Advanced Control for Constrained Processes and Systems: A Unified and Practical Approach

Control Engineering Series 75

Advanced Control

for Constrained

Processes and

Systems

Processes and Systems

Advanced Control for Constrained

and De Battista

Garelli, Mantz

Fabricio Garelli, Ricardo J. Mantz

and Hernán De Battista

The Institution of Engineering and Technology

www.theiet.org

978-1-84919-261-3

Advanced Control for Constrained

Processes and Systems

Fabricio Garelli is currently Associate Professor

at the National University of La Plata (UNLP) and

Official Member of the National Research Council

of Argentina (CONICET). He is the author of an

awarded Ph.D. Thesis and more than 30 journal and

conference papers. His research interests include

multivariable systems and constrained control.

Ricardo J. Mantz serves as Full Professor at UNLP

and is an Official Member of the Scientific Research

Commission (CICpBA). He is the author of a book

and more than 150 papers in scientific journals and

conferences. His primary area of interest is nonlinear

control.

Hernán De Battista is Senior Professor at UNLP

and Official Member of CONICET. He has published

a book and more than 70 journal and conference

papers. His research interests are in the field of

nonlinear control applications and renewable energy.

The three authors are with LEICI, EE Dept., UNLP,

Argentina.

This book provides a unified, practically-oriented treatment to many

constrained control paradigms. Recently proposed control strategies

are unified in a generalised framework to deal with different kinds of

constraints. The book’s solutions are based on reference conditioning

ideas implemented by means of supervisory loops, and they are

complementary to any other control technique used for the main

control loop. Although design simplicity is a book priority, the use of well

established sliding mode concepts for theoretical analysis make it also

rigorous and self-contained.

The first part of the book focuses on providing a simple description

of the method to deal with system constraints in SISO systems. It also

illustrates the design and implementation of the developed techniques

through several case studies. The second part is devoted to multivariable

constrained control problems: improving system decoupling under

different plant or controller constraints, and reducing the undesired effects

caused by manual-automatic or controller switching.

The key aim of this book is to reduce the gap between the available

constrained control literature and industrial applications.

Constrained Control.indd 1 20/09/2011 14:21:44

IET CONTROL ENGINEERING SERIES 75

Advanced Control

for Constrained

Processes and

Systems

PRELIMS 2 September 2011; 13:54:54

PRELIMS 2 September 2011; 13:54:55

Other volumes in this series:

Volume 2 Elevator traffic analysis, design and control, 2nd edition G.C. Barney and

S.M. dos Santos

Volume 8 A history of control engineering, 1800–1930 S. Bennett

Volume 14 Optimal relay and saturating control system synthesis E.P. Ryan

Volume 18 Applied control theory, 2nd edition J.R. Leigh

Volume 20 Design of modern control systems D.J. Bell, P.A. Cook and N. Munro (Editors)

Volume 28 Robots and automated manufacture J. Billingsley (Editor)

Volume 32 Multivariable control for industrial applications J. O’Reilly (Editor)

Volume 33 Temperature measurement and control J.R. Leigh

Volume 34 Singular perturbation methodology in control systems D.S. Naidu

Volume 35 Implementation of self-tuning controllers K. Warwick (Editor)

Volume 37 Industrial digital control systems, 2nd edition K. Warwick and D. Rees (Editors)

Volume 39 Continuous time controller design R. Balasubramanian

Volume 40 Deterministic control of uncertain systems A.S.I. Zinober (Editor)

Volume 41 Computer control of real-time processes S. Bennett and G.S. Virk (Editors)

Volume 42 Digital signal processing: principles, devices and applications N.B. Jones

and J.D.McK. Watson (Editors)

Volume 44 Knowledge-based systems for industrial control J. McGhee, M.J. Grimble

and A. Mowforth (Editors)

Volume 47 A history of control engineering, 1930–1956 S. Bennett

Volume 49 Polynomial methods in optimal control and filtering K.J. Hunt (Editor)

Volume 50 Programming industrial control systems using IEC 1131-3 R.W. Lewis

Volume 51 Advanced robotics and intelligent machines J.O. Gray and D.G. Caldwell

(Editors)

Volume 52 Adaptive prediction and predictive control P.P. Kanjilal

Volume 53 Neural network applications in control G.W. Irwin, K. Warwick and K.J. Hunt

(Editors)

Volume 54 Control engineering solutions: a practical approach P. Albertos, R. Strietzel

and N. Mort (Editors)

Volume 55 Genetic algorithms in engineering systems A.M.S. Zalzala and P.J. Fleming

(Editors)

Volume 56 Symbolic methods in control system analysis and design N. Munro (Editor)

Volume 57 Flight control systems R.W. Pratt (Editor)

Volume 58 Power-plant control and instrumentation D. Lindsley

Volume 59 Modelling control systems using IEC 61499 R. Lewis

Volume 60 People in control: human factors in control room design J. Noyes and

M. Bransby (Editors)

Volume 61 Nonlinear predictive control: theory and practice B. Kouvaritakis and

M. Cannon (Editors)

Volume 62 Active sound and vibration control M.O. Tokhi and S.M. Veres

Volume 63 Stepping motors: a guide to theory and practice, 4th edition P.P. Acarnley

