurate instrument is one where the mean is centred close to the actual value of the quantity being measured. An instrument can be accurate, but still have a significant amount of error on an individual measurement – the accurate mean can only be obtained by taking many repeat measurements. A precise instrument is one which, when measuring a constant quantity, returns output values which are very close to one another – the scatter between readings is small. It is possible for an instrument to be precise (high repeatability in measurement) but not accurate (with the mean some distance away from the true value of the quantity being measured). An ideal instrument is one which is both precise and accurate.

Figure 3 – accuracy and precision

2.2.4 REPEATABILITY AND DRIFT

In most instruments repeatability and precision mean the same thing. However, some sensors suffer from hysteresis . In these sensors the measurement is affected by what the variable being measured was doing prior to the measurement. It is most prevalent in systems which involve some sort of mechanical element in their sensing. For example, bourdon pressure sensors usually exhibit hysteresis – the measurement they produce will be different if the pressure was rising or falling immediately prior to the measurement. Drift is a medium to long term effect that causes some instr uments to lose mainly accuracy, but also possibly precision. For example, corrosion of a thermocouple will alter its thermoelectric properties and hence the voltage produced at a particular temperature.



INSTRUMENTATION

2.2.5 DELAY

Some instruments can take time to develop a measurement after the process is ‘sampled’. An example of these are chemical analysers – some of these are, in effect, automated analytical laboratories that can take several minutes to develop an output. Any delay in measurements for control can cause problems to a control system – the controller is looking at the process as it was some time in the past rather than where it is at present. In addition to delay, the instrument’s speed of response needs to be taken into account. A large resistance thermometer sensor will take much longer to respond to temperature changes than a tiny thermistor (this is simply because of the relative thermal capacities). 2.2.6 LINEARITY

Almost all commercial control systems are based around linear control algorithms and work best when controlling linear or nearly linear systems (a linear system is one where doubling a change in the input will produce double the effect on the output). Some transducers (e.g. orifice plates (see figure 4) and thermistors) produce outputs that are not linearly related to the quantity being measured. In modern instruments these signals will be linearised internally in the instrument, but high transducer non-linearity will reduce sensitivity in some areas.

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INSTRUMENTATION

Figure 4 – pressure drop/flowrate relationship for an orifice plate

2.2.7 CALIBRATION

Calibration involves matching the instrument’s span and zero to the quantity being measured. Tis will involve two or more standard measurements being made (for example, a pH meter would be calibrated using several standard buffer solutions) and the instrument adjusted. Calibration is a time consuming and sometimes difficult process. Many packaged instruments, such as RDs and pressure instruments, are factory calibrated and can be installed directly into the process. Others, like orifice plates, need to be calibrated in the field after installation. Some instruments, like pH meters, suffer from regular drift and need to be recalibrated on a routine basis. 2.2.8 NOISE

Noise is a random variation in the measurement signal. Noise can be generated by the process itself (e.g. by bubbles in the flow being measured by an orifice plate) or it can be generated in the measuring instrument or communication lines. If instrument generated noise is significant, then it’s better to pick the instrument that generates the least (see accuracy and precision above). 2.2.9 RELIABILITY

Instrumentation in a chemical plant needs to be highly reliable. Te measurements are used for control and ensure the safe operation of the process. Reliability specifications are usually provided on instrument data sheets and are often quoted as the mean time between failures (MBF). Tis data can be incorporated into a hazard analysis to decide whether instrument redundancy is required.



INSTRUMENTATION

2.2.10 SUITABILITY FOR PLANT

Te instrument must be capable of tolerating the physical conditions (e.g. temperature, pressure, vibration, etc.) that it will be exposed to and also be resistant to any chemical it is likely to come into contact with. Te instrument should also be compatible in an engineering sense with the rest of the plant – it should use similar thread sizes, flanges, etc, to other plant fittings and also have similar service (e.g. power supplies or instrument air) requirements to other plant devices. Finally, many companies tend to limit the number of suppliers they purchase from. Tis allows them to negotiate better deals and also allows more extensive stocks of spare parts to be kept. 2.2.11 COST

A cheap purchase price is not usually the best indicator of a good instrument choice. Te overall lifetime cost needs to be considered – more expensive instruments might last longer and require less frequent calibration. 2.2.12 BELLS AND WHISTLES

Since cheap microprocessors have come on the scene many instruments have a host of added features, such as averaging and storage of previous values. Tese are only useful if you actually plan to use them, but otherwise should be ignored when selecting an instrument.

2.3

INSTRUMENTS FOR TEMPERATURE MEASUREMENT

emperature measurement is one of the four most common measurements in a chemical plant (the others are pressure, flow, and level). 2.3.1 THERMOCOUPLES

A thermocouple is a sensor made from two wires with dissimilar thermo-electric properties (i.e. heat liberates electrons to different extents). Te wires are joined at each end and a small voltage is generated (by the Seebeck Effect ) which is proportional to the difference between the temperature at the two ends of the device

Figure 5 – A thermocouple



INSTRUMENTATION

Originally, the cold end of a thermocouple was kept at a constant temperature by sticking it in an ice and water bath. Nowadays, the cold junction is simulated by an electronic chip containing a thermistor and some fancy electronics. Te electronics also amplify the mV output of the thermocouple to something which is more usable in the rest of the instrument. It’s still possible to buy thermocouple wire (with two strands of dissimilar metals) for special applications, but the majority of industrial thermocouples are sold as packaged units with a transmitter attached (for example see figure 6). Different types of thermocouple are available that cover different ranges and have different applications – see table 1.

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INSTRUMENTATION

Thermocouple Type

Materials

Range

Comments

Type K

Chromel/Alumel

0OC to 1100OC

Very commonly used

Type T

Copper/Constantan

-185 OC to 300OC

Suitable for cryogenic applications

Type J

Iron/Constantan

0 OC to 750OC

Higher sensitivity than type K

Types B, R and S

Platinum alloy/ Platinum

0OC to ~1600OC

Very stable but expensive – used only for high temperatures

Table 1

Termocouples used to be the most common temperature measurement device in chemical plant, but are now being overtaken by RDs.

Figure 6 – a temperature probe assembly



INSTRUMENTATION

2.3.2 RESISTANCE TEMPERATURE DETECTORS (RTDS)

An RD, or resistance thermometer, is a device that uses a sensor whose resistance changes with temperature. Te most common type of process measurement RD is a device with a Platinum or Platinum alloy sensor (for stability) whose resistance increases with temperature (as it is a conductor). Termistors are semi-conductor based temperature sensors whose resistance decreases as the temperature increases. Te change is much less linear than that achieved by the Plantinum RDs and the overall accuracy of temperature measurement is also much less. However, thermistors can be made to be very small, and hence very fast, and are often used in applications where very fast temperature measurement is required (e.g. they are used to detect vortices in some vortex shedding flowmeters). Te sensor elements in Platinum RDs only generate a change in electrical resistance, and this needs to be measured by a bridge circuit. It’s very difficult to buy a platinum sensor on its own – most RDs are complete packages consisting of sensor, signal conditioning and transmitter (figure 6). Te sensing element in an Pt RD is bigger than that in a thermocouple, and so RDs are a bit slower. Tey are also more expensive. However, Pt RDs are more accurate and considerably more stable than thermocouples and are now the usual choice for temperature measurement between -200 oC and 500oC.

2.4

PRESSURE MEASUREMENT

Pressure measurement is very important in chemical plant both as a fundamental measurement, and also as an implied measurement of flowrate and level. Pressure measurement can be classed into four main categories: 1. Gauge pressure. Te pressure above the local atmospheric pressure (which changes according to altitude and weather conditions). If the instrument isn’t connected to a pressure source, it will read zero. Pressures below the local atmospheric may be registered as negative pressures, if the instrument is configured to do this. 2. Absolute pressure. Te instrument measures the absolute pressure – it will always generate some reading (except in a complete vacuum). Pressures below atmospheric will be registered as positive absolute pressures. 3. Vacuum. Sometimes used in vacuum systems. Te pressure below local atmospheric pressure is measured. (e.g. if local atmospheric pressure is 14.7 psia, an absolute pressure of 10.7psia will be measured as -4 psig on a gauge pressure device, and 4psi vacuum on a vacuum measuring device. 4. Differential pressure. Te pressure instrument has two measurement ports and measure the pressure difference between them. DP devices can be used as a part of flow and level measurement systems.



INSTRUMENTATION

2.4.1 BOURDON TUBES

Tese were the basis of the pressure gauges we’re used to seeing on old movies with steam engines, etc, and used to be common on chemical plant. Te sensing element is simply a coiled metal tube – pressure increases inside the tube cause an ‘unrolling’ force and this is used to drive the pointer on the gauge. Although cheap and still used on portable devices (e.g. car tire inflators), they are not popular in chemical plant applications as it’s awkward to get a signal suitable for transmission to a remote location (the control room).

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INSTRUMENTATION

Figure 7 – a locomotive pressure gauge based on a bourdon tube

2.4.2 MODERN PRESSURE SENSORS

Figure 8 – Pressure transmitters

Nowadays pressure sensors are normally bought ‘packaged’ in a small instrument that includes the sensor, signal conditioning and a transmitter (e.g. 4-20mA). Several different types of sensor are available, the two most common are: • Piezoresistive. Te sensing element is a ‘diaphragm’ of semi-conductor material. When the element is subjected to pressure, the diaphragm deforms and the movement is detected as a resistance change in the material.



INSTRUMENTATION

• Capacitance. In these instruments, one side of an electrical capacitor is formed by a diaphragm that is exposed to the pressure to be measured. As the diaphragm deforms, the pressure is measured by the change in capacitance Modern sensors are available for all pressure measurement applications. Tose used for differential pressure measurement are usually called DP Cells .

2.5

FLOW MEASUREMENT

Flow measurement is an area where the effect of changes in technology are most noticeable. Up until a few years ago almost all flow measurement was carried out using differential pressure devices (mainly orifice plates) but now a much larger ranges of flowmeters are commonly used. 2.5.1 DIFFERENTIAL PRESSURE DEVICES (ORIFICE PLATES, NOZZLES AND VENTURI METERS

Figure 9 – Orifice plate (from 1871!)

Orifice plates are essentially a plate with a hole in the centre which is fitted between the flanges at a pipe junction. Te flow through the pipe can be estimated by measuring the differential pressure over the orifice. Tere is a considerable subtlety in the design of the orifice plate itself (e.g. the ratio of the hole to the pipe, the entrance and exit shape of the hole), the positioning of pressure trappings (particularly the downstream trapping which should be as near to the vena contracta – the place where the diameter of the streamlines is least – as possible) and finally the position of the orifice plate itself (it needs to be a reasonable distance from things that cause significant disruption to flow patterns – bends, pumps, valves, etc.). Tere is a British Standard (BS EN ISO 5167) for the design of orifice plate (and nozzle and venturi meters) installations.



INSTRUMENTATION

Orifice plates used to be the standard method of measuring flowrates (both gases and liquids) in process plants and probably still represent the biggest number of installed flowmeters. However, they are no longer the first choice for new installations as alternatives which avoid the problems with orifice plates are now available at reasonable cost. Te main problems with orifice plates are: • Te orifice plate needs to be sited carefully – flow disturbances need to be avoided. • Measurements are subject to significant noise when the process stream contains bubbles or solid particles. • Te orifice will be eroded causing measurement drift over time, particularly if the stream contains abrasive particles. • Te orifice can become clogged, seriously affecting the measurement. • Te orifice plate causes a significant, unrecoverable, pressure drop – wasted energy. • Each orifice plate needs to be carefully calibrated in situ for accurate measurement (although often correlations are used in place of calibration, but this produces only approximate measurements of flow). • Te turndown ratio (the maximum reliable flow measurement divided by the minimum), or rangeability, is poor compared to more modern types of flowmeter.

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INSTRUMENTATION

Nozzle and venturi meters are Differential Pressure (DP) meters like the orifice plate, although they have lower unrecoverable pressure drops. Tey are however, very rarely used in chemical plant applications. 2.5.2 VORTEX METERS

Figure 10 – vortex meter

Vortex meters work by inserting a shaped body into the flowpath of the fluid. When this is done alternating, swirling, vortices are shed from the back of the body. Te frequency at which these vortices are shed is directly related to the fluid velocity. In the vortex meter the vortices are detected by temperature or pressure sensors built into the device. Vortex meters have a good turndown ratio (typically 20:1), low pressure drop and high reliability. Tey also have a stable long term accuracy and repeatability. Disadvantages are that they are not suitable for low flow velocities and care needs to be taken in their placement to avoid flow stream disturbances (just like orifice plates).



INSTRUMENTATION

2.5.3 CORIOLIS METERS

Te Coriolis effect was first discovered by the 19 th century mathematician Gustav-Gaspard Coriolis. He was concerned with the forces on a body moving from the equator towards the poles of the Earth. At the equator, the rotational speed of the Earth is just over 1,000 miles per hour in a West to East direction and everything at the equator that is ‘stationary’ with respect to the surface has this rotational speed too. At the poles the rotational speed drops to zero. Tis means that bodies moving North from the equator will tend to deflect to the East and those moving South to the West. o hold the body on a directly Northward (or Southward) path, a force (the Coriolis force) is required to decelerate the body to the local rotational speed. Te Coriolis Effect plays an important part in weather systems and is popularly claimed (wrongly) to determine the direction water goes down a plughole in the Northern and Southern hemispheres!

Figure 11 – operation of a coriolis meter

In a Coriolis flowmeter the effect is used by passing the fluid whose flow is to be measured through a tube that is oscillated in a limited rotary axis. As the fluid moves through the tube it goes from zero to maximum rotational velocity in one half of the tube and then from maximum to zero rotational velocity in the other half. Tis produces two Coriolis forces which produce a twisting force on the tube. Tis twisting gives a measure of the mass flowrate of the liquid in the tube. Coriolis flowmeters measure mass flowrate rather than velocity or volumetric flowrate. However, they can also be made to measure fluid density (by finding the resonant frequency of the tube), allowing volumetric flowrate to be estimated too. Tey have a very high turndown ratio (typically 100:1) and have high accuracy and repeatability. Although they normally have a low pressure drop, they can have problems with very viscous fluids. Tey also rely on moving parts (the tube) and electromagnets to drive the motion, so there may be questions about reliability (although there seems to be no data on this at present).



INSTRUMENTATION

2.5.4 OTHER FLOWMETERS

Tere are many other types of flowmeter in use including: Doppler; transit time (ultrasonic); and magnetic.

2.6

LEVEL MEASUREMENT

Te measurement and control of liquid levels within a chemical plant is one of the most important functions of the instrumentation. Liquid level controllers maintain the overall process mass balance and also maintain liquid seals (to prevent vapour going where it shouldn’t).




INSTRUMENTATION

2.6.1 DIFFERENTIAL PRESSURE MEASUREMENT

Figure 12 – DP cell for level measurement

A very common way of measuring liquid levels is to use a differential pressure instrument. One end (the ‘high’ pressure connection) is connected to a tapping near the bottom of the vessel, and the other to a tapping near the top. It’s important that the top tapping is in the vapour space above the liquid. Te differential pressure is a measure of the hydrostatic head in the vessel. If the density of the liquid is known, then the level can be easily obtained. One problem with this setup, if the fluid contains solids or is likely to form solids, is that the pressure tapping can become clogged with solid material. If the clog is partial the instrument response will become slower and slower, and if it clogs completely no measurement will be possible. 2.6.2 CAPACITANCE MEASUREMENT

Tis type of level measurement uses a long probe which is inserted into the tank as one side of an electrical capacitor, and another conductor (usually the metal wall of the vessel) as the other. As the liquid level in the vessel rises, the measured capacitance will change and this can be calibrated to provide a measurement of the liquid level.



INSTRUMENTATION

Instrument

Figure 13 – capacitance level meter

Capacitance measurement is very subject to errors caused by changes in the electrical properties of the liquid or coating of the vessel or probe. It is no longer very popular in the process industries. Another new, but similar, technique called Radio-Frequency (RF) admittance is however growing in popularity. 2.6.3 ULTRASONIC AND RADAR MEASUREMENT

Figure 14 – ultrasonic/radar level measurement

Ultrasonic and microwave measurement devices use a transmitter element which sends either an ultrasound or radar signal into the vessel from its top. Te signal bounces off the liquid surface and is detected by a receiver. Te distance between the unit and the liquid surface is obtained from the time lag between transmission and receipt of the return signal. Both types of device are independent of liquid density. Ultrasonic devices can be fooled by dense foam layers that deaden the sound signal. Both types of device are expensive compared to other level measurement methods, but radar devices are more expensive than ultrasound.



2.7

INSTRUMENTATION

CHEMICAL COMPOSITION

Te measurement of composition is one of the most desired, but also most difficult and expensive, measurements that have to be made in chemical and process plants. Composition is not just important in reactors, but also in separations like distillation columns, flash chambers, membrane units, etc. 2.7.1 PH METERS

Te pH of a solution is the negative logarithm to the base ten of the Hydronium ion concentration:

pH = − log10 H 3O

+

Te most common use of pH measurement is probably in waste treatment where it is important to ensure that waste water is close to neutral (pH 7) prior to discharge. pH is also important inside many process units to encourage particular reactions or to prevent (or encourage) precipitation of particular materials.




INSTRUMENTATION

Te standard method of measuring pH is using a pH electrode. Tose used in industry have to be much more rugged than those used in standard laboratory applications and often the electrode will have to be chosen to suit the particular process conditions. Generally, you’d buy the pH device as a self-contained transmitter – the signal from the device would match your instrumentation system (e.g. 4-20mA, digital, etc). 2.7.2 CHEMICAL ANALYSERS

Although science fiction V shows have devices like ‘ricorders’ that produce complete chemical analyses at the touch of a button, real analysers aren’t quite there yet. Te first difference is that most analysers need to sample the material to be analysed. Tis involves piping, valves, pumps and control gear that carry out th e sampling process. Sampling also introduces dead-time (time delay) into any measurement, and significant dead-time causes all sorts of problems for feedback controllers. Once the sample has been taken there are a variety of approaches to obtaining an analysis. However, the analyser is always designed to analyse for particular materials – they aren’t general purpose. Tis means that an analyser has to be designed and calibrated for a particular application which pushes the price up substantially. Some of the techniques used include ‘wet’ analysis (where the analyser is a little automated lab); chromatography; and modern methods like: NIR, MIR, UV-visible, Raman scattering, Fluorescence, NMR, Microwave, Acoustic, and Mass spectrometry techniques. 2.7.3 LABORATORY ANALYSIS AND INFERENTIAL CONTROL

Due to the cost and other problems with on-line chemical analysers, they are not very commonly used. Tis is beginning to change as new analyser technology is developed, but for now the most common way of dealing with control of compositions is to use periodic laboratory analysis coupled with inferential control. Te idea of inferential control is that we can use other measurements from a process to infer the compositions. Te simplest systems use just a single measurement (e.g. using a measurement of a tray temperature near the top of a distillation column to infer the tops composition), but others use several measurements combined using some sort of process model (e.g. using a tray temperature, a pressure measurement, and a knowledge of the equilibrium data to infer the tops composition). All inferential systems make assumptions about the process (e.g. about the ratios of the different components) and need to be corrected using periodic (once or twice a shift) laboratory analysis.



3

COMMUNICATION SIGNALS


MAIN LEARNING POINTS • Analogue communications • Digital communications • How to convert between signals and engineering units Process control systems are information processing systems. Tey gather inform ation about the process state from the instruments, then use this to decide what to do to move the process to a desired state, and then send information to the various final control elements (usually control valves) to produce the desired changes in the process. o handle this information there needs to be a means for moving it from the instruments to the controllers and then onto the final control elements. Tis is where process communications come in.

3.1

TYPES OF COMMUNICATION SIGNAL

Tere are a number of different sorts of signal that can exist in a process control communications system. Some plants may have just one type, but most have a mixture of different sorts of signal moving around the system. 3.1.1 ANALOGUE SIGNALS

Analogue signals are continuous and capable of taking any value at all within the range between their maximum and minimum values. Tey are called analogue signals because the level of the communication signal is directly analogous to the value that is being transmitted. 3.1.1.1

Pneumatic signals

Pneumatics are the oldest form of communication signal used for remote monitoring and automatic control in chemical plant. A pneumatic communication signal is an air pressure between 3 and 15 psig (the 3 psi offset zero allows tube breaks or malfunctioning instruments to be detected). Te signal is carried in small diameter (about 10mm) metal tubes. As the tube length increases, a significant dynamic lag develops as it takes time for the signal generator (instrument or controller) to add enough air to increase the tube pressure to the desired value. Tis limits the practical length of communication tube runs, and means that plants using this form of communication have to have a number of local control rooms near to the site of the instruments. Pneumatic communications are now obsolete, but may still be present in some very old processing plants.



3.1.1.2


Current loops

Te most common type of analogue signal used in chemical plant is the 4-20mA current loop. Te instruments/controllers using this communication system send an electrical current around a loop between the transmitter and receiver. Tis is a better communication signal than a voltage as it is independent of the length of the communication line. If a voltage signal was to be used there would be some voltage loss in the communication wire, and this would increase with line length. With a current loop, the transmitter simply increases the transmission voltage until the current around the loop matches the desired signal. In theory, 4-20mA signals can be carried on two wires (or even one if a common earth is used), but communication cables often include additional wires for power supplies and so three and four wire cable is common. Te signal wires will be electrically shielded (with the shielding earthed) or twisted into a twisted pair to reduce the effects of electrical noise.




3.1.1.3


Example calculation for analogue signals

A temperature instrument is adjusted to give a span of 20–120�C. It can be connected to either a pneumatic, or to a current loop transmitter and the conversion is linear. What will be the output of each transmitter type when the measured temperature is 85�C?          

           

            

3.1.2 DISCRETE SIGNALS

Chemical plants are full of devices that can only exist in only one of a limited number (often just two) of states (e.g. OFF or ON). Examples are switches for motors, pumps, agitators, etc, and also ‘instrument’ switches like level and temperature trips. Tere is no universal standard for discrete signals, but 0 and 24V are often used to indicate two states. 3.1.3 DIGITAL SIGNALS

Digital communications convert the value to be transmitted into a number and then send this number down the communication line. Since only one number can be transmitted at a time, digital communications are not continuous, but are sampled . Te information from a digital communications line is like a series of snapshots of the state of the quantity being measured. Digital signals are transmitted as binary numbers with voltages representing the two binary values (0 and 1). Te most common voltages used are 0V for 0 and 5V for 1, but other voltages are used for the ‘1’ digit. Te number of digits in the binary number that is transmitted depends on the electronics that have been selected, and affects the resolution of the value. Older systems used 8-bit analogue to digital convertors and so produced 8-bit numbers, which limited the resolution of the signal to one part in 256 (2 8). Modern systems use 12 or 16-bit convertors, giving resolutions of 1:4096 and 1:65,536 respectively.




3.1.4 EXAMPLE – RESOLUTION OF DIGITAL SIGNALS

Te output of a pressure instrument with a span of 0.5 to 5 bar is to be converted to a digital signal. Tere are two options for this conversion – and 8 bit convertor or a 12-bit convertor. What is the resolution available from both devices?        

    

   



   

What would the output (as a decimal) of the two devices be when the measured pressure was 3 bar?

      

  

  

  

 

141 = 8-bit binary 10001101       

     

    

2275 = 12-bit binary 100011100011

If the output from the 8-bit convertor was decimal 100, what is the pressure being measured?       

  

     

3.1.5 PARALLEL AND SERIES TRANSMISSION

Tere are two ways of transmitting a digital signal: in parallel or in series . Parallel communications have a signal line for each bit of the binary signal plus a number of extra lines for communication control purposes (so a 16 bit parallel communications line will have more than 16 wires). Serial digital communications transmits the binary digits (bits) in series, one after the other. Tere are always additional control bits before and after the digits of the number being transmitted, but all the digits are transmitted serially. Tis means that serial communications can be carried out with as little a two wires (or even one, if a common earth is used). Parallel communications are much faster, but the number of wires required economically limit the length of cables to very sort runs. Although slower, the speed of serial communications has increased dramatically in the last decade and is it is now the default type of digital communications for most applications.




Although digital signals have to be sampled and don’t give a continuous picture of what’s going on, this isn’t a particular problem in chemical plants since the sample intervals are normally many times less than the speeds of response involved in chemical plant operations. Digital communications also have considerable advantages over analogue communications. For analogue communications, there needs to be an individual cable connecting a particular transmitter to its receiver. If a plant has 100 instruments, then there needs to be 100 cables run back from the plant to the control room. With digital communications, this doesn’t have to be the case. Te digital communication can also be made to include an address of the instrument to be communicated with. Tis allows a single cable to be used to link multiple transmitters with multiple receivers. Digital communications also allow richer communication to take place between devices. As well as transmitting the value of the quantity being measured an instrument can send other information, such as the last time it was calibrated, or the rate of change of the measurement, etc. Te line can also be used to communicate in the other direction, for example the controller can use the comms line to tell the instrument to run self-diagnostics.

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3.1.6 PROCESS PLANT DIGITAL COMMUNICATIONS STANDARDS

Tere are a number of different digital communications standards in use in the chemical industries at the moment. Unfortunately, many of these standards are not interchangeable, and this means that it is often necessary to stick to a single supplier if digital communications are used. 3.1.6.1

HART communications

HAR (Highway Addressable Remote ransducer) http://www.hartcomm.org/index.html is a half-way house between analogue communications and full digital comms. HAR can be retrofitted to existing 4-20mA lines, and superimposes a digital signal on top of the analogue communications (just like home broadband rides on top of an analogue telephone signal – using the phone doesn’t stop the broadband working). Te digital signal can be used to provide two way communications between an instrument and central controller. Tis can be used for a number of purposes, e.g. device configuration; diagnostics and troubleshooting; accessing other measurement information. HAR can also be used to convert a 4-20mA line into a multidrop line. In this configuration multiple 4-20mA devices can communicate over the same cable – they share time on the cable and this sharing is controlled by the HAR protocol. 3.1.6.2

Fieldbus

Fieldbus is the generic name given to a number of standards that have developed since the 1990s. Te latest iteration of the standards is Foundation Fieldbus http://www.fieldbus.org/ which now has the largest installed base of all the standards. Fieldbus is a standard for fully digital plant communications. Fieldbus makes use of serial digital lines(called buses ) that are linked to multiple devices. Each device attached to a bus has an address, and can be talked to by prefacing any instructions with the device address. When a controller wants a measurement from an instrument on a fieldbus, the following sequence occurs 1. Te controller sends a message to the instrument (prefaced with the instrument’s bus address) with the instruction to send a measurement. 2. Te instrument takes the measurement and then sends a message to the controller (prefaced with the controller’s address) which contains the measurement that was asked for. Devices continuously monitor the bus, but only respond to messages with their address.



3.1.6.3


Ethernet

Ethernet is the name given to a family of standards used for office computer networks. Until relatively recently it hasn’t been considered for process plant control systems, as it was felt that these required much higher integrity than office based systems. However, the much larger installed base means that Ethernet technology moves faster than specialised process systems and is also much cheaper. It is probable that Ethernet based process control systems will become much more common in the near future. 3.1.6.4

Wireless communications

Wireless communications are starting to be adopted in some process industry applications. Tey have the advantage that they do not require wiring between the instrument and controller, which makes them suitable for distant or exposed locations (e.g. on offshore installations). Tey do require to be placed carefully to ensure that there is a good signal, and can be subject to interference (e.g. someone could park a lorry in front of the transmitter!)

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4

FINAL CONTROL ELEMENTS


MAIN LEARNING POINTS • Air-to-open and Air-to-close valves • Control valve sizing and valve characteristics Final control elements are the devices that take the output signal from a controller (which is a flow of information in some form) and converts it into something that can physically influence the behaviour of the plant (the manipulation). By far the most common final control element in the process industries is the control valve , but others such as conveyor belt speed controllers, or agitator speed controls are sometimes used.

4.1

CONTROL VALVES

Te most common type of valve used for control purposes is the globe valve . It’s called a globe valve because the valve body is usually fairly spherical and looks like a globe. Te valve stem is a metal rod that runs down through the valve, and attached to its end is the valve plug . Te stem is capable of moving up and down and, as it does so, it moves the plug away and towards the valve seat . Te plug and seat of the valve are very carefully machined components and give the valve its characteristic ; the relationship between the stem position and flow through the valve.

Figure 15 – A globe valve




Most control valves are pneumatically driven. Air is allowed to flow into a chamber with a diaphragm which is driven against a spring to move the valve stem. When the air pressure is released, the spring pushes the stem back towards its original position. Te pressure of the air that drives the valve is set remotely (usually by a controller) and the communication signal is converted to an air pressure by a device near the valve itself.

Figure 16 – air to open/close valves

Control valves can be configured (sometimes by simply flipping over the actuator assembly) as air-to-open ( fail closed ) or air-to-close ( fail open). Te choice is entirely dependent on what’s best for process safety. Control valves need a supply of special clean, dry, air called instrument air . If this fails, then there is a potential for a common mode failure that will affect multiple control valves. If this happens, then it is important that the valves will fail in a direction that will put the process into a safe state. For example, if a valve is used to regulate the cooling water supply for an exothermic reactor, then it makes sense to use an air-to-close valve (on air failure the valve will go full open). Conversely, a valve manipulating the steam to a distillation column reboiler will usually be air-to-open, so that the steam is shut off on an air failure.



4.2


CONTROL VALVE SIZING

Sizing a control valve doesn’t just mean choosing couplings that fit with the rest of the pipework – much more importantly the internals (valve plug and seat) need to be sized to give a valve that is appropriate to the application. An undersized control valve won’t be able to pass the correct flowrate. An oversized control valve may not be able to be turned down sufficiently to give good control of the process. It is important that valves are correctly sized for their application. Te basic valve sizing equation (for Fisher Valves) for liquids is:

Q = C v ( x)

where

∆ P

G

Q = volumetric flowrate through valve (US gallons/minute) C v (x) = valve coefficient (different for different valves and stem positions ‘x’). Obtained from valve manufacturers tables ∆P = Pressure drop over valve (psi) G = Specific gravity of liquid (water at 60�F=1.0)

Te equation is based on water and the actual flowrate may be different if the fluid viscosity is significantly different from water at the test conditions. Valve manufacturers provide various ways for compensating for this. Equations for valve sizing are also available for compressible and two phase flow. 4.2.1 VALVE CHARACTERISTICS

Figure 17 – types of valve trim




Te characteristic or trim of a valve is a description of how the flowrate through the valve changes with stem position. Tere are three common valve characteristics: linear ; quickopening ; equal percentage . Te valve characteristic is altered by choosing different designs of valve plug and seat from lists in manufacturers catalogues. Te linear trim is the easiest to appreciate. In this characteristic if the pressure drop over the valve is constant then the flow through the valve increases linearly with the stem position. Te quick opening characteristic is for use in applications where high flow is required quickly – small initial movements of the stem as the valve opens produce large increases in the flowrate. Te equal percentage is the least obvious of the characteristics – a percentage change in the stem position will produce an equal percentage change in the flowrate through the valve. Te reason that equal percentage characteristics are often used is to do with the installed characteristic of the valve. Valves only represent part of the process piping and hence part of the pressure drop – to accurately predict how a valve will respond in service we need to calculate the installed characteristic.

.





Let’s assume that we can represent the flow/pressure drop relationship of the pipework with a similar relationship to the valve, i.e. Qvalve

=

∆ P valve

C V valve ( x)

G

Q pipework = C V pipework

∆ P pipework

G

Obviously, the valve is connected to the pipework, so the flows are equal:

Qvalve

= Q pipework = Q

Also, the total pressure drop over the pipework and valve is fixed so, ∆ P valve + ∆ P pipework = ∆P total

Now

∆ P pipework G

∴

 Q =  C V 

pipework

   

2

Q ∆ P total  = −  C V G 

∆ P valve G

pipework

Q = C V valve

   

2

Q ∆ P total  ( x) −  C V G 

pipework

   

2

  Q    = ∆ P total −  Q  C V ( x)   C V G    valve

pipework

 1 1 Q  + 2  C V ( x) C V  2

valve

pipework

 1 1 Q= +  C V ( x) 2 C V  valve

2

   

2

 ∆ P  = total 2  G 

pipework

  2  

−1

2

∆ P total G

Tis expression tells us how the flow will vary with pressure drop and valve stem position for the whole system (valve and pipework) and will allow us to generate an installed characteristic for a valve.




It’s easy to these equations into a spreadsheet, and that’s how I’ve created this example. First of all let’s look at a design where most of the pressure drop in the system is over the control valve. o do this I’ve set the pipework Cv to 5. Let’s use a linear characteristic: Stem Posn %

0

10

20

30

40

50

60

70

80

90

100

CVvalve

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

CVpipe

5

Table 2 – Linear characteristic

Putting the numbers into the spreadsheet produces the following:

  

         

  



 

    











 

Figure 18 – Comparison of characteristics for a linear valve with equal Delta P

As you can see, the installed characteristic is slightly different from the valve on its own, but it still follows a roughly linear relationship. Tis is desirable as we would usually like the flowrate to increase approximately linearly with stem position. Now, let’s look at what happens when the pressure drop over the valve is normally only a small fraction of the overall pressure drop. o generate the curves, I’ve set the pipework CV to be equal to 0.5 (roughly a third of that of the control valve at nominal conditions):




  

         

  



 

    











 

Figure 19 – comparison with low valve Delta P

You can see that the valve now behaves very differently when it is installed in the pipework. Te installed characteristic is now very far away from linear and looks like a quick-opening valve. Tis is a big problem since it’s usually a good idea to minimise the pressure drop over the valve as far as possible – pressure drop over the valve is wasted energy.

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Let’s now look at what happens with an equal percentage valve. I’ve generated some equal percentage CV s in the table below (NB the C V values here have just been generated for the example – they are not general and you need to check valve tables for real values). I’ve generated the coefficients so that the valve produces the same flow as the linear valve at maximum opening. Stem Posn %

0

10

20

30

40

50

60

70

80

90

100

CVvalve

0.04

0.059

0.087

0.129

0.191

0.282

0.418

0.618

0.915

1.352

2

CVpipe

0.5

Table 3 – Equal percentage characteristic

Using the spreadsheet calculator, the following graph is produced:

Figure 20 – Installed characteristic for an equal-percentage valve

You can see that, when the pressure drop over the valve is a fraction of the overall pressure drop, an equal percentage valve produces an installed characteristic that is much closer to the ideal line.




Pressure drop over a control valve is wasted energy and you’d normally want to keep it as low as practicable. For most installations, therefore, at nominal flows the pressure drop over the control valve will be only a small part of the overall pressure drop, and an equal percentage valve will normally be chosen. Te exception is where the pipework pressure drop is unusually small (e.g. in short lengths of pipe): in these cases linear characteristics will produce the best results. Quick opening characteristics are normally only used in onoff control systems. In real situations, where the control valve is placed at the outlet of a centrifugal pump, the installed characteristic is also affected by the pump curve (the relationship between discharge pressure and delivered flow). In real life, specifying a control valve isn’t simple! 4.2.2 SIZING CONTROL VALVES (ONE METHOD)

1. Identify what the valve is to do. What’s the fluid, the nominal flowrate, the flowrate range, the pipe size and the pressure drop available? Te pressure drop over the valve should normally be around 25–40% of the total, but can go down to 15% in long lines. Care needs to be taken if there is a possibility of flashing or cavitation. 2. Calculate the valve C V required to pass the desired nominal flow. 3. Look through the valve sizing charts and find the size that gives the desired C V when the valve is about 60–70% open (it’s necessary to allow some movement either side of the nominal flow for control) 4. Calculate the installed characteristic for the valve. Ideally the maximum flow through the system should be around 1.4 times the nominal (this is a rule-of-thumb so treat it with caution!). Te minimum flow that is expected operationally should be achieved when the valve is more that 10% open – flowrates through a valve at low openings (less than 10%) tend to be quite variable. (Note: control valves are not designed to shut off flows – there is always leakage. Tere needs to be an additional stop valve in the line if it is desired to close the line completely).



5

DIAGRAMS FOR PROCESS CONTROL SYSTEMS


MAIN LEARNING POINTS • Te difference between PFDs and P&IDs • How to read a basic P&ID Diagrams are important for all sorts of engineering and control is no exception. Te primary diagram used by process control engineers is the Piping and Instrum entation Diagram (P&ID).

5.1

PROCESS FLOW DIAGRAMS (PFDS)

Process flow diagrams are one step above process block diagrams. Tey show major pipelines and the major process units. Tey are very useful for explaining the overall layout of a process and are often included alongside process descriptions.





Figure 21 – A PFD

PFDs may include some information on control, but this is there to help in the process discussion and is not for engineering purposes.

5.2

PIPING AND INSTRUMENTATION DIAGRAMS (P&IDS)

Figure 22 – a partial P&I diagram of the process in figure 21




A P&I diagram contains much more detail than a PFD. Te P&ID will contain ALL of the piping in the process, including things like drain lines and vents. Te diagram will show all of the valves (including stop and check valves) and other pipefittings (like strainers). All of the instruments and control loops will be shown and also details of alarms and other emergency control system components. Te P&I diagram is a proper engineering tool. It is used for HAZOP studies before the plant is built and is an important tool during the design and commissioning stages. P&I diagrams are also available to plant engineers (they are often kept in the control room) who have to maintain and develop the plant once it is running (although P&I diagrams on operating plant can quickly get out of date and have to be checked before use). 5.2.1 SHOWING INSTRUMENTATION ON A P&ID

Figure 23 – a P&ID control system device

Te standard method of showing instruments on a P&ID is to show the device inside a device bubble. Inside the bubble is the devices tag name, which consists of two parts: a tag identifier that gives information about what kind of instrument is being referred to; and a tag number, which is used to identify the particular instrument. Attached to the outside of the instrument bubble, and connecting it to the other elements of the P&ID are the communication lines .



5.2.1.1


Device bubble shapes Not normally accessible by

Accessible to the operator;

Mounted in

main control

the field

panel

the operator;

Local panel

behind the

accessible to

panel or

the operator

password protected

Distinct elements Shared display/ control in a computer control system Computer logic function Programmable logic controller Table 4 – Instrument bubbles

Te picture used (see table 4) for the device bubble identifies the type of device represented (e.g. a discrete device or an entry on a shared display), where it is located (e.g. in the control room or out on the plant), and whether it is normally accessible to the operator (e.g. is it hidden away or locked by a password). 5.2.1.2

Tag identifiers

Te tag identifier describes the type of variable being handled and the sort of devices or functions being used. Different letters and placements are used to achieve this (see table 5).




Letter

In 1st position

A

Analyser

Alarm

C

Anything

Controller

F

Flowrate

I

Current

Indicator

L

Level

Light, or low

P

Pressure

R

Radiation

Recorder, or printer

T

Temperature

Transmitter

Modifier (if used)

Following letters

Ratio or fraction

Table 5 – A short list of tag identifier letters

What type of instrument would have a tagname of IR001? A temperature indicator (a gauge or display with the instantaneous temperature value displayed) recorder (something that stores previous values of temperature).

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5.2.1.3


Communication lines

Figure 24 – some examples of P&ID connecting lines

Te lines that connect the various elements on a P&ID contain useful information too. Te type of line used provides information on the sort of connection that it represents. Figure 24 shows some examples that are commonly used. 5.2.2 AN EXAMPLE P&I DIAGRAM

Figure 25 – an example of a P&ID

FC001 is a controller that controls the tube side flow, with the flow being monitored by a flow transducer (F001). A recording and indicating device(located on a shared display in a control room) is also connected to the transducer to give an indication of the current value and to store old values of the flow. Tere’s also a low flow alarm attached to the inlet process line – presumably to warn about potential overheating.




Tere’s a vent on the shell side of the exchanger that’s closed by a hand valve. On the outlet of the vent is a high pressure alarm – this will trigger if the vent is left open. Te shell side pressure is monitored and displayed at the heat exchanger (PI002). Te tube side outlet temperature is displayed, recorded and controlled (CIR001) by a controller over a data link. Te valve on this loop is operated pneumatically by the data/pressure convertor PY001. Tere’s a high temperature alarm (with a flashing light, and presumably a siren) on the tube side outlet.

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6

INPUTS AND OUTPUTS IN CONTROL SYSTEMS


MAIN LEARNING POINTS • Te difference between process engineering and process control inputs and outputs • Manipulations and disturbances • Controlled and auxiliary outputs Control systems process information. Tey gather data about a process from instruments, figure out what should be done to move the process to a desired state and then send information back to the process to implement the changes. Inputs and outputs, in a control sense, are inputs and outputs of information (data) and are quite different to what chemical engineers normally understand by these terms.

6.1

PROCESS INPUTS

Tere are only two sorts of process input (in control engineering): manipulations and disturbances . A manipulation is an information input to a process that comes from the control system of interest. It is usually a signal sent to a valve. Te signal will cause the valve to move, which will change the flow through the valve and hence change the conditions in the process. A disturbance is an input to a process that changes outside of the reach of the control system of interest (the control system has no influence over the value of a disturbance input). For any process, there will be an almost limitless number of potential disturbances; they can arise from a variety of sources, for example: • Raw materials variations (e.g. changes in physical or chemical properties will affect the process) • Environmental disturbances (e.g. changes in relative humidity and air temperature will affect cooling water temperature). • Disturbances caused by process equipment (e.g. catalyst fouling will change reactor reactivity) • Disturbances caused by other control systems (e.g. an upstream controller might reduce a flow entering the process).




Te main goal of process plant control systems is to regulate against the effects of these disturbance inputs. Tey do this by making changes to the manipulated inputs to counteract the effect of the changes in the disturbance inputs (e.g. if the catalyst in a reactor degrades it might be necessary to decrease the flow through the reactor to increase residence time, or the temperature might be increased – by changing cooling/heating flows – to increase reactivity).

6.2

PROCESS OUTPUTS

From a control viewpoint a process output is a flow of information coming from the process; they are always the outputs of measuring instruments – there is no other way of getting information from the process. Outputs are also classified into two categories: control variables and auxiliary outputs . Controlled variables are the outputs of the process that have to be held close to particular values (called desired values or setpoints ) for the process to be doing what it’s supposed be doing. Te controlled variables will be attached to controllers that will be trying to hold the values of these variables at their setpoints. Auxiliary variables are additional process outputs that are monitored for a variety of reasons. Tese could be: • o provide more information to operators. Sometimes, particularly in fault conditions, extra information helps operators decide what needs to be done. • o provide alternative control variables in special circumstances. Under fault conditions, or if a process needs to switch into a different operating mode (e.g. when changing product type) some of the existing controlled variables may be swapped with auxiliary measurements (the degrees of freedom of a process limit the number of things that can be controlled simultaneously). • o provide information for feedforward control. With this type of control, information on the current value of disturbances is required. Although a disturbance is a process input, any measurement of it is a process output and would be classed as an auxiliary output.



6.3


PROCESSES IN CONTROL ENGINEERING

A process in control engineering isn’t a sulphuric acid plant, or a distillation column. Instead it is something that converts process input information into process output information. A process control computer could be disconnected from the process it is controlling and reconnected to a simulation and it would continue to operate (and this is the way some are tested). Te control system is only concerned with the processing of information. Te basic process in control engineering is the single-input/single-output (SISO) system. Tis is a process that converts one input information stream into a single output stream. Most real outputs are affected by multiple inputs, producing multi-input/single-output (MISO) systems. Real chemical plants have multiple inputs and multiple outputs, with outputs being affected by several inputs and inputs influencing several of the outputs, and these are classed as multi-input/multi-output (MIMO) systems. As we’ll see later, when linear control system analysis is applied we can break MIMO systems into a combination of SISO sub-systems.




6.4


AN EXAMPLE OF VARIABLES AND PROCESSES

Consider the simple process shown in figure 26. Even though the process is simple it is possible to identify 7 output variables, 2 inputs and 11 SISO processes linking them.

Figure 26 – A simple process example

Output variables

FLA001, FIR001, FT001, PI002, PHA001, TCIR001, THAL001

Input variables

FC001 (output), PY001

SISO processes

FC001 (output) to FT001, FIR001, FLA001, PI002 (since it could affect shell pressure), PHA001, TCIR001 (input), andTHAL001 PY001 to PI002, PHA001, TCIR001(in), andTHAL001



7

INTRODUCTION TO FEEDBACK CONTROL


MAIN LEARNING POINTS • • • • • •

Elements of a feedback loop Positive and negative feedback Forming block diagrams from P&IDs and vice versa Direction of control action Controller hardware Introduction to control loop fault diagnosis

Feedback control is going on everywhere you look. Your own body has a multitude of feedback mechanisms that regulate your digestion, blood pressure and heart rate and stop you from falling over when you walk. Te essence of feedback control is that it is the output of the process, the controlled variable, which is monitored. If a disturbance enters the process that causes the controlled variable to move away from the desired value, the controller sees this and starts to move a manipulated variable to try to counteract the effect of the disturbance. Te controller continues to monitor the output and can see the effect that the changes in the manipulated variable are having – the controller can increase the amount of manipulation if the output isn’t changing quickly enough, or it can reduce the amount if the output change is too fast, or too large.

7.1

FEEDBACK CONTROL AND BLOCK DIAGRAMS

Figure 27 – A feedback control system




Block diagrams are commonly used to illustrate feedback control systems. Tey can also, for linear systems, be used to help analyse control system behaviour through the rules of block diagram algebra. In the diagram in figure 27 we have a ‘process’ block on the right of the diagram. Tis represents the process we are trying to control and has a manipulated input and disturbance inputs too (if the process is linear, this block could be further broken down into a number of SISO blocks). Te output of the process block is the controlled variable, this is measured by the measurement system and the measurement (the controlled value (CV) or measured value (MV)) is fed back to the comparator (part of the controller and marked with the Greek letter Σ). Te comparator calculates the arithmetic difference between the measured value and the desired value , or setpoint (SP), for the controlled variable. Tis difference is called the error (ε). Te error signal is then fed to the controller which contains a control algorithm, and the output(OP) from the controller is sent to the final control element and hence to the process. A continuous loop exists in the system between the controller, process and measurement loop – this is called the feedback loop. Block diagrams are easy to develop directly from P&I diagrams (figure 28).

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Figure 28 – block diagram from P&ID

7.2

POSITIVE AND NEGATIVE FEEDBACK

A negative feedback system will always try to reduce the size of the error signal. A positive feedback system will act to increase the size of the error. Control systems always use negative feedback.

7.3

CONTROL LOOP PROBLEMS

As you can see from the block diagrams in figure 27 and 28, a feedback control system is a system with several interacting components. Tis is often forgotten about in industry and problems concerning poor control are often blamed on the controller. In many cases, however, it is another part of the loop that isn’t performing correctly. Controllers nowadays are electronic devices and are very reliable. If the loop had been working previously, but has now gone faulty, it is much more likely that it’s a component other than the controller that is causing the problem. In diagnosing control problems, it is important to check other loop elements before touching the controller. Some of the potential loop problem are described in the tables below.




7.3.1 PROBLEMS WITH THE MEASUREMENT Potential problem

Diagnostics

Complete instrument or communications failure

Is there a signal? Is the signal within the expected range? Some digital instruments may provide their own diagnostics

Incorrect calibration (zero, span or linearisation)

Is the value coming back sensible? Does the value tie in with other plant measurements? (It is necessary to check the instrument over a range of operating values if this is a suspected problem).

Incorrect instrument selection

Are there intermittent problems? Does the instrument behave poorly under some process conditions?

Excessive noise in signal

Poor instrument positioning (near sources of electrical interference)? Poor filtering?

Table 6 – measurement problems

7.3.2 PROBLEMS WITH THE CONTROL VALVE Potential problem

Diagnostics

Complete valve or communications failure

Does the valve responds to control signals (it is possible to check the stem position on the valve, or it can be seen from flow rate changes)?

Characteristic problems

Is the installed valve characteristic approximately linear?

Range problems

Is the valve spending a lot of time saturated at one end of its movement (i.e. fully open or fully closed)?

Excessive hysteresis

Open the valve and check the flowrate at fixed stem positions and then close the valve and check again – flowrates at the fixed positions should be similar.

Table 7 – control valve problems




7.3.3 PROBLEMS WITH THE COMMUNICATIONS Potential problem

Diagnostics

Complete communications failure

Is there a signal? Is it within the expected range?

Noise

Is it an instrument problem? Interference? Incorrect cable? Poor cable runs?

Digital systems not operating correctly

Are the correct software drivers loaded? Has the system been properly configured? (Digital systems are complicated!)

Table 8 – communication problems

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7.4


DIRECTION OF CONTROL ACTION

All feedback controllers have a switch or button that allows the direction of control action to be switched. Usually, the switch is marked with the two possible positions reverse (REV) and direct (DIR). A direct acting controller is one whose output will tend to increase as the measurement signal increases. A reverse acting controller is one whose output will tend to decrease as the measurement signal increases. Why do we need the option to switch the direction of action? Consider the level control systems shown in figure 29.

Figure 29 – level control manipulating inlet

If the valve in the level control loop is air to open, imagine what we’d want to happen if the level in the tank (the measurement) started to rise. Te controller needs to act to reduce this increase in level, and so move the measured level back towards its setpoint. Te only way it can do this is to reduce the flowrate coming into the tank by altering the position of the valve it is connected to. Since the valve is air to open, to get a reduction in flow it is necessary to reduce the output of the controller. So, in this configuration an increase in the level should lead to a reduction in the controller output – we’d want to set the direction switch to reverse acting. Now consider the system in figure 30.




Figure 30 – level control manipulating outlet

Tis is exactly the same tank, but we are now using the bottom valve as a manipulation. In most processes we have multiple manipulations that can affect a particular controlled variable, and the task of choosing appropriate pairings isn’t trivial – this will be discussed later in the course. For now, let’s think about what happens when the level increases (some other control system has opened the top valve). Now we want the exit flow to increase to reduce the measured level back towards the desired value. o do this, since we are assuming air to open valves, we need to increase the controller output. So, in this case, the direction switch should be set to direct acting. It’s important to remember that the direction of the operation of the control valve needs to be taken into account too. If the valves above had been air-to-close (fail open) valves, then the direction of control actions would be the opposite of those chosen. Choosing the wrong direction of control action will convert a control system into a positive feedback system. Usually this will be pretty obvious – changing the setpoint will cause the process to move in the opposite direction (and usually, depending on the setup of the controller, it will keep moving). In slower systems, however, this may not be immediately obvious – it’s always worthwhile trying to get the direction right and not rely on trial and error.



7.5


CONTROLLER HARDWARE

Figure 31 – a pneumatic controller

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Feedback controllers exist in many different forms. Te controller in figure 31 is a pneumatic controller – it is entirely mechanical and the algorithm is implemented by a complex arrangement of nozzles and bellows. Pneumatic controllers used to be widespread throughout the chemical industry. With the development of cheap, and more flexible, microelectronics they are now very rare. Tey are sometimes used in potentially flammable atmospheres (since they don’t use electricity they are inherently safe) but modern, flammable atmosphere safe, controllers are replacing them in this application too. Although the controllers themselves are being replaced, the human machine interface (HMI) developed for these controllers is still seen in their modern equivalents. Te scale on the front (marked 0–100) shows the measured value (on the left) and setpoint (on the right). How this was represented depended on the controller, there could either be moveable pointers that moved up and down the scale, or the pointers could be fixed and the scale could move. Tis controller has a switch on the bottom left marked Man/Auto. In the Man (manual) position, the controller algorithm is switched off and the feedback loop is broken. Te controller is in an open-loop condition and turning the knob on the right (marked ‘Man’) will directly alter the controller’s output and hence the position of the valve it is attached to (the output is shown on the scale on the bottom part of the faceplate). When the controller is in the ‘Auto’ condition, the controller algorithm is operational. In this position, fiddling with the ‘Man’ knob won’t do anything – the valve is now being adjusted by the controller. Instead, it’s possible to adjust the controller setpoint by turning the knob marked ‘SE’ which is halfway up the faceplate on the right. Tere are other adjustments available – the direction of control action and controller algorithm adjustments, but these are hidden away either at the back of the controller or inside the case. Tese are regarded as ‘engineering’ parameters and should not be altered by the process operators. When the controller is installed in the control room, these engineering adjustments will be completely inaccessible unless the controller is physically removed from the control panel.




Figure 32 – an electronic controller with traditional faceplate

Some modern, electronic, PID controllers use a similar faceplate design as the old pneumatic controllers (figure 32). It gives a clear indication of measured value and setpoint, especially if you are used to looking at displays of this type. Te modern controllers, however, are considerably more sophisticated and will include many additional features such as alarms, self-tuning, a choice of control algorithms, etc. Most controllers of this type are no longer single loop – they are actually multiple controllers in the same box and the display can be switched between each controller.

As engineers engine ers and operators operat ors who were used to the old ‘faceplate’ style of controllers controll ers become fewer, new controller designs based on LED displays are becoming much more common (figure 33). Tese controllers only really differ in HMI – they still have multiple extra functions and often contain multiple ‘loops’ – they can be used to control several variables simultaneously.

Figure 33 – an electronic controller with LED display




Te trend in most process plants is to move away from discrete loop controllers and instead incorporate control loops into a computer based control scheme. For small installations, these loops might be incorporated in a device called a Programmable Logic Controller (PLC). Larger installations (anything bigger than a dozen loops) will usually have a Scanning Control and Data Acquisition (SCADA) computer based system that will contain feedback controllers, but will also present the operators with a set of nice mimic displays too. Tese systems are discussed in more detail later.

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8

INTRODUCTION TO STEADY-STATE AND DYNAMIC RESPONSE

INTRODUCTION INTRODUCTI ON TO STEADYSTEADYSTATE AND DYNAMIC RESPONSE

MAIN LEARNING POINTS • • • • • •

Steady-state gain Introduction to non-linearity Basic types of dynamic response: time delay; integrators; self-regulators; instability First- and second-order response Measures used to describe controlled responses How to fit first-order plus dead-time (FOPD) models to high-order step responses.

As chemical engineers en gineers we are used to thinking t hinking about most mos t processes in terms term s of their steadysteady state behaviour – when forming mass and energy balances the first thing that is usually done is that the accumulation term (the d/dt) is set to zero. In the past most chemical engineers were destined for large continuous plant, where steady -state analysis was reasonably appropriate for most purposes. Steady-state analysis, however, is never appropriate for control – we are very concerned with how things change dynamically. Nowadays, even for general chemical engineers, the increasing importance of batch production of high value speciality chemicals to the chemical industry means that an understanding of dynamic behaviour is vitally important.

8.1

STEADY-ST STE ADY-STA ATE GAIN GAI N

It might seem odd to start a section on dynamics with a description of a steady-state phenomenon. However, the steady state gain is an important factor in the dynamic response of the system – it shows where the system will end up if the response is allowed to complete. Te steady-state gain of a component, or system (a group of components), is defined as the steady-state change in the output signal divided by the steady-state change in the input signal, it can also be expressed as:   




Figure 34 – gain in a non-linear system

In a linear system, the steady-state gain is constant throughout the systems range, but non-linear systems (i.e. all chemical processes) have gains that vary with the point they are measured (figure 34). For these systems it is important to state where a gain has been obtained – for most process gains, this will be at the nominal operating point of the process. All the components in a control system will have a steady-state gain. It is possible to calculate the overall gain of a group of blocks directly from a block diagram (figure 35), e.g.

Figure 35 – A block diagram with gains

  

 



 



 



 



 



 



 

   

Steady-state gains can be obtained from experiments on plant or simulations (by making a small change in the input and wait until the output settles) but they’d be more commonly obtained by more sophisticated system identification methods that allow model information to be obtained from suitably stimulated process input-output data. Gains can also be obtained from process models: consider this model for an isothermal CSR, with a second-order rate expression. 

 



      




at steady-state: 

       

o find the gain between F and C A , we could make small changes in F and observe the change in the concentration. However, we can also differentiate the equation wrt to F (i.e. look at how it responds to differential changes in F):    

 

  

  

 

 

 

 

   

            

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8.2


DYNAMIC RESPONSE

Dynamic response is the time varying or transient behaviour of a system immediately and soon after it is subjected to a change in input. Te dynamic response of a system is affected by the size and number of capacities that are present. Tese capacities are places where conserved quantities (i.e. total mass/moles, component mass/moles, and energy) are held up within the system. For total mass, capacities are as simple as the volume of vessels, reactors, etc. – the larger the capacity, the slower the dynamic response is likely to be. Te order of a dynamic response is directly related to the number of capacities (holdups) in a particular system between the input and output. Each of these capacities will need a firstorder differential equation (a mass, component or energy balance – mechanical systems will include momentum balances too, which are fundamentally second-order, but most process industry problems don’t require these) to describe its behaviour. A third-order process will contain three capacities, and will be described mathematically by three inter-related firstorder differential equations leading to the overall dynamic response being defined by a third-order differential equation. Te systems we deal with in the chemical industry tend to be very high-order – the simplest system that can be imagined is a tank, a level measuring instrument and a valve – all of these will have, at least, first-order dynamics, leading to a minimum of a third-order process. Something like a distillation column can easily have dynamics of the order of a hundred or more. High order dynamics can introduce very interesting dynamic behaviour, but a lot can be understood by looking at the behaviour of lower order systems (which make up the components of the high-order response). 8.2.1 DYNAMIC RESPONSE – DEAD TIME

Process

t=0 t=0

td

Figure 36 – a dead-time process

Dead time (sometimes called distance-velocity lag ) is, in some ways, the simplest sort of dynamic response that can be observed. If dead-time is present in a system the output will not change (it will be dead) for a period of time after the input has changed (see figure 36).




Figure 37 – distance-velocity lag

Dead-time is fairly common in process industry systems and can be caused by a number of factors. Probably the easiest to understand (although the least likely in practice) is the scenario that gives dead-time its alternative name – distance velocity lag (figure 37). In this situation, it is assumed that the ‘process’ is a long pipe, of length ‘d’, with a measurement device at the exit. Fluid is flowing through the pipe in a pure plug flow manner at velocity ‘v’. If a change (e.g. temperature or concentration) is injected into the fluid at time t=0, no change will be registered at the measuring instrument until the element of fluid has had time to move down the length of the pipe. Tis will take a time equal to the distance (length of the pipe) divided by the velocity. Putting instruments at the end of long pipes is not really good practice, and so pure distance-velocity lag isn’t common in real situations. In real processes, dead-time is typically associated with the movement of materials in large vessels. We are used to assuming that vessels are perfectly mixed, but this is rarely the case. In an imperfectly mixed vessel, if there is a change in one of the inlet streams that change will not immediately be seen in all parts of the vessel instantly. Instead there will be a delay (dead-time) before anything at all will be seen at a particular point. An instrument inserted into the vessel will not immediately detect changes in the vessel contents caused by changes in an input stream. Tis dead-time will be variable and dependent on the size of the vessel, agitation conditions, and the flowrates through the vessel. Another potential source of dead-time in the process industries are chemical analysers. Some of these analysers take a sample from the process and then take time to develop an output. When the dead-time becomes large compared to the other dynamics present in a process, it can cause real problems to feedback control systems. Tese controllers rely on being able to immediately see the effect their manipulations are having on the controlled variable. If significant dead-time is present, then the feedback controller is seeing the output of the process as it responds to an input made a dead-time ago in the past. Tis temporal decoupling of the input and output can cause issues with stability and special techniques may have to be used to control such systems.




8.2.2 DYNAMIC RESPONSE – INTEGRATORS

Figure 38 – an integrating process

An integrator is a process element that simply integrates input changes over time. Te easiest process related example is the level in a tank with a pumped discharge. Te pump prevents the outlet flow being significantly affected by the level in the tank. In this example, if the inlet flowrate changes by a step, then the level in the tank will increase in a ramp (since no extra flow will be leaving the tank). Te tank is integrating the change in the inlet flow over time.








8.2.3 DYNAMIC RESPONSE – SELF-REGULATING SYSTEMS

Figure 39 – a self-regulating process

Te outputs of most of the processes encountered in the process industries will not continue to grow indefinitely after an input change (i.e. they are not integrators). Instead they will tend to approach a final value asymptotically over time. An example of a self-regulating process is the level in the tank that was used in the integrator example, but with the pump replaced with a flow restriction. Te flow out of the tank is now a function of the pressure drop over the restriction, and hence the level in the tank. Now when the flowrate into the tank changes by a step, the level will again start to rise but as it does so it will increase the pressure drop over the restriction and hence the discharge flowrate. Eventually, the level will rise far enough that flowrate out of the tank matches the flowrate in, and the level will stop rising (mathematically this will take an infinite time, but for practical purposes the time required can be assumed to be limited). 8.2.4 DYNAMIC RESPONSE – UNSTABLE SYSTEMS

Some systems are dynamically unstable – when an input changes, the output will grow without bound (in theory to infinity, but in practice until something hits a limit or breaks). Tis growth can either be linear (in the case of integrators), exponential, or oscillatory.

Figure 40 – unstable process responses




Some processes are fundamentally open-loop unstable – to see an example of one, try balancing a pencil on the end of your finger. An example from the chemical industries is an exothermic CSR, operated at its unstable temperature point. For these processes to operate, active control is required to stabilise the system around the desired conditions. Instability can also arise as a result of control action. Using the wrong direction of control action can produce unstable controlled responses, and should always be avoided. Even if the correct direction of control action is selected it is still possible to destabilise all practical processes by making the controller too aggressive in its control action. Excessive control action is the usual cause of oscillatory instability. 8.2.5 DYNAMIC RESPONSE – FIRST-ORDER SYSTEMS

First-order systems are described by first-order differential equations and always are formed by taking balances (mass, component or energy) around a single capacity. Te standard equation for a first-order system is: τ

where

dy* * + y* = K mu* + K d d dt

the time constant – a factor that determines the speed of response and is dependent on the size of the capacity involved   = the output of the process (the asterisk has a special meaning that is dealt with later)  = the steady-state gain associated with the manipulated input the manipulated input   the disturbance steady-state gain – the steady-state gain associated with the disturbance input  the disturbance input   =



=

=

=

First order processes are the fundamental building block of all chemical process responses. Some examples of systems that will be governed by first-order dynamics are: the temperature of a thermometer bulb; the level of a tank; the reactant concentration in a reactor; the mole fraction on a plate in a distillation column.




Figure 41 – a first-order step response

First-order systems can be self-limiting or unstable (unstable first-order systems will have a negative sign in front of the   term. Te response of a stable first-order system to a step input always looks like figure 41. Stable first-order systems always move at their fastest rate the instant the step is applied, and then get slower as time moves on.






Te final change in the output is equal to the steady-state gain times the change in the input. First-order responses will be approximately 95% complete after three time constants and 99% complete after five time constants (the equations will be obtained later). 8.2.6 DYNAMIC RESPONSE – SECOND-ORDER SYSTEMS

In process industry situations, second-order systems are normally formed as a result of two first-order systems acting together. Momentum balances will produce equations which are fundamentally second-order (they model position, velocity and acceleration – velocity is the first-derivative and acceleration the second-derivative of position) but these are rarely required when considering process engineering systems. Te standard form of a stable second-order differential equation is:                     

where

= natural period of oscillation (not to be confused with the time constant of a first-order equation  = damping factor 

A second-order system’s response to step-changes has richer behaviour than first-order systems, and the form of the response is dependent on the damping factor.

Figure 42 – second-order overdamped response to step input




Figure 42 shows the situation when the damping factor has values greater than one. Tis type of response is known as an overdamped response. Te final value is still dependent on the steady-state gain (since steady-state isn’t a dynamic phenomenon, it is independent of the order of the dynamics in the system). Note that second-order (and higher-order) systems don’t start moving at their maximum speed until after a lag period – the system has built in ‘momentum’ and needs to accelerate. When the damping factor becomes equal to one, the system is said to be critically damped . Te response looks very like an overdamped response, but represents a limiting case. As the damping factor drops below one, the response becomes underdamped , and produces the oscillatory behaviour shown in the figure 43.

Figure 43 – underdamped second-order response




8.2.7 DESCRIPTIVE TERMS FOR SECOND AND HIGHER-ORDER RESPONSE

Figure 44 – terms to describe responses

Rise time

Te time required to rise to the new setpoint for the first time after a setpoint change. More aggressive control reduces the rise time

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Decay ratio

Settling time


Te ratio of the heights of the first and second peaks of a response after a setpoint change (the ratio should also be fairly consistent on the following peaks too. Decay ratio may also be used to describe response on disturbance changes. Te settling time is the time required for a response to settle within a given band (often 5%) of the setpoint after a change. Settling time tends to increase as the aggressiveness of control increases, and so there is a direct conflict between minimising settling time and rise time.

8.2.8 FITTING A SIMPLE FIRST-ORDER MODEL TO HIGHER ORDER RESPONSES

Tere is often a need in dealing with control problems to obtain some sort of model of a particular process (remember that in control engineering a ‘process’ is simply something that converts input information to output information, and could be part of a unit operation, a measurement instrument, etc.). It usually isn’t practical, or even desirable, to obtain the full first-principles (based on fundamental balances) models and some sort of approximate model that captures the main features of a response is better. Te most common type of approximate model used for this purpose is a first-order plus dead-time model (FOPD). Tis can be represented by the differential equation: 

  

        

Figure 45 – a step response from a seventh order system




Te model has three parameters that need to be ‘fitted’ to make the model resemble the target system. Tese are: the time constant (τ ); the steady-state gain (K); and the dead-time (  ). One way of fitting this sort of model is to perform a step-test on the system to be modelled. Tis involves putting in a step into the process and recording the response. Tis will only work on over-damped higher order responses: the FOPD model cannot represent overshoot or oscillation. A typical response that might be obtained from a high-order system is shown in figure 45. As the order of the response increases, the length of the acceleration lag time also increases, producing an effect that looks very much like dead-time (although the output is changing from time zero, the changes are very small). o fit a FOPD model we can use the solution of the model’s response to a step change, and this is:        

 





where is the size of the input step. Steady-state gain can be determined by dividing the final steady-state change in output by the steady-state change in input. In the example in figure 45 a step of 1 unit was used, leading to a change of 1 in the output, and so the steady-state gain is 1/1 = 1. Tis leaves two parameters to fix: the time constant and the dead-time. Tese can be estimated by taking any two points on the curve. Any points can be used, but it makes sense to choose points which are reasonably far apart and in regions of the curve where the time and change are easy to measure. I suggest the points where the response is 30% and 90% complete. Te times at these points are read off from the response that’s being modelled (see figure 46).




Figure 46 – obtaining FOPDT fitting information





At the 30% point  

        

 

  



    



 



 

    

and at the 90% point  

         

 

       



 



 

    

Combining these two equations gives the values for the two dynamic parameters:           

In this example,

   and    ,

giving    and   




Te fitted model is shown in figure 47.

Figure 47 – High order response with fitted FOPDT model



9

DYNAMIC MODELLING

DYNAMIC MODELLING

MAIN LEARNING POINTS • Laplace transform solution of simple linear ODEs • ransfer functions and block diagrams • How to recognise response components (i.e. steady-state gain, order, poles, zeroes and time delays) in transfer functions and explain the contribution they may make to the final response • Forming simple dynamic models from continuity equations (mass, component mass and energy balances) Dynamic modelling is the modelling of process dynamics. It involves forming the differential equations, in most cases simplifying them if analytical (mathematical) solution is required, and then actually solving them (either analytically or numerically). Te most common technique used for analytical solution in control is Laplace transform analysis.




9.1

DYNAMIC MODELLING

LAPLACE TRANSFORMS

When a differential equation (in the ‘t’ or time-domain) is mathematically transformed through the use of Laplace transforms it becomes an algebraic equation (in the ‘s’ or Laplace domain). Tis algebraic equation can be manipulated and solved using the normal rules of linear algebra to produce an ‘s-domain’ solution. Tis solution is then inverted back into the ‘t-domain’ using tables of inverse transforms. 9.1.1 DEFINITION

If f(t) is a function in time, then its Laplace transform is defined as: 

  

    

   

Some important properties of Laplace transforms (from Marlin 1995): 1) A Laplace transform does not exist for all functions. Sufficient conditions for its existence are: a) f(t) is piecewise continuous. b) Te integral has a finite value (i.e. f(t) does not increase faster than e -st decreases. (Don’t worry about what ‘s’ actually is – it’s only a mathematical symbol and has no physical meaning at all. If you think too much about it you’ll end up joining the long list of mathematicians who’ve gone insane!) 2) Laplace transformation converts a function from the ‘t-domain’ into one in the ‘s-domain’, and the s domain function can have a complex (i.e. real and imaginary) representation. 3) Laplace transformation is a linear operation. i.e.               4) ables of Laplace transformations are commonly used to convert equations (they are available in text books). Tese tables are also used to provide inverse transformations.

9.2

DERIVATION OF BASIC TRANSFORMS

9.2.1 CONSTANT             



  

   

 



 


 

 


DYNAMIC MODELLING

Note that dt=d(t-td) because td (the time delay) is a constant. If the integration variable is now transformed:      





 

    

 

     

 



     

Note, by definition, that     for    



 



  



  

 



     

   

9.3

SOLUTION OF DIFFERENTIAL EQUATIONS USING LAPLACE TRANSFORMS

For this example I shall use the differential equation: 

  

     

where   is subjected to a step of 5 units (i.e. its value jumps from 0 to 5) at time t=0. 9.3.1 STAGE 1 – CONVERT THE ENTIRE EQUATION INTO THE S-DOMAIN

Since we are using deviation variables (see later for a definition of these), the initial values will all be zero (this is another very good reason for using deviation variables to solve control problems).

 

  

    

         

Note that y *(s) is the unknown output function that we are trying to obtain (in the s-domain).



DYNAMIC MODELLING

9.3.2 STAGE 2 – REARRANGE THE EQUATION ALGEBRAICALLY TO OBTAIN THE ANSWER (IN THE S-DOMAIN) 

       





      





   

   

9.3.3 STAGE 3 – USE A TABLE OF INVERSE TRANSFORMS TO INVERT THE SOLUTION BACK INTO THE ‘T-DOMAIN’

At this stage it is usually necessary to manipulate the s-domain function into a form that matches one, or more, of the tabulated functions. Tis is actually the most difficult part of the whole process. In this case we can see that

  

could be factorised to

 



 

and both of these factors appear in tables of inverse transforms: 















  



   



o invert the equation, we need to use partial fractions and evaluate A and B: 



   

 





  



       

and equating terms: s: 0 = 5A+B 1: 15 = A so A=15 and B=-5x15, and so     

  



 

  

  



 

  





DYNAMIC MODELLING

So, the ‘t-domain’ solution is: 

        

9.4



TRANSFER FUNCTIONS

ransfer functions are widely used to represent the s-domain dynamics of processes. Te definition of the transfer function of a process is simply:

  

         

for example, for a first-order process



  

    

              



 

 

   

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DYNAMIC MODELLING

NB: the second form of y*/u* with a single ‘s’ is simply a shorthand way of writing the ratio. Te transfer function contains all the information about how the process it describes will behave in response to any input. Te transfer function is a very powerful tool for handling linear process dynamics.

9.5

BLOCK DIAGRAMS

Block diagrams are a very useful way of graphically representing and, through the use of block diagram algebra, solving linear process control problems. Block diagrams are based around s-domain representations of the various system elements. Block diagrams are constructed from two types of blocks: 9.5.1 ADDITION/ SUBTRACTION BLOCK

Tis block adds (figure 48), or subtracts (figure 49), the signals supplied to it as inputs. i1(s) o(s)

+

i2(s)

o(s) = i1(s) + i2(s)

+ Figure 48 – Addition block

i1(s) +

i2(s)

o(s)

o(s) = i1(s) + i2(s)

Figure 49 – Subtraction block

An alternative notation is to use a circle contain the Greek letter ‘Σ’, with the signs on the signal lines attached to the block.



DYNAMIC MODELLING

9.5.2 TRANSFER FUNCTION BLOCK

Tis block contains a transfer function block – it can only ever have a single input and a single output (figure 50).

i(s)

5

o(s)

3s+1 Figure 50 – Transfer function block

9.6

BLOCK DIAGRAM ALGEBRA

As well as representing dynamic and control systems graphically, block diagrams can be used to combine the individual transfer functions to obtain the overall dynamic response. Te only rule of block diagram algebra is concerned with blocks in series. Consider the system in figure 51. o2(s)

i1(s)

TF1

TF1 i2(s) =o1(s)

Figure 51 – two TFs in series

Now, the overall transfer function for this system is:   

Because RULE:

9.7



 

is the same as

 

            

 .

for blocks in series, the overall transfer function is simply the product of the individual transfer functions .

SOLUTIONS OF RESPONSES FOR HIGH-ORDER SYSTEMS

Although Laplace transforms can be inverted for high order systems, the algebra involved in factorising the s-domain solutions into forms available in tables of inverse transforms can be very compicated.



DYNAMIC MODELLING

However, a great deal can be said about the form of the response of a high-order system simply by looking at the system transfer function. 9.7.1 FINAL VALUE THEOREM

Tis theorem is used to obtain the final steady state ‘t-domain’ solution directly from the s-domain solution:  

  

 

  

e.g. for a first-order process subjected to a unit step (a step of value 1):      

  







   

            

For stable systems subjected to a finite input change it’s possible to use a variant of this theorem to get the steady-state gain – just set ‘s’ to zero in all the terms of the transfer function. Tis works even with very complicated F’s!

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DYNAMIC MODELLING

9.7.2 GENERALISED DYNAMIC RESPONSE

Tis section is concerned with the information on the dynamic characteristics of the response that can be obtained from the transfer function. Tis information comes from the roots of the denominator (poles) and the numerator (zeroes). 9.7.2.1

Poles

Te denominator of a transfer function, also known as the characteristic equation, determines the overall form of the response of the process represented. Te order of this equation determines the order of the system response (i.e. if the highest power in ‘s’ is 4, then the transfer function represents a fourth-order system, and the corresponding t-domain differential equation would be fourth-order). Te roots of the characteristic equation are called the poles of the system and each root contributes something to the overall response (think of what you would do if you were trying to invert an s-domain solution – the first thing required is for the denominator to be factorised into bits that can be looked up in a table of inverse transforms). Obviously, the number of poles for a transfer function is the same as the order of the transfer function. Poles that have real values always lead to pure exponential terms appearing in the t-domain solution. If a pole has a negative real value (e.g. a factor like (s+1) – ‘s’ has a value of -1), then it will give rise to a term of the form e − in the t-domain solution, i.e. a term that will decay exponentially as time increases. If, on the other hand, the pole has a positive real value (factors like (s-1)), then it will give rise to a term of the form e i.e. one which increases exponentially with time. erms of this type cause the system to be exponentially unstable – no matter what the other terms are, a single unstable pole will make the whole response unstable. α t

α t

,

In process engineering problems, complex poles always appear in conjugate pairs (i.e. a + ib and a – ib). Complex poles give rise to sinusoidal terms in the t-domain response. If the real part of the pole (the ‘a’ bit) is negative then the sinusoid will decay away exponentially with time (whether the oscillation is apparent in the t-domain response depends on the relative values of all the poles of the transfer function). If the real part of the pole is positive, however, then the t-domain term will be a sinusoidal oscillation that grows exponentially in amplitude with time (oscillatory unstable). A single pair of such complex poles will cause the whole system to be unstable, regardless of what the other poles are.



9.7.2.2

DYNAMIC MODELLING

Zeroes

Te roots of the numerator of a transfer function (if any) are called the zeroes of the process. Zeroes modify the behaviour, but don’t change the overall order of a system’s dynamic response (unless they exactly equal a system pole and cause pole-zero cancellation – in this case the order of the response will be reduced by one for every cancellation). Zeroes with negative values will accelerate the initial response, and can cause overshoot even in processes with no complex poles. Systems with positive zeroes are more difficult from a control point of view since they exhibit what is known as inverse response. A system with inverse response initially responds in the opposite direction that its steady-state gain would indicate. Tis causes obvious problems with feedback control were the direction of control action is chosen on the basis of the sign of the steady-state gain on the manipulation term. Systems with positive zeroes always occur because there are two, or more, routes whereby an input can affect the output, but with opposite gains, for example for the system shown in figure 52.

Figure 52 – a system with a positive zero

    

   



   

                     

 

  

Tis is a second-order system with two negative poles and a single, positive, zero. Te response of this system to a positive unit step is shown in figure 53.



DYNAMIC MODELLING

Figure 53 – step response of an inverse response

Inverse response isn’t uncommon and can be seen in processes such as boilers and distillation columns. It can, however, cause big headaches when setting up feedback controllers.

.




9.8

DYNAMIC MODELLING

FORMING DYNAMIC MODELS

For many control purposes, when dynamic models are required they are produced by fitting simplified models to process data (e.g. the FOPD model fit that was described earlier). Producing a dynamic model from first principles is a major undertaking, not just because of the number of equations involved but also because of the need to obtain good estimates for all of the many parameters in the equations (e.g. heat and mass transfer coefficients). However, for some purposes, it is necessary to produce models that closely resemble the real process. For standard processes, this can often be done by using the ‘stock’ models that are available in the dynamic parts of process simulation packages (e.g. Aspen Dynamic). In theory, these models can be produced as a follow on from steady-state flowsheet modelling, by simply adding the various capacity parameters necessary for dynamic modelling (remember that capacities are what make processes dynamic). In reality, the modelling process is a lot more complex, and often special models need to be written to deal with non-standard bits of equipment. Although real dynamic modelling can be difficult and complex, the ideas behind it are relatively simple and involve only one equation – the continuity equation. As chemical engineers you’ll be very familiar with this equation already, although you’ve probably been calling it a mass balance or an energy balance or a component balance. Te full equation is always done over a capacity (something that has the capability of holding some of the quantity being balanced) and has the form:             

Te continuity equation needs to be applied to a conserved quantity : total mass (or moles); component mass (or moles); energy; momentum. Momentum balances are unusual in process engineering, and so we are normally concerned with just three quantities (total mass, component mass and energy). Forming the accumulation term is easiest if the following approach is taken:    

 

          

Remember that continuity balances are always made over a capacity.



DYNAMIC MODELLING

When you form continuity balances you should always get in the habit of checking the units of each term – this will check dimensional consistency, but will also highlight mistakes that may have been made in forming the equations. erms in a mass, or component mass, balances always have units of mass/time. Energy balance terms always have units of energy/ time. Remember to check the consistency of both the mass or energy units AND the time units used in the equation (i.e. don’t mix hours and minutes). 9.8.1 LEVEL IN A TANK WITH A FREE DRAINING DISCHARGE

Figure 54 – level in a free draining tank

We need to use a total mass balance to model the system  

               

Assuming constant and equal densities in all streams  

      

Assuming exit flowrate will be proportional to the square root of the pressure head,   



    


 


DYNAMIC MODELLING

9.8.2 CONCENTRATION IN A CSTR

Figure 55 – concentration in a continuous stirred tank reactor

Tis can be a little more complicated if we assume that the total mass balance is not constant, and a good bit more complicated if constant temperature is not assumed (i.e. if we need a dynamic energy balance). Let’s look at the simplest case first. Assume constant and equal densities in all streams; perfect level control (with the previous assumption this gives a constant mass balance and Fin=Fout); perfect mixing; perfect temperature control (i.e. constant temperature – no need to consider the effect of temperature on reaction rate).

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DYNAMIC MODELLING

All we are left with is a component balance for the reactant (and another for the product if we want to model this).  

                 

Assuming a first order rate expression (you’d normally know what the reaction kinetics were)          



 

     



And that’s all there is to it! If we remove the perfect level control assumption, then we need to include a total mass balance (and the inlet and outlet flows might be different)  

     

  

   

Te component balance also needs to be reworked as V is no longer assumed constant  



       

 



 



       

we can get an expression for dV/dt from the total mass balance 

 

             

 

      



DYNAMIC MODELLING

Relaxing the level control assumption hasn’t changed the order of the response for the reactor concentration to changes in inlet flow or concentration. If we go a step further and relax the perfect temperature control assumption, we need to add an energy balance to the system (assuming constant and equal specific heat capacity)



                       

 

  



                      

 



 



 



                 





 

 





  

         



 



Te component balance will also need to be modified to take into account the temperature dependent rate constant, giving:  



       



 

Note that the energy balance contains the concentration and the component balance contains the temperature – it isn’t possible to solve these equations individually. Tey need to be solved simultaneously and will produce second order dynamics in both the concentration and temperature responses. 9.8.3 TEMPERATURE OF A THERMOMETER BULB

Figure 56 – temperature of a thermometer bulb



ANALYTICAL SOLUTION OF REAL WORLD MODELS

10 ANALYTICAL SOLUTION OF REAL WORLD MODELS MAIN LEARNING POINTS • • • •

Non-linearity Linearisation Deviation variables Step-response solution for a simple, but realistic, process

Laplace transforms are a very powerful method of solving differential equations, but they are limited to linear differential equations. Tere is, in fact, no general solution method for non-linear differential equations. Unfortunately, almost without exception, the models that are produced for process engineering problems will involve non-linear equations. Tese non-linear models can be solved using numerical (dynamic simulation) techniques, but analytical (mathematical) solutions have advantages. It’s much easier to understand the overall behaviour, and sensitivity, of a solution by looking at an equation than it is by looking at the results of multiple simulation studies. Linear solutions also allow more advanced analytical techniques to be used for controller design.

10.1 TYPES OF NON-LINEARITY Before considering how we can deal with non-linearity it is worthwhile looking at the sorts of non-linearity that can arise in process industry models. A differential equation is non-linear if a non-linear function, or multiplicative combination, is applied to any of the time-varying (inputs or outputs) terms. 10.1.1 FUNCTIONAL NON-LINEARITIES

Functional non-linearities are the easiest to spot – a non-linear function is applied to input or output terms. Te following are examples of process engineering equations with functional non-linearities:  





    

         




It is possible to subject linear differential equations to non-linear inputs and have something that is perfectly solvable (since the differential equation itself is linear): 

         

if     then this can be inserted into the equation: ,



     

Tis equation can be solved. 10.1.2 COMBINATIONAL NON-LINEARITIES

Combinational non-linearities occur when two, or more, time varying terms are multiplied, or divided, together. Tey can be awkward as an equation can change from being linear to non-linear depending on the assumptions that are made as to what terms are time varying. For example, consider the reactant balance in a simple CSR:  



     

If we assume that only the inlet concentration (  (and also, since it’s the equation output, the outlet concentration) is variable, then the equation is linear. However, if we also allow the flowrate through the reactor ( ) to vary as well, then we end up with two combinational non-linearities ( and  )

10.2 LINEARISATION OF NON-LINEAR EQUATIONS One way of dealing with non-linear equations is to approximate (linearise) them with linear equations. Tis only works if the amount of variation is limited to a small region around the point where the equation is approximated (the point of linearisation). In most control problems in the process industries we are concerned with disturbance rejection around the nominal flowsheet conditions and linearised equations can give reasonable approximations. Te process of linearising an equation involves identifying all the non-linear parts of the equation and then replacing them with a linear approximation. Tis can be understood either graphically or with reference to aylor series approximation.




10.2.1 GRAPHICAL INTERPRETATION OF LINEARISATION

Figure 57 – graphical linearisation

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In figure 57, ‘X’ is the time varying quantity (input or output) that is subjected to some non-linear function, producing the relationship shown in the blue line on the graph. If we want to approximate this function with a straight line, we first need to pick where we want to form the approximation – the linear approximation we get will vary radically with the point of linearisation that is chosen. In this case we’ve chosen to linearise around the nominal steady-state (which is what’s usually chosen for control). o approximate the nonlinear function at this point, we draw a straight line through the point of linearisation with a slope which is tangent to the curve at that point. Te equation of this straight line will now give use the linear approximation to the function, i.e.

   

 

 

      

or       



   

10.2.2 TAYLOR SERIES INTERPRETATION OF LINEARISATION

A aylor series:      



 

    

  

  









can be used to approximate any function to any desired degree of accuracy. For linearisation, we can’t use any terms after the first order terms – if we do we’ll end up with non-linearities (e.g.   ) in our ‘simplified’ expression. If we omit all terms which are second-order and higher then we get:       



   

which is exactly the same as that obtained from the graphical interpretation.




Tere are advantages in thinking about linearisation in terms of the aylor series. Te first is that it allows us to gauge how accurate our approximation will be. For aylor series approximation, the error is of the same order as the first-term that is omitted. For linearisation this is: 

  

  







So, the linearisation accuracy is dependent on the second-derivative of the non-linear function, and on the square of the distance from the point of linearisation. Te second derivative can be thought of as a measure of the non-linearity of the function at a particular point – high values of second-derivative means that the slope of the function is changing rapidly, i.e. it is highly non-linear. Te second advantage of the aylor series interpretation is that it can be easily extended to multi-variable (combinational) non-linearities, e.g.                       

 

 

     

 

    

    

10.3 SIMPLIFYING EXPRESSIONS THROUGH DEVIATION VARIABLES In control problems we are usually interested in how things change around a particular operating point – usually the nominal steady-state. Leaving steady-state information in our equations can make things really messy. Tis mess comes from two sources: linearisation, and initial values in Laplace transforms of derivatives. Linearisation always produces a whole bunch of steady-state terms that need to be included in the linearised equation (e.g.    ). When we take the Laplace transform of a derivative of a variable with a non-zero initial value (i.e. it has a steady-state component), then we get an expression of the form: 

 

    

Higher-order derviative will produce more steady-state terms.




All this steady-state information makes the equations messy and difficult to handle and contributes absoultely nothing. Te steady-state information will be the same at the end of the solution as it was at the beginning. Deviation variables are a mathematical trick that get rid of the steady-state components of a solution and make equations much easier to handle. Te definition of a deviation variable is:      

Te value of the deviation variable (marked with an asterisk) is equal to the full-value variable (which changes with time) minus the steady-state value of the variable (that is fixed). It’s possible to convert an equation to deviation variable form by inspection, although care needs to be taken to take the deviation of complete non-linear terms (rather than the nonlinear function of the deviation), e.g.  



    





becomes  









  

 

Using deviation variables makes things much simpler, e.g. 

 

       

  



  

   

         

 



      

10.4 PROCEDURE FOR SIMPLIFYING AND SOLVING A NON-LINEAR MODEL Te following is the best procedure to be followed when analytically solving non-linear equations: 1. Identify non-linear terms and draw a bracket around them 2. ake the deviation of all the time-varying terms – remember to take care with non-linearities. 3. Linearise the non-linear parts of the expression 4. Solve the model using Laplace transforms 5. If required, add back the steady-state components.

10.5 PUTTING IT ALL TOGETHER – A REACTANT BALANCE FOR A CSTR A continuous stirred tank reactor (CSR) is used to breakdown a material in a reaction with a second order rate law:     

Te reactor operates at constant density and has perfect level and temperature control (the total mass and energy balances are steady-state). Te nominal operating conditions for the reactor are shown in table 9.




Operating volume

3 m3

Flowrate through the reactor (inlet and outlet)

1m3.hr-1

Inlet concentration of reactant

50 kg.m-3

Outlet concentration of reactant

0.1 kg.m-3

Table 9 – reactor conditions

Develop a dynamic model of the reactor around its nominal operating conditions and show how it responds to a) a step change in the flowrate from 1 to 1.1m 3.hr-1; b) a step change in inlet concentration from 50 to 55 kg.m -3. Te first thing to do is to form the continuity equations necessary for modelling the reactor. We’re told that we have a constant total mass balance and a constant energy balance (and reactor temperature), so the only equation we need to form is the component mass balance for the reactor:  

                

It’s always worthwhile, at least initially, to write down the equation in words first. Now let’s add the maths:  

        



or  



     



since the liquid volume is constant. Check the units of each term – the flow rate x concentration terms are kg/hr, as is the reaction rate. Te term inside the bracket on the accumulation is kg, and a d/dt derivative is being applied to it, which converts it to kg/time unit. Since the RHS of the equation is using hours as the time unit, this is the unit that the derivative will be expressed in too. Te units in the equation are fine.




Te next stage is to identify non-linearities. We know that the C 2 term will be a functional non-linearity, since C is the output of the equation and so is time varying. Tere are two other possible ( and ) combinational non-linearities in the equation, if F is allowed to vary. We know that we’ll have to vary F to get the answer to part (a), so it makes sense to include it as a potentially time varying term. In control problems the more variables that are allowed to change with time, the more complicated the solution and so it’s important to only allow things to vary if you have to. At this point we’ve identified the time varying quantities; all the other terms in the equation will be constants (at least from the point of view of this problem). It’s worthwhile getting the values of these constants in now:  



     



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‘k’, the reaction rate constant, is a constant but we haven’t been given its value. We do, however, have the nominal steady-state values for the other variables and so can calculate ‘k’ from a steady-state balance: 

 

   

 





 



          



 

Inserting this back into the dynamic equation gives  



     



Bracketing the non-linear terms and taking deviation variables:  

 

 



 



 

 

Now we need to linearise the bracketed non-linear terms 





 



 









 





      



    





      

   



 



 

 

  





 

 

 



 



Substitute the linearised approximations back into the original equation:  











       



 






Rearranging  









     



Converting to standard form: 















     





We We can see a lot about the sort of response we can expect just by looking at the equation. Te equation is first-order and is stable, so we know the shape of the response to a step change in input. Te time constant of the response is 3×10 -3 hrs, or 10.8 seconds – after a step, we can expect the response to be 63% complete after 10.8sec (one time constant), 95% complete after 32.4sec (3 time constants) and 99% complete after 54 seconds(5 time constants). Te steady-state gain on flowrate changes is 0.04995 – if we change the flowrate by 0.1 m3.hr-1, we can expect the final outlet concentration (steady-state) to change by 0.004995 kg.m-3. Te gain on the inlet concentration is 10 -3 – a change of 5 kg.m -3 in the inlet concentration should produce a final outlet concentration change of 5×10 -3 kg.m-3. Te t-domain response to a step in F* we’ll get from this system is described by the equation: 



     







PID CONTROLLER ALGORITHM

11 PID CONTROLLER ALGORITHM MAIN LEARNING POINTS • On-off control and deadbands • Te components of a PID algorithm algorithm and how they contribute to the overall overall controlled system behaviour • Te effect of controller gain, reset time and derivative time constant on a controlled system’s response • Some of the different forms of the PID algorithm I’ve already discussed the basic idea of feedback control, where the controller takes a fedback measurement of the controlled output, compares it with a setpoint, and then computes a manipulation value that will bring the two closer together. We haven’t so far considered the algorithms that can carry out this computation, but we’ll do so in this section.

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11.1 REALLY REALLY SIMPLE FEEDBACK CONTROLLER CONTROLLER – ON-OFF

Figure 58 – pure on-off control

Te simplest type of feedback controller is one that implements an on-off control algorithm. In this algorithm, the controller output has only two states: fully on; or fully off. Let’s say the process to be controlled has a negative overall gain (i.e. a fully on controller action will produce a negative change in controlled variable output). In this case, if the measurement rises above the setpoint the controller will open its output fully and so drive the controlled variable back down. Te controller will hold its output on until the controlled variable crosses the setpoint and becomes less. At this point, the controller output will switch to fully off, to raise the output once more towards the setpoint. Tis behaviour will repeat at a frequency which is dependent on the dynamics in the system, producing a fast oscillation like that shown in the figure 58.

Figure 59 – on-off with deadband




Te high frequency oscillation of pure on-off control holds the controlled output close to the setpoint at all times (provided the control effort is sufficient) but is often not acceptable due to the wear it causes to the final control element which must switch between fully on and fully off at a high frequency. In situations where this is likely to be a problem (i.e. almost always) on-off control may be implemented with a deadband around the setpoint. Te deadband, which is often made adjustable, is a region around the setpoint where the controller takes no action at all. If a deadband was added to the controller in the example above, then the controller would not change state the first time until the controlled variable moved past the upper edge of the deadband. Tis would cause the controlled variable to start to move down, back towards the setpoint and cross back into the deadband region. Te controller takes no action and the controlled variable moves further down, and eventually crosses the setpoint. Te controller still takes no action, until the controlled variable crosses the lower edge of the deadband. At this point, the controller switches the output to fully off and the controlled variable begins to rise again. Tis behaviour continues for as long as the controller is switched on, causing a lower frequency oscillation which is dependent on the dynamics of the system and on the width of the deadband – larger deadbands will cause lower frequency oscillations. Te behaviour of an on-off controller with dead-band is illustrated in figure 59. Deadbands are sometimes used with more sophisticated controllers too as they prevent the controller taking action when the controlled variable is oscillating around the setpoint value due to noise. On-off control is common in domestic applications – most central heating systems operate using this type of control. However, the continuously oscillating nature of the response is not desirable in process engineering applications, where there are usually several hundred individual controllers involved.

11.2 PROPORTIONAL-INTEGRAL-DERIV PROPORTIONAL-INTEGRAL-DERIVA ATIVE (PID) CONTROL Te Proportional-Integral-Derivative controller is almost universally used in feedback control applications in the process industries. Even when more sophisticated controller techniques, such as predictive control, are used they often cascade down onto lower level PID controllers that actually make the changes to the process.




Te PID algorithm was first developed by an engineer who was designing an automatic steering system for ships in the US Navy. He observed that the human helmsman, who was given a bearing to steer by the captain, adjusted the position of the ships wheel according to three factors: how far the current bearing was from the desired bearing (a big difference would result in a big change in wheel position – the action is proportional ); how long the bearing had been different from the desired bearing (if a difference was persisting, then the helmsman would turn the wheel further – effectively integrating the error); how quickly the actual bearing was changing (if the actual bearing was changing very quickly towards the desired bearing, then the helmsman would see that the time based derivative was too high and move the wheel back a bit). Te earliest PID controllers implemented these human generat ed control rules by mechanical means, with bellows, nozzles, flappers and compressed air. Soon, however, there was a need for analysis and the PID algorithm was expressed mathematically. Tere are many different forms of the PID algorithm, but the one we’ll mainly be using in this course is what is known as the classical form:      

 

  

 

 

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Where









=

=

=

=



=



=



=


control action (controller output) a switch, to switch the controller between direct (‘+’) or reverse (‘-’) action error =    controller gain, an adjustable parameter integral time constant, also known as reset time, an adjustable parameter Derivative time constant, an adjustable parameter Te nominal controller output at zero error, an adjustable parameter.

Te PID controller can be used in a variety of different ways, and the individual parts (proportional, integral and derivative) can be switched off to make the algorithm suit different applications. Te most common way PID controllers are used in the process industry is as a PI controller (with the derivative switched off), P controllers (integral and derivative switched off) are sometimes used for level control, full PID control is used on fairly slow non-noisy systems. Te other possible control modes (I,ID,PD) are very rarely (never?) used in the process industries and derivative-only control is never used, as it wouldn’t work! It is useful to consider each of the three control modes individually, however.

11.3 PROPORTIONAL ONLY CONTROL Tis is a PID controller with the integral and derivative actions turned off (by setting the respective time constants to infinity and zero). Te algorithm is now:       

Proportional action provides the fastest response of the three terms when an error enters the system. It generates a change in the controller output instantaneously, and the size of the change is proportional to the size of the error.




Figure 60 – a P-controlled level

When used on its own, as a P controller, proportional action does have limitations. Consider the system shown in figure 60. When the system is at its nominal steady-state (steady-state at flowsheet conditions) the error in the controller will be zero (the level will be at the setpoint) and the manipulated exit valve will be held open, by the bias term, far enough to make sure that the exit flowrate matches the inlet flowrate. If a disturbance now enters the process that causes the inlet flowrate to rise, the level in the tank will start to increase. Te controller will detect this increase, and will start to open the valve. If the gain is very large it will open the exit valve a long way, to bring the level back towards the setpoint very quickly. However eventually, provided the system is stable, the controller will reach a steady-state where the outlet flowrate matches the inlet flowrate, and the level will stop changing. However this steady-state will only occur if there is a non-zero residual steadystate error called the steady-state offset . If the offset isn’t present (i.e. the error is zero) the output of the controller will be equal to the bias and the flow out will be equal to the original flow. Te only way the system can come to steady-state under proportional-only control is to have a steady-state offset. Tis is a ‘feature’ of proportional-only control and occurs on all disturbance changes, and on almost all setpoint changes (the one exception is when controlling a system with an integrator, such as the system in figure 60) where setpoint changes will be tracked without offset. Te amount of offset can be reduced by increasing the gain (as the gain tends to infinity, the offset tends to zero), but in practical systems stability considerations limit the maximum value of gain that can be used.




Te most common use of pure proportional control is in level control, where exact control of the level isn’t usually required – all that is important is that the level is kept between certain limits(although in practical situations a little integral is still added to ‘centre’ the response). In these situations, allowing the level to vary can be a positive advantage, as the capacity can smooth out variations in the input signal. Figure 61 shows the level in a system like that in figure 60 with a very high gain proportional controller, with the input flow being subjected to a sinusoidal variation.

Figure 61 – Level in a high-gain P controlled tank

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Te setpoint of the controller is set at 1, and you can see that the high gain of the controller is very successful in holding the level close to this value.

Figure 62 – inlet and outlet flows at a high gain

However, now look at figure 62 – this shows the input (red) and output (blue) flowrates from the tank (you won’t be able to see the two traces as they overlap). Te high gain means that the controller is moving the valve a long way in response to level changes, and the variations in the inlet flowrate are being passed straight through to the outlet. Dropping the controller gain results in much more variation in level (figure 64), but also reduces the variation in flowrate that is passed through the tank (figure 63). Te tank is being used for surge control .

Figure 63 – inlet and outlet flows at low gain




Figure 64 – Level changes at low gain

11.3.1 CALCULATING THE GAIN FOR LEVEL CONTROL APPLICATIONS

If the plan is to use the capacity of a vessel to even out variations in the inlet flow, then it is possible to calculate an appropriate gain directly from a knowledge of the maximum allowable variations in the level, and the maximum changes in the disturbance flowrate. Te maximum variation in level will be when the system comes to steady-state after a maximum change in disturbance flowrate. At this point, the manipulated flowrate needs to be equal to the disturbance flowrate, so the change in the manipulated flowrate needs to equal the change in the disturbance, i.e.     

Hence, the gain can be calculated. Note that the gain that is calculated is the product of the controller and valve gain (i.e. the gain between the measurement and the change in flowrate). Example: What gain would be required to limit changes in level to ±0.5m, when the inlet flowrate changes by ±5m3.h-1.   





 

 





Te controller gain would need to be obtained from this value from a knowledge of the valve gain. Adjustments would also have to be made to deal with the dimensionless gains that are used in all controllers. In practice the gains on level control systems are usually adjusted by trial and error, guided by prior knowledge.




11.4 INTEGRAL ONLY CONTROL Although integral-only control isn’t commonly used (and is impossible to implement using the classical PID algorithm) it is useful to consider its behaviour as it sheds light on the contribution integral action makes when mixed with the other control modes. An algorithm for integral-only control is:    

  

Te integral gain,  is an adjustable constant. In the classical algorithm it is made up of two other constants, i.e. ,

 

 

changing either  or  will change the value of the integral gain, and hence the effect of integral action. However if the controller gain is changed then this will affect the proportion al and derivative components as well (which makes controller tuning a bit easier). In mixed mode (e.g. PI or PID) controllers the relative effect of integral action is adjusted by changing the integral time constant.

360° thinking

.

.



.





Now, let’s look at an integral-only controller’s response to a constant error (let E is a constant). In this case the controller output is:   

   where

  

     

So, a pure-integral controller will respond to a constant error with a controller output that increases linearly with time, with a gradient which is dependent on the size of the error and on the integral gain. Tis is the big advantage of the integral term – while an error is present in the system, integral action will always be changing the controller output to try to eliminate the error. Te integral part of a PID control will only stop changing the controller output when the error becomes equal to zero. A controller which has integral action enabled will not suffer from steady-state offsets – these will always be eventually eliminated by the integral part of the algorithm. Tere is a practical downside to the continuous integration of the error and hence the continuous change in controller output. In real systems there is a limit on the range of any manipulation that can be applied – a valve can’t be more closed than fully closed, nor more open than fully open. A pure integral controller won’t recognise this – it will continue to integrate the error even when the controller output has reached it high or low limit (this is known as output saturation). Tis causes problems when the error reduces – the large error integral that has been built up will hold the output against the limit for a long time, resulting in the measured value grossly overshooting the setpoint. In extreme cases this behaviour, which is called integral saturation or reset windup, or just windup, can cause the output of the controller to oscillate between its high and low limits. All controllers are protected against local windup (windup caused by the limits of that controller being reached). Tis is often done by simply switching off the integration of the error when an output limit is reached, and then switching it back on when the output moves off the limit. Saturation is a potential problem, however, when multiple controllers are connected in a cascade arrangement – this is described later.

11.5 DERIVATIVE ACTION Derivative only control is never used. Te reason is clear to see when the equation for derivative-only control is considered:

    

 

 




Derivative action works on the derivative of the error. It only changes the controller output when this derivative is non-zero. Provided the error isn’t changing, derivative action will do nothing at all, regardless of the actual value of the error. As a mechanism for reducing error, derivative action is useless. When working with the other control modes, however, derivative action can result in significant control performance improvements. Derivative action generates a controller output change which is proportional to the rate of change of the error. If the error derivative is large and positive (i.e. the error is rapidly increasing) then derivative action will make a big positive change in the control action – it will apply lots of effort to try to reduce the future error. On the other hand, if the error derivative is large and negative (i.e. the error is rapidly decreasing) then this is probably because excess control action has already been applied and the measured value is likely to significantly overshoot the setpoint. In this case (with a large negative error derivative) derivative action will make a big negative change in the control action to try to reduce the rate of setpoint approach. Using derivative action alongside the other control modes can stabilise the controlled response and allow higher gains and shorter integral time constants to be used, and so improve the quality of control. However, despite the potential improvements that derivative action can provide, there are two reasons that it isn’t frequently used: it’s awkward to tune; and it has real problems with noisy systems. Derivative action is difficult to tune because it only really improves controlled response through its interactions with the other control modes. Changing the gain or integral time constant will change the effect that the derivative action has. Tis can lead to a long, and expensive, trial and error tuning process. However, the second problem (it’s sensitivity to noise) is even more serious.

Figure 65 – Moisture measurements from a dryer in a whisky distillery




Figure 65 shows some moisture measurement information from a grain dryer in a whisky distillery. Te important thing to notice is the spikes and ‘rapid’ fluctuations in both traces. Te real process was a big rotating dryer (over 4m long and 2m in diameter) which contained several tonnes of grain. Tis had a time constant measured in hours, and this can be seen clearly on the trace on the right, where the controller moves the moisture content from just under 15% down towards the setpoint of 12.5%. On top of the real process variation there is a whole lot of random noise that is superimposed. Te grain in the dryer isn’t perfectly mixed and the infra-red sensor (used for moisture measurement) only looked at a small portion. Sometimes the grain that was measured could have come from direct contact with the heated surface and so be much dryer than the bulk, and other times grain that hadn’t really touched the heaters would be scanned. Tese variations gave ‘spikes’ in the moisture measurement.








Imagine what would happen if a measurement signal of this sort was fed directly into a controller with derivative action. Te derivative part of the controller generates a change in output that is proportional to the error derivative, and the spikes would produce huge values of this (even if the error wasn’t large, the derivative is). Tis would cause the derivative action to make large changes to the controller output, which would then be applied to the process causing large, real, changes to the controlled variable. Very quickly the whole system would become unstable. If derivative control is to be used on a system, then any noise needs to be filtered out. Tis is relatively straight forward when the noise is of a significantly different frequency, compared to real process changes. In temperature control in large tanks the noise frequency will be multiple Hz, compared to the vessel time constants of several hours and the noise can be almost completely removed without affecting the process signal. In faster systems, like flow control, where the noise and real measurement change at similar rates it is impossible to remove the noise without significantly degrading the process measurement, and derivative action should never be used.

11.6 PROPORTIONAL-INTERGRAL (PI) CONTROL PI control is by far the most common type of feedback control in the process industries. It is achieved by simply setting the derivative time constant to zero, producing the PI algorithm:      

 

  

With the classical algorithm, the controller gain affects both the proportional and integral parts of the algorithm. o change the relative balance between the two, the integral time constant is adjusted. In the PI algorithm, the proportional part provides the immediate, fast, response to errors entering the system. Te integral part of the algorithm then removes any residual steadystate error.




11.7 PID CONTROL RESPONSE

Figure 66 – a PID controlled response

Figure 66 shows the results of a simulation of full PID control of a third-order process. Te top plot shows the values of the controlled variable (in red) and the constant setpoint (the green line). Te process was disturbed at time t=0 by injecting a step disturbance, and the PID controller attempted to counteract the effects of this disturbance. In the three plots below the controlled variable, I’ve separated out the contributions made to the overall controller output by the proportional, integral and derivative parts.




At point ‘A’ the disturbance has caused the controlled variable to move away from the setpoint, but the error is fairly small. Proportional action has gone positive, but isn’t too large as the error is small. Integral action has also gone positive, but the effect is small, because the error and the length of time it has existed are tiny. Derivative action has gone positive, and to a larger extent than the other two control modes. Although the error is small, the error derivative is large. By applying a large positive control action the derivative term will act to reduce this error derivative and so reduce the amount of deviation from the setpoint. At point ‘B’ the controlled variable has reached its maximum positive deviation from the setpoint. Te proportional action is now generating its maximum positive effect (remember that it generates an action which is proportional to error). Te effect of integral action has increased, but is still well below its maximum value – the time hasn’t been sufficient to build up a big error integral. Derivative action is at zero as the direction of change switches.






At point ‘C’, the error is still positive but the controlled variable is moving back towards the setpoint. Te proportional term is still producing a positive control action, but less than the maximum. Te integral term is adding a large positive contributi on, as it has been integrating the error over all the time since the disturbance entered the system. Derivative action is now producing a negative contribution to the overall control action – it is reducing the effect of the other two control modes. Tis is because the error derivative is now negative. Derivative action is slowing the rate of approach to the setpoint and hence the size of the subsequent undershoot of the setpoint. At point ‘D’ the controlled variable dips below the setpoint, and the error becomes negative. Proportional action switches negative as a result, and is trying to drive the controlled variable back up. Integral action remains positive – it has built up a big positive integrated error. Te output from the integral term is a bit less that its maximum value because the negative error has started to eat away at the accumulated positive error integral. Te derivative term is still negative as the error derivative is negative, and derivative action is working with the proportional term to pull the controlled value back towards the setpoint. At point ‘E’ the system has now almost reached steady-state. Te controlled variable is sitting on the setpoint and so the error is zero. Te proportional and derivative terms’ contribution have dropped to zero as the error and error derivative are zero. Integral action is, however, significantly non-zero. Tis is because the integral action is applying all the steady-state correction that is required to precisely counteract the effects of the disturbance. Although the other two control models are doing nothing at the final steady state, they did contribute significantly to the dynamic behaviour of the response.

11.8 OTHER FORMS OF PID ALGORITHM Te classical form of the PID algorithm is only one of many that are available. In the past individual manufacturers had their own takes on the algorithm and supplied controllers with these ideas built in. Nowadays most modern controllers offer a choice in the type of algorithm that the controller uses. Tere usually aren’t strong reasons to use one algorithm over another; it’s often just a matter of taste and what the particular control engineer is used to. 11.8.1 PARALLEL, OR NON-INTERACTING, ALGORITHM   

   

  

 

 

In this algorithm the proportional, integral and derivative terms have their own independent gains. Adjusting the proportional gain no longer affects the other two terms.




11.8.2 SERIES ALGORITHM    



 



  

 

 

Tis is a bit of a mess of an algorithm that is a historical artefact; it can be implemented using a single pneumatic or electronic amplifier. Te problem with the algorithm is that all of the terms interact with each other making it difficult to relate the output of the controller to the individual modes (which is handy to be able to do for controller tuning). 11.8.3 ALGORITHM TWEAKS

Tere are lots of minor and not so minor tweaks for the PID algorithm that may be implemented in particular controllers. Derivative action is sometimes based on the derivative of the measured variable, rather than the error. Tis deals with the potential problem that can be caused with the standard method (derivative of error) when somebody introduces a step change in setpoint (and so creates an infinite error derivative!) Almost all practical derivative action is implemented with a built-in first-order filter. In early controllers this was essential, as it was the only way that the derivative could be obtained – an analogue mechanism can’t ‘save’ old values like a digital system. With current controllers, the filter provides protection against sudden changes in setpoint (if the derivative is error based) and spikes in the measurement (although the measurement should already be filtered sufficiently outside of the controller). Modifications can also be made to proportional action. Using the square of the error dramatically increases the change on large errors, but reduces the action on smaller errors. However, this produces a non-linear controller that can be awkward to tune. 11.8.4 DIGITAL IMPLEMENTATIONS OF THE PID ALGORITHM

Te PID algorithm needs to be altered to work in digital systems that rely on sampling the process (the measurements are numbers that represent snapshots of the process state). Te positional algorithm is a direct conversion of the analogue algorithm into its digital equivalent, and generates the actual value of the controller output:

       

 



    

      


 



or        

 

   

       

Te control algorithm gives the change required in the controller output, and so this needs to be added to the previous output. Te reason that this form of the algorithm is popular is because it provides bumpless transfer from manual to automatic operation in the controller. Most processes are moved to new operating points under manual control. When the operator gets the process near to where it should be they will flip the switch to put the controller into automatic mode. With the positional algorithm, if the error is not exactly zero then the proportional term will cause a sudden change in the controller output and this will be transmitted to the process causing a sudden disturbance (a bump). If the velocity algorithm is used, then a non-zero initial error won’t cause an immediate proportional response (since the proportional action operates on the change of error). Instead, integral action will activate (this will be tuned to be much less aggressive than proportional) and make gradual changes in the controller output to reduce the error.



CONTROL SYSTEM ANALYSIS

12 CONTROL SYSTEM ANALYSIS MAIN LEARNING POINTS • Analysis of simple feedback control systems using transfer functions and block diagrams • Analysis of the response of first- and second-order process under pure proportional control • Analysis of the response of first-order processes under pure integral control. Control system analysis involves using mathematics to understand the behaviour of control systems. Tis lets us predict how particular systems will respond and, more interestingly, allow us to design control algorithms and systems that will produce particular desired behaviours.

12.1 ANALYSIS OF A TYPICAL FEEDBACK CONTROL SYSTEM ransfer functions, which we have already covered, and block diagrams are a very powerful way of analysing control systems. A typical feedback control system is illustrated in figure 67.

Figure 67 – a typical feedback control system

GC is the transfer function for the controller algorithm; G CV is the control valve F; G P is the manipulation process transfer function (i.e. the ‘process’ by which the manipulation affects the controlled output); G d is the disturbance process transfer function; and G m is the transfer function of the measuring instrument.    is the Laplace transform of the setpoint signal (expressed in deviation variables);

   a disturbance signal; and    the controlled variable.

Gd and Gp represent the model of the whole 2 input/single output process that is being controlled. Te input to G P is the manipulation signal, which is being adjusted by the control loop.




Te control valve and measurement transfer functions are real – there is a gain between the controller output and the flowrate, and the measurement and the signal transmitted back to the controller, and both devices will have dynamics. However, for simplicity, we’ll be assuming that the dynamics are very fast (i.e. time constants close to zero) and that the gains are absorbed into the process transfer functions (i.e. G p contains not just the process gain, but the gains of the control valve and measuring instrument too). Te equation can therefore be simplified to                  

or   

    

  

     

  

12.2 THE PID ALGORITHM AS A TRANSFER FUNCTION o carry out a control analysis on a PID-controlled system, we need the controller transfer function. Te classical algorithm is:      

   





 

Tis needs to be converted into deviation variable form: 





    





   







and then into Laplace transforms: 



      

     

  

   



     

     

and so the transfer function of the PID controller is:   

   

   

  

  




12.3 ANALYSIS OF PROPORTIONAL CONTROL OF A FIRST-ORDER PROCESS For a proportional controller  

 

and for a first-order process   

 



  



 

if the time constants for the disturbance and manipulation are the same (as they often are). ‘u’ is the symbol normally used for the manipulated variable, ‘d’ for a disturbance, and the ‘K’s are the manipulation and disturbance steady-state gains. Note these are shown as positive in this example, but can be either positive or negative – it depends completely on the process model. We can represent this controlled system on a block diagram shown in figure 68.

Figure 68 – A first-order process with proportional control

Forming the overall (closed-loop) transfer functions:        

  

  

  

 



      

 

        

  

  

  

  

       

  




We can look at the steady-state behaviour of this system by setting terms with ‘s’ to zero:

 

    

 

     

 

If the system was open-loop (with the controller switched off), then the steady state change in the output on a disturbance change would be   . Adding proportional control has reduced this change in the output by a factor of     . Te closed loop disturbance gain of the system is now:     

When the disturbance changes, there will be a steady-state offset even when the controller is active. However this offset will be smaller when the controller is active than when the system is open-loop. Te controller gain,  is an adjustable parameter and can be altered to provide any desired reduction in offset – as the gain approaches infinity, the offset will approach zero. ,





Tere will also be an offset on setpoint changes, as the closed loop gain is less than one. Te size of the offset will be given by: 

     

 

A controller with no offset would have a setpoint gain of one. Again, larger values of controller gain will make this residual steady-state offset smaller. Now let’s look at the effect of control on dynamic performance. o do this, rearrange the closed loop Fs slightly to get them into standard form:    

 

   

      

  

   

      

  

Adding the controller has not changed the order of the response – the controlled process will still respond in a first-order manner, but it has changed the gains (as we’ve already seen) and the time constant. Te time constant has been reduced by a factor of     and so the controlled process is faster than the open loop process. Te higher the controller gain is set, the faster the controlled response. ,

In a pure first-order process there is no limit to how high the controller gain can be set. It is impossible to destabilise the controlled response by increasing gain. However, all practical processes are third-order or higher (see earlier) and these can always be destabilised by excessive controller gain. Eliminating offsets by using very large controller gains is never practical.

12.4 EXAMPLE OF A FIRST ORDER PROCESS UNDER PROPORTIONAL CONTROL A stirred tank with refrigeration coil is used to cool a process stream. Te inlet temperature of the process stream is subject to disturbances and it is desired to use a proportional controller to regulate the outlet temperature of the tank by manipulating the power of the refrigeration unit. Te transfer functions of the system have been estimated as:   

   

   

   

  




where  is the tank outlet temperature,  in, the inlet temperature and Q the refrigeration power in W. Te time constants of the Fs are in minutes. If a proportional controller is used, what gain is required to reduce the steady-state change in outlet temperature to 0.1 oC after the inlet temperature changes in a step by 5 oC? Sketch the response of the controlled system and indicate how long it will take to come to steadystate. What will be the change in refrigeration power at the new steady-state? Normally I’d draw a block diagram of the controlled system, but since we’ve already had several of these let’s just insert the controller algorithm directly into the Fs:             

Note that I’m using a direct-acting controller – this is because the gain on the manipulation process is negative. Substituting for the manipulation in the Fs gives:   

   

   

   

       

Moving  to the LHS of the equation  



   



   

   

   

  

we’re just interested in disturbance rejection, and so we can set the setpoint change to zero and re-arrange: 



  



    

 

Te steady-state gain is given by: 







 



 

  

and so the appropriate value of the gain can be calculated:   

at this gain, the time constant will be reduced to:    

     




Figure 69 – response of the example 1st order process under proportional control





Te final refrigerator power change can be calculated by using the controller algorithm at the final steady-state conditions:        

12.5 EXAMPLE OF A SECOND-ORDER PROCESS UNDER PROPORTIONAL CONTROL A process has the following transfer functions:   

  

   

  

  

   

 

A proportional controller is to be used to regulate against disturbances and to provide setpoint tracking. Answer the following: a) Sketch the open loop disturbance response b) What is the maximum gain that can be used in the proportional controller before the response will tend to oscillate? c) At this gain, what is the steady-state offset on disturbance changes, as a percentage of the open loop change expected? d) At the same game, what is the offset on setpoint changes, as a percentage of the change in setpoint. a) Te steady-state gain on the disturbance is -2. o find out more about the response we need to get the roots of the characteristic equation: 

 

   



 





so, the roots are -0.5 and -1. Te roots are both negative, real and distinct – the response is stable and overdamped (Figure 70).




Figure 70 – open-loop disturbance response from example

b) Adding a proportional controller (the gain on the manipulation is positive, and so a reverse acting controller is required).     



  

       

     

        



      

  

     

   

      

   

       

 

 

     

 

  

o avoid oscillation, we need to make sure that the roots of the characteristic equation stay real. Te roots are:



 

      

For the roots to stay real, the term inside the square root must evaluate to a number greater than, or equal to zero:                  




12.6 ANALYSIS OF INTEGRAL CONTROL OF A FIRST-ORDER PROCESS A pure integral controller has the transfer function: 

   

   

Inserting this into the same first order process we used for proportional control gives the block diagram in figure 71.

Figure 71 – Integral control of a first-order process

Forming the closed-loop Fs:     



 

  

   





  

   

  

    



  

      

  

   

  

        

  

multiplying top and bottom of the disturbance term by ‘s’ to get rid of the 1/s, and rearranging:   

   

    

  

   

    

  

Te steady-state gain on setpoint changes (found by setting terms in ‘s’ to zero) is    



and so perfect steady-state setpoint tracking is achieved. Te steady-state gain on the disturbance term is zero – when the system comes to steady-state the effect of the disturbance will be completely eliminated. You can see that the controller gain,  appears in the characteristic equation. Te form of the second order response can be altered by changing the controller gain. Higher gains will lead to less and less damping (moving an overdamped process eventually to underdamping). ,



CONTROLLER TUNING

13 CONTROLLER TUNING MAIN LEARNING POINTS • • • • •

What’s involved in configuring a controller to suit a process What is a good controller performance Algorithmic methods of controller tuning (open-loop, closed-loop and lambda tuning) rial and error tuning Control loop health monitoring

All controllers need to be tuned to suit a particular process application. In the case of PID controllers it’s necessary to set appropriate values for the adjustable constants (controller gain, reset time and derivative time constant). Tere are a variety of methods for doing this that are discussed in this section. Modern control systems can also monitor the controlled system behaviour over time and use this information to spot potential problems. Tis loop monitoring is also discussed in this section.

13.1 WHAT NEEDS TO BE DONE TO TUNE A PID CONTROLLER? Tere are a number of stages involved in setting up a PID controller for a particular application: 1. Te direction of control action needs to be specified. Tis is completely dependent on the process (manipulation) gain and the type of valve (air-to-open or air-toclose) that is used, but the switch in the controller needs to be set in the ‘direct’ or ‘reverse’ position before proceeding. 2. It is necessary to decide what types of control modes are required. A proportionalonly controller is the simplest, but has a problem with offset. PI is a bit more complicated to tune, but doesn’t have offset problems. PID can, potentially, give the best results but extreme care needs to be taken with noise. If derivative action is to be used, then noise filters need to be in place before tuning takes place. 3. Te controller constants need to be set at values appropriate to the process. High gain processes usually have low controller gains. Processes with long time constants usually have longer integral time constants. Most controller tuning will involve some amount of trial and error. Te process of setting the controller constants to suit a particular process is known as controller tuning .



CONTROLLER TUNING

Integral Absolute Error (IAE): Tis is a measure that integrates the absolute value of the error signal over a particular test period. All of the academic measures require the test period (usually after a disturbance or setpoint change) to be stated as part of the problem definition. Te absolute value of the error is taken to avoid negative errors cancelling out positive values (if the absolute wasn’t taken then a system in sustained oscillation would have an error integral of zero).  

 

IAE treats all errors equally. Tere is no weighting against very large errors, nor against errors that persist for a long time. Integral Squared Error (ISE): Tis measure integrates the square of the error over the test period.  



 

ISE weights against larger errors (because it squares them). o optimise for ISE, a controller will have to eliminate larger errors quickly and this may mean tolerating smaller errors for a longer time. Integral Time-weighted Absolute Error (ITAE): Tis measure integrates the absolute error, but weights the error with the time.  

  

Because of this time weighting, errors that exist later in the experiment will have a much larger effect than errors at the start. A controller optimised for IAE will tend to eliminate errors quickly, even if this means larger errors in the early part of the response.



CONTROLLER TUNING

Figure 72 – A PI controller optimsed for the three response measures

Figure 72 shows the response of a PI controlled system (a third-order system with a negative zero) with the gain and integral time constant optimised for the three different control measures. ISE is producing the fastest response. Te controller is trying to eliminate the large error as quickly as possible. Te aggressiveness of the controller is causing slightly larger overshoots, but the larger errors are being eliminated quickly. Te ISE tuned controller is taking longer to eliminate the residual steady-state error – the tuning emphasises proportional action for maximum speed of response, and small errors are acceptable. Te IAE tuning isn’t as aggressive as ISE – all errors are treated equally. Te IAE tuned controller is the least aggressive. Te priority with this controller is to damp down oscillation – errors that exist later in the test will be highly weighted by the measure. 13.2.2 PRACTICAL MEASURES OF CONTROL PERFORMANCE

Te academic measures are of little use in industrial applications. It is virtually impossible to get a fixed period of operation where other disturbances are absent from the system and this makes the comparisons using the academic measures impossible.



CONTROLLER TUNING

13.3 SOME METHODS OF CONTROLLER TUNING Tere are a number of ways in which at least initial estimat es of the correct tuning parameters for PID controllers can be obtained. None of these methods are foolproof, however, and the very best controller tuning often requires some trial and error. In industry, it is relatively common to find controllers that haven’t been tuned at all – the instrument people set the correct direct of control action and leave the default factory settings for the control parameters. Te main reason for this is that controller tuning can be time consuming and also requires engineers with the required skill set – these are relatively rare. However, often, good tuning can pay for the time taken many times over. 13.3.1 CLOSED LOOP METHODS – ZIEGLER-NICHOLS

Tis method requires the controller to be put into automatic and set up for proportionalonly control. A series of small setpoint changes are then made and the response of the loop observed. Te object is to get the loop into a sustained oscillation by altering the controller gain. If oscillations in the loop die away after a setpoint change, then the gain is increased. If they start to grow (i.e. the system is unstable) then the gain is reduced (quickly!) Once sustained oscillations are achieved, the controller gain is noted (this is called the ultimate gain ) and the period of oscillation (known as the ultimate period ) is also measured.Tese values are then used to obtain the controller constants from table 10. K C

P

PI

PID





-

-



-

  

 





 





Table 10 – Ziegler-Nichols settings

Te Ziegler-Nichols settings can result in rather aggressive control, and alternative settings have been suggested by yreus and Luyben (able 11).



CONTROLLER TUNING

K C



PI

 

PID







-





 

Table 11 – Tyreus and Luyben controller settings

Te Zielger-Nichols method sounds attractive at first, as the process remains under control during the required tests. However, there are a number of problems with it that means that it is rarely used in practical situations: • Many processes have slow dynamics, and it can take a long time to form a pattern of oscillations that can be used to determine whether they shrinking, growing or holding steady. • All processes are subject to random disturbances which will almost certainly interfere with a long duration test. • Te method requires the process to be driven to the edge of stability. Without careful monitoring of the test this could lead to serious problems. 13.3.2 OPEN-LOOP METHODS – PROCESS REACTION CURVE

Process information for tuning can be obtained by carrying out a step test on the open loop system. Tis is done by putting the controller in manual and making a small step change in output. A first-order plus dead-time model is then fitted to this resulting output response (see earlier in the course) producing values for the manipulation process gain,  the time constant, τ , and the dead-time,  and the controller parameters obtained from one of the sets of published formulae (see tables 12 and 13). ,

,

K C





-

-



-





  

P





PI

 

 

PID

 



Table 12 – Ziegler-Nichols open loop tuning parameters



CONTROLLER TUNING

13.3.4 LAMBDA (OR IMC) TUNING

Tis is a ‘model based’ technique that seems to have become popular in industry (particularly in the USA). Te technique is basically a model-based control design called Internal Model Control , but many of those writing about it seem to think that it has some sort of magical powers! Te advantage of model based control is that you can design the controller to produce a desired response rather than the response being adjusted after installation by altering controller parameters. A true model-based design would require high-order, accurate, models, but the lambda tuning technique approximates the process model by using a FOPD (first-order plus dead-time) model. Tis model approximation is the same as that used in Ziegler-Nichols and Cohen-Coon tuning, but those methods use tuning constants that minimise some error measure (e.g. ISE). Lambda tuning, on the other hand, uses tuning constants that should always produce an overdamped response to setpoint changes. It is still necessary to identify the gain, dead-time and time constant for the approximate model, but lamda tuning introduces another, design, parameter ‘λ’ that allows engineers to tailor the controlled response to different applications. o tune a process using lamda tuning, the engineer first performs a step test and estimates the model gain (K), time constant ( τ ) and dead-time (  ) (or identifies the model in some other way). Te value of ‘ λ’ then needs to be chosen. ‘λ’ is essentially the closed-loop time constant (if the model was perfect), and so the controlled response to a setpoint change will be complete after 3λ to 5 λ. However, this is only true in general if the approximate model is a good representation of the real process. Model error can mess up lambda tuning and produce responses with oscillation. o avoid this large values of ‘ λ’ have to be used and these provide what is known as robustness to the controller design (the closed loop response will behave in the expected way even when there are fairly large errors in the model). A common recommendation for lambda is that it should be three times the value of the assumed process time constant or dead-time, whichever is bigger. Many authors suggest modifications to this for different types of process, but the closed-loop response is always slower that the open-loop response.



CONTROLLER TUNING

Once lambda is chosen, the following rules are used for PI controller tuning:   

      

where

 



=

=



=

 =



controller gain integral time constant lambda process gain process time constant process dead-time

=

=

Advantages of Lambda tuning are: • Te slow setpoint reponse means that changing setpoints has limited effect on other loops in the process. Tis has made lambda tuning popular in the paper industry. • Multiple loops can be ‘synchronised’ to have similar closed loop responses. • Important loops can be given precedence by allocating smaller lambda values to them. • Te method is robust and tolerant to pretty poor process testing and model-fitting. Disadvantages of Lambda tuning • Te response is really slow – slower than open loop • As a result of the slow response, disturbance rejection is terrible • Special tuning rules need to be applied for non-standard processes (e.g. integrators or open-loop unstable/oscillatory) 13.3.5 AUTOTUNING

Many PID controllers are sold with an autotuning feature. Usually this is a specific function that needs to be activated, runs for a period, and then stops. adaptive controllers that continuously modify their parameters to match changing process conditions are popular in academia, but very uncommon in industry. Using an adaptive controller requires absolute confidence that the adaption algorithm won’t do something horrible.



CONTROLLER TUNING

13.3.6 TRIAL AND ERROR TUNING

rial and error tuning involves someone with some expertise playing with the loop and adjusting the tuning constants to achieve the desired performance. Skilled tuners can produce good results in less time that it takes to run Ziegler-Nichols or reaction curve tests. uning of important loops will always be finished with some manual tweaking as experts can always produce more tailored tuning that the general algorithms used in the methods or in auto-tuning algorithms. Te methods used for manual tuning vary with the person doing the tuning, but one procedure is: 1. 2. 3. 4. 5.

Set up the controller in P-only mode Adjust gain until approximately ¼ decay ratio on small setpoint changes If offset unacceptable, then reduce gain by around 20% and add integral action. Adjust gain/integral time constant according to the form of response obtained. Derivative control needs special considerations

At step 4, the gain and integral time constant needs to be adjusted – the map shown in figure 64 could be useful.

Figure 73 – Tuning map for PI control

Te ‘ideal’ tuning in figure 73 is in the centre of the map, with quick rise time, settling time and quarter decay ratio. At the bottom left the gain is too low (the immediate change in output on setpoint change is small) and the integral time constant is too long (it’s taking ages for the controlled variable to rise to the setpoint). At the top left, the gain is too high (the process has been driven into sustained oscillations) but the integral time constant is still too long – the centre of the oscillations is taking ages to centre on the new setpoint. Te rest of the map is self-explanatory.



CONTROLLER TUNING

13.4 CONTROL LOOP HEALTH MONITORING Controllers that were initially well tuned sometimes become less effective as time goes on. Tis can because of process changes, such as heat exchangers fouling or catalysts degrading, that cause the gains and dynamic parameters of the process response (and hence the required tuning) to change. Operating points may also change – production levels can be varied and, in some plants, the grade or even type of product produced can be changed. Often these changes in the gains and dynamic parameters of the process cause only gradual reductions in controller performance that are not really noticed until the effects become really bad. Some modern SCADA (Scanning Control And Data Acquisition) systems can provide control loop health monitoring, which can monitor the loops in a plant and provide early warning of potential problems. Some of the things that can be monitored are: • Te fraction of time a loop spends in auto. If this changes, with the loop spending more time in manual then it suggests that operators are unhappy with the loop performance. • Te percentage of the operating time the output from the controller is saturated. All controllers will occasionally saturate (the output bumps against a limit) but when they do they are no longer adequately controlling the process. An increasing length of time spent saturated suggests that the available control effort is no longer suitable for the process – perhaps the valve needs resized or pipework cleaned. • Te oscillation index is a measure used to characterise the amount of oscillation in a controlled response. If this changes significantly it indicates that something has happened to put the loop out of tune. • Variability in controlled variable and manipulation can be measured in a number of ways (e.g. by calculating the standard deviation over a fixed, moving, period) If the process is assumed to be operating in a roughly constant way, then changes in variability suggest something has changed in the loop. • IAE and other control measures can be used in a moving period basis (e.g. the IAE is calculated over 50 hours, but the period covered moves forward every five minutes) and used as alternative measures of controlled variable variability. • Stiction represents the force required to get something moving from a standing start, and takes into account the impulse but also the ‘stickiness’ involved. Control valves drive valve stems up and down through sealing systems. When an air pressure is applied, the valve won’t start moving until the pressure reaches a level sufficient to overcome the stiction between the stem and the seal. As the seal wears, or gets contaminated, the stiction involved will change, and consistent changes may suggest the need to service the valve.



MORE ADVANCED SINGLE-LOOP CONTROL ARRANGEMENTS

14 MORE ADVANCED ADVANCED SINGLE-LOOP SINGLE-LO OP CONTROL ARRANGEMENTS MAIN LEARNING POINTS • Extensions to basic feedback control: cascade; selective and override control • Ratio control • Steady-state and dynamic feedforward control Up to now we’ve been talking about a standard feedback loop, where there is a controller, final control element, process and measuring device all connected together in a loop. In practice there are often modifications made to this scheme for various purposes. Also, there feedforwa rd control . Tese are is a completely different type of single-variable control, called feedforward the subjects of this chapter.

14.1 CASCADE CONTROL

Figure 74 – reactor control without a cascade




Cascade control is very common in the process industries. o understand how it works, consider the process in figure 74. Tis represents a CSR with both the inlet and outlet valves being manipulated. Te outlet valve is being used to control the level in the reactor, and the inlet to control the outlet concentration by varying the flow through the reactor (and hence the mean residence time). Let’s look at the operation of the concentration controller. Tis will work for changes in most of the potential disturbances: e.g. inlet concentration changes; temperature changes; etc. However, it won’t give the best possible performance for one of the most common types of disturbance: pressure variations in the feed line. Tese pressure variations could be caused by upstream changes (e.g. a change of level in a vessel) or by variations in density or and/or viscosity in the feedstream. Te signal from the controller only sets the stem position of the valve, and if the pressure drop over the valve changes, then this will quickly lead to a change in the flowrate being delivered by the valve. Te change in flowrate will then change the mean residence time in the reactor and lead to a gradual change in the outlet concentration. Te concentration controller will detect this and act to eliminate the disturbance, but if the reactor is large, then the dynamics will be slow and it could take a considerable time for the controller to alter the inlet valve position to suit the new pressure. A better way of regulating against inlet flow line pressure variations is shown in figure 75. In this P&ID a flow controller has been added onto the inlet flowrate. Tis flowrate can now be regulated against disturbances in the flow line pressure. Te reponse of the loop will be very fast – the only significant dynamics are those of the valve and these will have a time constant of seconds, or less. Tere is a big problem with this scheme, however, and that is that we’ve given up controlling the outlet concentration from the reactor. Any disturbances, other than flow line pressure changes, will now cause the outlet concentration to drift from its desired value.

Figure 75 – Reactor with inlet flow control




Figure 76 – Reactor with cascade control

Cascade control is widely used in the process industries. Te most common application are controllers cascading onto flow controller secondaries – that way the primary controllers are adjusting flowrates rather than valve stem positions, but other cascade loops are used too. For cascade to be applicable, the following conditions must be present: • Te overall process must be made up of at least two sub-processes, and the outputs of the sub-processes must be measurable • Te secondary process (the flow system in the example) must have a strong causal effect on the primary (the outlet reactor concentration in the example). • Te secondary process needs to be at least five times as fast as the primary (if it isn’t then cascade won’t produce performance improvements). Cascade control is easy to set up, provided it’s done in a systematic way. 1. Set-up the secondary controller first. Switch the controller to accept a local setpoint and then tune it using one of the techniques discussed earlier. 2. Prepare the primary. primary. Te measurement and setpoint limits lim its will be set as normal, but the output of the controller is now going to the setpoint of the secondary. If the control system in use simply specifies outputs as a percentage (i.e. 0–100%), then nothing special needs to be done. However, many SCADA systems use engineering units, and appropriate units and ranges need to be set to make the output signal match the setpoint of the target secondary controller (for the example above, the units might be set to m3.h-1, and the limits set to whatever are appropriate limits for the flowrate (but see below about saturation).




3. Connect the primary output to the secondary setpoint (with a wire, or a software link) and then flip the secondary controller’s setpoint source switch from local to remote (so that the setpoint is now taken from the output of the primary). Put the secondary controller into AUO. 4. Now tune the primary as normal – the secondary controller effectively becomes part of the process being controlled. Integral saturation can be a problem in higher level controllers in a cascade system. single loop controllers are usually protected against saturation in their own outputs (e.g. when the output hits a limit, the integral action is switched off). However, the primary controller in a cascade loop isn’t directly connected to the process. It is possible for the primary to set an output that causes the secondary controller to saturate (i.e. the valve moves to a limit). Without extra protection, the primary won’t know this, and will continue to integrate the error. o deal with this there needs to be extra communication between the secondary and the primary to inform the primary of the saturation in the secondary – extra logic can then switch off the integral action in the primary. Most controllers have features that allow this extra anti-windup protection to be setup, but sometimes the engineers who have installed the control system don’t setup the protection properly. Tis should always be checked if a cascade loop is suffering from large overshoots on setpoint or disturbance changes.

14.2 SELECTIVE OR AUTIONEERING CONTROL

Figure 77 – temperature profile in a tubular reactor




Obviously a single temperature sensor is not going to be able to reliably capture the maximum temperature over the length of the reactor. Instead it will be necessary to use multiple sensors. However, this leaves us with the problem of how to connect these to the temperature controller. A controller can only deal with a single input. Te way around this is process the signals, using what is called a computational unit , to extract the maximum and then feed this to the controller input. Te control scheme is shown in figure 78. In this case we are using a unit to extract the maximum signal, but computational units can be used to extract the minimum and for other functions too. Tese computation units are available in all SCADA systems, but were also available, as discrete boxes, in the days of pneumatic controllers. Te type of control scheme that has been set up for the reactor is called an auctioneering or selective control system.

Figure 78 – a selective control scheme

14.3 OVERRIDE CONTROL

Figure 79 – a flooding distillation column




We are limited in the number of things that we can simultaneously control in a plant by the available degrees of freedom (this concept is explained in the control system design section). Sometimes, however, it is necessary for variables that are not usually controlled to override an existing loop to maintain process operation, or to avoid damage to equipment. For example, consider the system in figure 79. Te bottoms mole fraction (of the most volatile component) of this column is normally controlled by manipulating the steam flow to the reboiler. However, under a fault condition it is possible for the bottoms mole fraction to rise excessively. When this happens the controller increases the steam, and hence the vapour rate up the column to try to drive the volatiles away. At some point this vapour rate becomes so large that it interferes with the movement of liquid down the column and the column floods. At the flooding point the column is useless: not only bottoms mole fraction control is lost, but also the tops. A way to prevent this happening is to install the override control scheme shown in figure 80. In this scheme a differential pressure cell is fitted over a section of the column. Rises in the DP will indicate an approach to the flooding condition (as more vapour tries to force its way up the column). A pressure controller is setup to control this differential pressure by manipulating the steam flow. However, the mole fraction controller is still there to control the mole fraction under normal conditions, and this wants to manipulate the steam flow valve too. It is impossible for two outputs to be connected to the valve simultaneously, so the most appropriate one must be selected by a computational unit (in this case a minimum unit needs to be used). Te scheme works are follows. Under normal conditions the DP will be well below the setpoint of the pressure controller, and so the pressure controller will be demanding a large steam flow to try to drive the DP upwards. At the same time the mole fraction controller will be operating, but will be requesting a smaller steam flow. Te ‘min’ computational unit will select the minimum signal and so will connect the mole fraction controller to the valve. Under the fault condition, the mole fraction controller will demand more and more steam, until the DP eventually crosses the DP setpoint in the pressure controller. At this point, the output from the pressure controller will become the smallest and it will be connected to the valve. Differential pressure control will override bottoms mole fraction control. When overridden the bottoms mole fraction controller is no longer operating – we have lost control of the bottom composition. However the column will still be operating and control should still be possible at the top of the column.




14.4 RATIO CONTROL Ratio control is a common requirement in chemical processes. Many of the systems we work with require streams to be held within a certain ratio of each other, e.g. reactant streams into a reactor; reflux ratio in a distillation column; liquid to gas ratio in an absorber. Te controller used for ratio control is the first example of non-feedback control in the course.

Figure 81 – Ratio control

A ratio control scheme always consists of at least two streams. Te first is called the wild stream. Tis stream is not manipulated by the ratio scheme and represents a disturbance to the ratio being controlled. Te other stream is the manipulated stream and this is the stream that is adjusted by the ratio controller. It is common to manipulate the stream through a cascade to a secondary flow controller – that way it is the flowrate of the stream that is manipulated rather than the valve position. An example of ratio control is given in figure 81. In this case the controller is setup to control the reflux ratio of the column. Te distillate stream (monitored by FI001) is the wild stream – it is manipulated by the level controller, but is a disturbance to the ratio control system. ML001 is the ratio controller itself. It is just a multiplier that multiplies the measured flowrate of the wild stream by the reflux ratio (which can be set in the device, or set remotely by another controller in a cascade) and then sends the result to the setpoint of the secondary flow controller (FC001). Ratio controllers do not usually measure the ratio of the flows (the controlled variable), but instead measure the wild stream (a disturbance). Tis makes ratio control a simple form of feedforward control rather than feedback control.




14.5 FEEDFORWARD CONTROL Feedback control systems operate by monitoring the controlled variable, a process output, and adjusting the manipulation to drive this output towards the setpoint. Te problem with a feedback control system is that a disturbance entering the system has to actually affect the process before it will be detected at the output and the correction process started. If the process includes large capacities, then large amounts of material can be altered by the disturbance and it can take a long time for the system to recover to the setpoint value. Feedforward control offers an alternative strategy to improve disturbance rejection in processes with large capacities. A feedforward controller is one which measures the disturbance, a process input, rather than the controlled variable. Te controller uses a model to estimate the effect this disturbance will have on the controlled variable and then another model to calculate the manipulation change which is required to precisely counteract the effects of the disturbance. In theory, if both the disturbance and manipulation models are perfect, it is possible for a feedforward controller to reject a disturbance with no change at all being observed in the controlled variable.

Figure 82 – A block diagram showing feedforward control

Let the models of the process be represented by the equation           

where  and  are the model transfer functions for the manipulation and disturbance effects.



14.6


STEADY-STATE FEEDFORWARD CONTROL

Tere are two basic types of feedforward controller. Te steady-state feedforward controller is designed around steady-state models of the manipulation and disturbance effects. Tese can be obtained from first principles steady-state modelling (and so can be made non-linear) but it’s much more common to use gain-only models. Tese gains can be obtained from transfer functions, if these are available, or from simple tests on the real process or on a steady-state simulation model (e.g. an Aspen flowsheet).

Figure 83 – A steady-state feedforward controller

Te modelled system for gain-only models is:            

as before, this can be re-arranged into a feedforward controller:   

 

   

 

 

if we use a simple first-order process as an example system we get the block diagram shown in figure 83. Te transfer functions for the controlled system can be obtained by looking into the block diagram from the output: 

  





  





   

 

 

  

                                        




If we have a perfect model (    , and    ) and the disturbance and manipulation dynamics are identical (   ), then the system reduces to:        

    

  

So, in a steady-state feedforward controlled system with equal manipulation and disturbance dynamics a perfect model will result in perfect disturbance rejection. When the disturbance changes it will be immediately cancelled by manipulation changes made by the controller and no deviation will occur in the controlled variable. Te setpoint response is less exciting. Although setpoint changes are tracked exactly (if a perfect model is used) the speed of tracking is just the open loop speed of the process. Setpoint tracking will be much slower than can be achieved with a feedback controller. Now, let’s consider what happens if we have equal disturbance and manipulation dynamics, but imperfect steady-state models:                  

     

Te effect of the disturbance is no longer zero. It is now a first-order process with dynamics the same as the open-loop process and with a gain of: 

  

 



Tis means that a steady-state error will be left when the disturbance changes. Provided  the model is at least somewhere nearly correct (    and    ), the controlled gain  will be much less than the uncontrolled gain, but there will be some steady-state change in the output. Similarly, the gain on the setpoint F is no longer 1 and so perfect set-point tracking will not be obtained – there will be an error. Errors in the gains in models for feedforward controllers always produce steady-state errors in the controlled variable after a disturbance or setpoint change. Finally, consider the case where we have a perfect model, but different manipulation and disturbance dynamics (in this case the time constants are not equal).   

    



    

  

    

  




Figure 84 – Dynamic error in feedforward control

Tis sort of transient error is called dynamic error. 14.7

DYNAMIC FEEDFORWARD CONTROL

If the manipulation and disturbance dynamics are very different then the amounts of dynamic error may be large. In these cases it may be worth considering a full dynamic controller (where dynamic process models are used instead of steady-state ones). For a first-order process, we have the following assumed model: 

  

 

  



 

 

  





and rearranging this into a dynamics feedforward controller equation gives:



  

    

 

 

     



  





Te setpoint controller function is potentially troublesome. If a step is made in the setpoint, then this transfer function will generate an infinite controller output. Additionally, if there had been any dead-time in the F inverting it would lead to positive exponentials in ‘s’ – representing prediction rather than time-delay terms and producing what is known as a physically unrealisable controller. For these reasons, and because steady-state controller servo response is poor, feedforward control is never used for setpoint tracking. We’ll proceed on this basis by setting the change in the controller setpoint to zero.




Inserting the controller into the process gives: 

  

 

  



     

   

                  



  

              

In the case of a perfect model (the corresponding gains and time constants are equal) perfect disturbance rejection is achieved. If the dynamics are correct, but the gains are inaccurate, then there will be a residual steadystate error on a disturbance change. Even if the model is incorrect worthwhile reductions in dynamic error can be achieved. If the gains are correct, but the time constants are inaccurate then there will be a dynamic error in the response (it’s easiest to see this by assuming that it’s only the disturbance time constant that’s inaccurate). Again, if the models are nearly correct then the controlled behaviour will be much better than a steady-state controller. 14.8

FEEDFORWARD/FEEDBACK CONTROL

Perfect modelling is never possible – there will always be some errors – and so perfect disturbance rejection isn’t achievable from a feedforward controller. Feedforward control is also very poor at tracking setpoint changes. For these reasons feedforward control is seldom used on its own and is almost always combined with a feedback controller to produce as feedforward/feedback controller . Tere are a number of proposed arrangements for this in the literature, but the most sensible is shown in figure 85. In this arrangement all setpoint tracking is dealt with by the feedback controller, and the feedforward controller doesn’t get involved. When a disturbance enters the system it is detected by the feeforward controller, and this immediately outputs a manipulation signal that should counteract the disturbance. If this works, then there will be no change in the controlled variable, and the feedback controller won’t get involved. However, if there is model error in the feedforward controller then there will be some change in the controlled variable, and this will be detected and acted upon by the feedback controller.



DESIGN OF CONTROL SYSTEMS

15 DESIGN OF CONTROL SYSTEMS MAIN LEARNING POINTS • • • • •

Steady-state control envelopes Multi-variable processes How to determine the number of things that can be controlled Plant mass balance control How to select control loops

Te design of a control system for a processing plant is a major task, involving many different areas of expertise. As chemical engineers we are most likely to get involved in specifying what loops are required, what other measurements are necessary and what safety systems may be needed. We also might get involved with control valve and instrument selection. Some chemical engineers, who specialise in control systems, also get involved with specifying the control system architecture – what hardware and communication systems will be used. Electronic, electrical and instrument engineers are usually involved in the design of the physical installation. Tis section of the course is to give you an introduction to what is involved in loop selection in a control system design.

15.1 CONTROL ENVELOPE Imagine you have a job packing shelves. You are expected to be able to lift a variety of packages from floor level onto the shelving. Tere will be a maximum weight of box that you’ll be able to lift and this will be set by your physical makeup. If a bigger box comes along, you won’t be able to handle it. Just like the big boxes, there are physical limits on the size of disturbances that a control system can handle. Tese limits are set by the degree of variability built into the control valves, i.e. by how much control effort is available. Te limits to control action are determined by steady-state considerations, but have important implications on dynamic behaviour near the edges of the envelope.




Consider a mixing vessel which is used to further dilute a low-concentration salt stream prior to waste treatment. Te salt stream flows into the vessel and is mixed with a flow of water that is manipulated by a controller that is controlling the exit salt concentration from the vessel. Te level in the vessel is perfectly controlled and there are no significant density differences between the streams. Te potential disturbances to the system are the flowrate and inlet concentration of the salt stream. Te steady-state component balance for the system is given by:           

o work out the control limits we need to place limits on the manipulated variable and set the outlet concentration to the setpoint value – this will give us two equations: one for the upper limit on the manipulated variable and another for the lower:                

and these can be arranged to produce the equations for the two edges of the control envelope:  

 

         

Let’s put some numbers in and calculate the control limits. Assume that the normal inlet salt concentration is 0.01 kg.m-3 , and that the desired exit concentration is 0.001 kg.m -3. If the nominal flow of salt solution is 1m 3.min-1, this gives us a nominal diluent flow requirement of 9 m 3.min-1. Assume that we choose a valve that allows us to vary the diluent flow between 2 and 12.6 m 3.min-1. Putting these numbers into the equations above generates the curves shown in figure 86.




For all the combinations of inlet flowrate and salt concentration inside the green area, steady-state operation (and hence control) is possible. It isn’t possible to control the process if the disturbance combinations fall in the red areas (outside of the control envelope ). At the edges of the envelope, the manipulation will be hard against one of the controller output limits. Dynamic operation near the edges will almost certainly result in the controller output saturating, producing poorer control performance than will be achieved further inside the envelope. Earlier I described a rule of thumb for control valve sizing (the valve should be sized for 1.4 times the nominal flow). Tis is fine for a general rule, but control system designers should always consider the effect this may have on the control envelope – processes with very low process gains may need a much bigger range of manipulation variability to be successfully controlled.

15.2 MULTIVARIABLE PROCESSES In the course so far we’ve considered control systems with a single manipulated and a single controlled output. Real processes are much more complicated with multiple controlled outputs, manipulations and disturbances. Figure 87 shows an s-domain block diagram for a 3 input/2 output Multiple-input/Multiple output (MIMO) system.

Figure 87 – a 3 input/2 output MIMO system block diagram




Te s-domain representation of a MIMO system is a simplification of most real MIMO processes as the s-domain necessarily represents a linear (or linearised) model. However, it is useful for discussing the major features of such systems. Te main thing to notice is that each input is capable of affecting either, or both, outputs. Tis means that a disturbance entering the process can change both of the system outputs. It would be possible to setup control loops to control the outputs connecting  to  and  to  , but it is also possible to setup an alternative control combination where  is used to manipulate  and  manipulates  . Either of these control schemes may be used to control the process, although it is likely that one of the loop combinations will be better than the other. If there are equal numbers of manipulated and controlled variables( say ‘n’), then the number of possible loop combinations is  i.e. if there are 4 controlled variables there are    different ways of combining the manipulations and controlled variables in loops. Choosing the best way to combine controlled outputs and manipulations in a multi-loop control system is not a trivial task, and there is no general method to achieve the best performance. Some rules of thumb can be used to at least eliminate the worst loop combinations: • Choose loops where there is a strong causal relationship between the manipulation and disturbance • Choose loops that minimise the dead-time between the manipulation and disturbance • Choose loop combinations that minimise the interaction between the loops • Choose loops with a reasonable process gain (this limits the manipulation range required) • Where possible, choose loops with an approximately linear relationship between the manipulation and disturbance (often this isn’t possible). Another alternative to controlling these MIMO or multivariable systems is to use a full multivariable controller. Tis is a controller that considers the system as a whole and doesn’t decompose the control into single loops. Tis type of controller has been present in the oil industry for many years (e.g. Dynamic Matrix Control) and is getting increasingly popular in other applications. Multivariable control is beyond the scope of this introductory text.

15.3 HOW TO DETERMINE THE NUMBER OF CONTROLLED VARIABLES In our discussion of control we have automatically assume d that we know what the controlled variables of a system are. In real situations, this isn’t predetermined and the first job of the control system designer is to decide what should be controlled on a process. Also, the designer isn’t free to choose as many controlled variables as he/she thinks are necessary – they will be limited by the available degrees of freedom in the system.




It’s actually really difficult to sit down and work out the number of degrees of freedom involved in most realistic process systems, and practical control engineers never bother to do this. Instead, they judge the number of control loops required from experience. Usually this isn’t too hard to do, but care does need to be taken. Generally it’s much more likely for less experienced engineers to have too many controllers than too few. A rough rule of thumb is the maximum number of things that can be controlled in a system is equal to the number of manipulable streams entering or leaving the capacity. Tese streams can be mass or energy streams. However, it is necessary to have a mass or energy balance on the system so it isn’t possible to control ALL the mass or energy streams to particular values. 15.3.1 CONTROL OF A BLENDER

Figure 88 – a simple blender

If we consider the simple mixing process (figure 88) in isolation (i.e. all three streams can be manipulated) then we have three potential manipulations, three loops and three possible control variables. Te choice of what could be controlled is varied, but some combinations are not possible (see the table 14).




Some possible controlled

Some combinations that are not possible

variable combinations

Two inlet flows, blender level

All three flows (once you’ve picked two, the third is fixed)

One inlet flow, one outlet flow, blender level

Anything involving the inlet concentrations (there is no causal link between the manipulations and the inlet concentrations.)

Blender lever, outlet flow, outlet concentration

Any combination that doesn’t include blender level (failing to control the inventory will result in the vessel overfilling or emptying.)

Blender level, one inlet flow, outlet concentration. Table 14 – Control configurations for a blender

15.3.2 CONTROL OF A REACTOR

Tis simple reactor (figure 89) has three streams – two mass and one energy. Assuming the reactor operates in isolation and none of the three streams are being set by another system, there are three potential manipulations, three control loops and three controlled variables. Some possible and impossible combinations are listed in table 15.

Figure 89 – a simple reactor




15.3.3 CONTROL OF MULTIPLE UNITS

Figure 90 – blender/reactor combination

When units are joined together, degrees of freedom are lost due to shared streams. In the example shown (figure 90) the blender output now becomes the reactor inlet stream. Tis removes a degree of freedom (controlled variable) from either the reactor or the blender. 15.3.4 SELECTION OF CONTROLLED VARIABLES

Degrees of freedom, or other methods, tell us how many things may need to be controlled to fix a system, but they don’t tell us what the best controlled variables may be. Some rules of thumb for selecting appropriate controlled variables are: • Inventories (levels in liquid systems and sometimes pressures in gas systems) always need to be controlled and should be the first controlled variables that are selected. • Other controlled variables should be aligned to the strategic goals of the unit. If a distillation column is intended to purify a volatile compound, then the tops composition needs to be controlled (either as a composition, or as some inferred composition measurement, such as temperature). • Controlled variables should be readily measured. Compositions are very important in many chemical process units (e.g. distillation columns, absorbers, reactors) but composition is often rather difficult to measure. In many of these systems other variables which are related to composition (e.g. top plate temperatures in a distillation column) are used as control variables instead. • Controlled variables need to be strongly influenced by at least one of the available manipulations. If there is no strong causal relationship between manipulations and controlled variables, then good control will not be possible.




15.4 PLANTWIDE MASS BALANCE CONTROL In a complex processing plant there needs to be some point at which the overall production rate for the process is set. When this production rate is changed then all the individual units within the production process need to change their output to suit the new production rate. At first glance, this seems to be a hugely complex problem that will require complex control calculations. In fact it is easy to achieve using the interactions between individual unit inventory controllers. Te first thing that needs to be decided is what end of the process will set the production rate. It might be assumed that the best place to do this is at the output end ( downstream mass balance control ) and for some processes this is the appropriate thing to do. However, for others, such as processes involving distillation columns in the main process route, it is often better to adjust the production rate from the raw materials end ( upstream mass balance control ). Figure 91 is an example of downstream mass balance control. In this process the production rate is set at the output by flow controller FC001. For the process to maintain a mass balance, all of the units on the main process route need to maintain their inventories by manipulating their input streams as shown. If FC001 increases the production rate, this will start to reduce the level in the third unit. LC003 will try to counteract this by increasing the flowrate into the unit, which in turn will reduce the level in the second unit. In this way, the change in the production rate at the output is transmitted backwards through the controlled units to produce an increase in raw materials into the process.

Figure 91 – Downstream mass balance control




Upstream mass balance control is shown in figure 92. In this case the production rate is set at the raw materials end by flow controller FC001. If this flowrate is increased, then the level in the first unit will start to rise causing level controller LC002 to open the valve and allow more flow into the second unit. Trough the interaction between the inventory controllers the increase in the flow of raw materials will make its way through to the output of the process. Where processes have side-streams (e.g. a process has a distillation column with the bottoms on the main process route and the tops as a side-stream) then the side stream inventory controllers always need to be configured to manipulate the outlet stream, regardless of the type of mass balance control. Tis is because the production rate is set on the main process route and the side-stream has to take whatever has been set for the main process. An example of side stream mass balance control is shown in figure 93.

Figure 93 – Upstream and downstream mass balance control on a column with a major product in

the bottoms



CONTROL SYSTEM ARCHITECTURE

16 CONTROL SYSTEM ARCHITECTURE MAIN LEARNING POINTS • Effect of technology on process plant control rooms • Human factors in control systems Control systems are implemented by a combination of hardware and software and have been affected more by the changes in technology in the last thirty years than probably any other system in process plants. Te introduction of new technology has completely changed the way in which plants are operated, the number of people involved, and the jobs that they do.

16.1 THE EFFECT OF TECHNOLOGY ON PROCESS PLANT CONTROL ROOMS Before the widespread use of electrical communications signals almost all measurement and control signals were transmitted by pneumatic signals (3–15psi) passing through narrow diameter brass tubes. Tese tubes limited the distance a signal could be transmitted, not just due to the cost involved in the tubing, but also because the dynamics of transmission. When an instrument at one end of a tube changed its output air pressure, a significant dynamic lag existed due the air volume in the tube – the signal at the other end took time to reach the transmitted pressure. Tis lag grew as the length of the tube increased, and this meant that tube runs had to be kept relatively short.

Figure 94 – a control room in 1971




Figure 95 – a modern control room

Te control rooms themselves looked very different from modern rooms. Figure 94 shows a petrochemical plant control room in 1971. At this time the only visual display units were cathode ray tubes and the computers that were available were too large, fragile and lowpowered to be used to drive chemical plant display systems. Instead the control panel is made up of various gauges and other instruments which had a direct pneumatic connection with the instrument concerned. Te large circular devices you can see on the control panel are chart recorders. Tese recorded the trends of certain key variables in ink on a circular paper chart. Tese charts were replaced at frequent intervals and, along with paper records produced by the operators, they represented the only historical data that was available on plant operation. Contrast figure 94 with the control room shown in figure 95. Figure 95 is the control room for the same plant (South Hampton Resources, exas) but in 2014. Modern instrumentation now is almost exclusively based around analogue electrical or digital communications. Te length of cable runs is relatively unimportant – they no longer affect the signal being transmitted. As a result, most plants now have centralised control rooms rather than distributed rooms. Te control rooms may be sited some distance from the plant (for safety reasons) and very few instruments are now field located. Tis means that fewer operators are required and that, in some factories, they rarely go out on plant. Modern control room displays are computer driven and present a large amount of information to operators on paged screens. Historical data is now directly recorded onto disc and is easily retrievable by process engineers looking for information about the process behaviour.




Te working environment for operators has also considerably improved. Since they were based on plant the old control rooms could be noisy, hot and uncomfortable. Modern control rooms are air conditioned and much more like a standard office environment.

16.2 HUMAN FACTORS IN CONTROL ROOM DISPLAYS Te old control rooms HMI (human-machine interface) were pretty primitive and operators need significant amounts of training just to remember what particular instruments were telling them. Some companies made attempts to improve things by physically embedding the instruments (i.e. cutting a slot for them in the plywood) in plant ‘mimic’ diagrams that were painted on a wall in the control room. Due to the number of instruments that a typical chemical plant requires for control, this strategy never worked too well. Modern SCADA (scanning, control and data acquisition) systems now include editors that allow engineers to create plant displays and embed the output of instruments or operator adjustable controls. Te displays can be set up in a hierarchy that allow operators to bore down through general plant information into very specific displays that represent particular process units.

Figure 96 – a display that doesn’t follow ASM guidelines




Figure 97 – an ASM compliant display

A big message from the ASM publications on operator displays is that the use of colour should be minimised and only used to highlight abnormal conditions. Plant mimics are greyscale so that they enhance rather than detract from the information that is being presented. ‘Tree dimensional’ images of plant equipment are also avoided as these distract from the information. Instead shapes filled with a neutral grey are used to represent the process items.

Figure 98 – annunciator panels in an electricity substation




Alarm handling is another important area in HMI design. Alarms are generated by the normal process control system (as opposed to SIS (safety instrumented system) events) when a process value, or rate of change, exceeds pre-set high or low limits. Te object of alarms is to warn the operators of unusual events. In the pre-computer age (and still in some modern) control rooms alarms were shown on annunciator panels. Tese were panels of colour coded (usually amber/yellow for warnings and red for serious problems) lights with text on the front describing the alarm involved (e.g. ‘Reactor emperature High’). Te lights were normally off, but would flash when an alarm condition was breached, often accompanied by a siren sounding. Te control room operators would ‘accept’ the alarm by pressing the face of the annunciator and operating a switch – this stopped the flashing and siren, but left the alarm illuminated for as long as the condition persisted. Annunciator panels limited the number of alarms that could be presented to operators, as there was a limited amount of wall space in the control room. When computer based systems were first introduced, however, this limitation disappeared. Alarms were now presented to operators in an alarm list that had an almost unlimited length. In the early days of computer control systems, engineers tended to add alarms to almost every variable just to be ‘on the safe side’. When an incident occurred this meant that operators were bombarded with dozens of alarms related to a single fault. Te stress and pressure of dealing with multiple alarms meant that operators found it very difficult to diagnose and deal with the real problem behind the alarm conditions. Alarm management, which involves many things including careful selection of alarms and operator training, is now taken very seriously in the process industries. Te aim is to provide operators with sufficient warning of abnormal events without overloading the operators’ ability to cope.

16.3 DISTRIBUTED CONTROL SYSTEMS Distributed control systems (DCS) are now widely used in the process industry. Tis has really been driven by the use of microprocessor technology, which provides control system devices (instruments, controllers and valves) with a degree of ‘intelligence’ that wasn’t available in the past. A DCS distributes the information gathering and decision making tasks in a control system amongst multiple devices. Tese devices are additionally normally arranged in a hierarchy where devices at different levels have different sorts of decision making tasks.



BIBLIOGRAPHY

17 BIBLIOGRAPHY Tis text has covered the IChemE syllabus and provided an introduction to the field of chemical process control. For those who wish to study the subject in more detail, there are a wide range of more advanced textbooks available. Some are listed below.

Principles and practice of automatic process control , Smith and Corripio; Wiley, 3 rd Edition 2005 : Aimed at the control of chemical processes. I find it a bit dry and difficult to read, but others don’t!

Process control: designing processes and control systems for dynamic performance , Marlin; McGraw-Hill, 2nd Edition 2000: Easy to read and stronger on control system design than most of the competition. Process dynamics and control , Seeborg, Edgar, Mellichamp and Doyle; Wiley, 4 th Edition 2016: I like this book as it’s fairly comprehensive and easy to read. Essentials of process control , Luyben and Luyben; McGraw-Hill, 1996: A standard textbook for many courses, but I find it really hard to get into. Chemical process control: introduction to theory and practice , Stephanopoulos; Prentice-Hall, 1984: Fairly old, but still worth a read (and easy to get into). Process automation handbook: a guide to theory and practice , Love, Springer 2007: Not a textbook, but an encyclopaedia of just about anything concerned with process control. Worth having a look at. Industrial automation, IDC echnologies; BookBoon: Hardly any equations and good textual descriptions of many areas of basic control. Very strong on communications. Process control, Automation, Instrumentation and SCADA , IDC echnologies; BookBoon: Companion book to the one above.

Control Engineering , Atherton; BookBoon: Almost all equations, but very good. An introduction to control theory.



APPENDIX

APPENDI APPE NDIX X THE USE OF SOFTWARE FOR TEACHING PROCESS CONTROL AT STRATHCLYDE UNIVERSITY Chemical engineering students typically find process control a very difficult subject to grasp. One of the main reasons for this is that control is fundamentally dynamic, whereas almost everything else in the chemical engineering curriculum is taught as steady-state. Another reason is that control is a systems based discipline, where looking at one element in isolation is rarely useful. Te behaviour of a control system is the result of multiple subsystems responding to each other, and this is very difficult for students new to the discipline to visualise. o deal with these problems I’ve always used computer simulation to support my control classes. When I started teaching (in 1986) Strathclyde had just joined a teaching experiment run by IBM using their mainframe based Advanced Control System (ACS). Te mainframe was based at Imperial College in London and about half a dozen other UK universities were connected to this by landline. Although there were problems in running in this way, working with ACS really opened my eyes to what could be possible. Due to the limited number of terminals that we had we ran the ACS work as a laboratory with groups of students were rotated through the computer room during a working week. During each lab session the students worked through a series of set tasks that were based on a course developed at Purdue University (one of the first Universities involved in the IBM experiment). ACS was popular with the students and we also ran several introductory control classes for industry using the system. Te experiment was abandoned after a couple of years. I think IBM realised that mainframe computers weren we ren’’t where the future futu re of process computing was going. We’ We’d d also had significant problems with the reliability of the landline down to London and couldn’t justify the costs associated with maintaining this. I searched for alternative pieces of software that could support dynamic simulation in chemical engineering control classes and came across a program called UCONLINE that was being developed by a team led by Prof. Alan Foss at UC Berkeley.



APPENDIX

UCONLINE was quite different from ACS in that it ran on microcomputers (which is what we called PCs at that time!) using MSDOS. In the late eighties and early nineties microcomputer prices had fallen to the level where they were affordable to purchase in numbers suitable for teaching, and Strathclyde began creating PC laboratories across the campus. Tis meant that we were able to include computer simulation as a class activity where the whole class met in a computer room once a week to do dynamic simulation work. Although MSDOS-based, UCONLINE was a powerful tool for teaching. Students could change valve positions and watch the effects on the process. Tey could add their own control arrangements, ranging from basic PID up to more complicated systems with deadtime compensators, decouplers and feedforward controllers. Tey could then simulate the complete control system and tune and adjust their controllers as required. When Alan Foss retired, support for UCONLINE UCON LINE disappeared and we were forced to look for a new way of using simulation in our classes. For a number of years we used the blockstructured dynamics simulation languages, VisSim and Simulink. Tese are powerful pieces of software, but are really designed for real simulation modelling and not for teaching. Te diagrams the students were producing also looked nothing like the P&IDs that chemical engineers use every day. Tis really hit home when a former student wrote a letter complain ing that he hadn’t been taught about P&IDs. He had, of course, but I realised that he had spent most of his time looking at block diagrams and hadn’t realised the importance of P&IDs. We We did try to use Aspen Dynamic for teaching (Aspen Dynamic is the dynamic modelling add-on for Aspen Plus, the steady-state flowsheet modeller). Tis had the advantages of being a package that was used in industry and that it produced control diagrams that were very similar to standard P&IDs. However the software is complicated to use and we found that our control class wasn’t teaching control, but was instead training students to use the software (badly!).



APPENDIX

When I started to design the new introductory control class (which is the material covered in this book) I realised that I needed better software to support the simulation elements. I could find nothing available that met my needs and so, with a group of colleagues decided to build my own. Te main requirements of the software were: • It had to represent the process and control system on a standard P&ID (Figure 99) • Learners should be free to add instruments and controllers in any way they wished • It had to mimic the elements on the P&ID with virtual devices (created as users added P&ID elements) that could be attached to a virtual control panel or SCADA screen (Figure 100). • It had to include a lesson system that presented material to learners and also measured their performance (by, for example, comparing their control layout with an instructors). • It had to be capable of simulating the system (process plus attached controllers and instruments in real and accelerated time). Te software, called PISim has been in development over a three year period and has been used in the last two cycles of the control class. Even though the software used by the students was at a relatively early stage of development it has proven to be easy to use and popular. Some of the student comments from the 2016/17 session were: ‘I think the PISim element of the course was extremely useful’; ‘very useful in showing how control systems work’; ‘Practical simulations with PISim were fun’; ‘PISim was a very effective teaching tool’.


Essential Process Control for Chemical Engineers.pdf

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