Volume 64 Control theory, 2nd edition J.R. Leigh

Volume 65 Modelling and parameter estimation of dynamic systems J.R. Raol, G. Girija

and J. Singh

Volume 66 Variable structure systems: from principles to implementation

A. Sabanovic, L. Fridman and S. Spurgeon (Editors)

Volume 67 Motion vision: design of compact motion sensing solution for

autonomous systems J. Kolodko and L. Vlacic

Volume 68 Flexible robot manipulators: modelling, simulation and control M.O. Tokhi

and A.K.M. Azad (Editors)

Volume 69 Advances in unmanned marine vehicles G. Roberts and R. Sutton (Editors)

Volume 70 Intelligent control systems using computational intelligence techniques

A. Ruano (Editor)

Volume 71 Advances in cognitive systems S. Nefti and J. Gray (Editors)

Volume 73 Adaptive Sampling with Mobile WSN K. Sreenath, M.F. Mysorewala,

D.O. Popa and F.L. Lewis

Volume 74 Eigenstructure Control Algorithms: applications to aircraft/rotorcraft

handling qualities design S. Srinathkumar

Advanced Control

for Constrained

Processes and

Systems

Fabricio Garelli, Ricardo J. Mantz

and Herna´n De Battista

The Institution of Engineering and Technology

PRELIMS 2 September 2011; 13:54:55

Published by The Institution of Engineering and Technology, London, United Kingdom

The Institution of Engineering and Technology is registered as a Charity in England & Wales

(no. 211014) and Scotland (no. SC038698).

† 2011 The Institution of Engineering and Technology

First published 2011

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British Library Cataloguing in Publication Data

A catalogue record for this product is available from the British Library

ISBN 978-1-84919-261-3 (hardback)

ISBN 978-1-84919-262-0 (PDF)

Typeset in India by MPS Ltd, a Macmillan Company

Printed in the UK by CPI Antony Rowe, Chippenham, Wiltshire

PRELIMS 2 September 2011; 13:54:55

PRELIMS 2 September 2011; 13:54:55

To Lau (F.G.), Lilian (R.M.) and Vale (H.D.B.)

PRELIMS 2 September 2011; 13:54:55

PRELIMS 2 September 2011; 13:54:55

Contents

1 An introduction to constrained control 1

1.1 Motivations 1

1.2 Types of constraints 2

1.2.1 Physical limits 3

1.2.2 Structural constraints 4

1.2.3 Dynamic restrictions 4

1.3 Some typical effects of constraints 5

1.3.1 Controller windup 5

1.3.2 Plant windup 7

1.3.3 Control directionality problem 9

1.4 Other constraint implications 10

1.5 Different approaches to constrained control 12

1.6 Book philosophy 13

1.7 Short outline of the main problems to be addressed 14

2 A practical method to deal with constraints 17

2.1 Introduction 17

2.2 Preliminary definitions 18

2.3 Sliding mode reference conditioning 18

2.3.1 Basic idea for biproper systems 18

2.3.2 Illustrative example 21

2.4 Biproper SMRC: features and analysis 23

2.4.1 VSS essentials 24

2.4.2 SMRC operation analysis 28

2.4.3 Implementation issues 31

2.5 Strictly proper SMRC 32

2.5.1 Normal form 33

2.5.2 Method reformulation 34

2.5.3 Illustrative examples 36

2.6 SMRC and non-linear systems 42

2.6.1 Geometrical interpretation of SM 42

2.6.2 Geometric invariance via SMRC 44

2.6.3 SMRC in strictly proper non-linear systems 47

2.7 Robustness properties 48

2.7.1 SM existence domain 49

2.7.2 SM dynamics 51

3 Some practical case studies 53

3.1 Pitch control in wind turbines 53

3.1.1 Brief introduction to the problem 53

3.1.2 Pitch actuator and control 55

3.1.3 SMRC compensation for actuator constraints in the pitch

control loop 56

3.1.4 Application to a wind energy system for water pumping 57

3.2 Clean hydrogen production plant 59

3.2.1 Brief introduction to the problem 61

3.2.2 System description 62

3.2.3 SMRC algorithm to deal with electrolyser constraints 66

3.2.4 Simulation results 67

3.3 Robot path tracking 70

3.3.1 Brief introduction to the problem 70

3.3.2 Classical control scheme for robotic path tracking 71

3.3.3 Tracking speed autoregulation technique 73

3.3.4 Application to a 2R manipulator 75

3.4 Control of a fed-batch bioreactor 80

3.4.1 Brief introduction to the problem 80

3.4.2 Process model 80

3.4.3 Reference seeking for overflow avoidance 82

3.4.4 Simulations 84

4 Relevant tools for dynamic decoupling 87

4.1 Preliminary concepts 87

4.1.1 Multivariable system models 87

4.1.2 Multivariable poles and zeros 88

4.1.3 Closed-loop transfer matrices 90

4.1.4 Internal stability 92

4.2 MIMO controller parameterisation and approximate inverses 92

4.2.1 Stabilising controller parameterisation 93

4.2.2 Internal model control 94

4.2.3 Interactor matrices 95

4.2.4 Approximate model inverses 99

4.3 Dynamic decoupling of MIMO systems 99

4.3.1 Minimum phase systems 100

4.3.2 Non-minimum phase systems 102

4.3.3 Unstable systems 106

4.4 Performance limitations in non-minimum phase systems 107

5 Constrained dynamic decoupling 111

5.1 Introduction 111

5.2 Control directionality changes 112

5.3 Dynamic decoupling preservation by means of SMRC 115

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viii Advanced control for constrained processes and systems

5.3.1 Method formulation 115

5.3.2 Sliding surfaces design 117

5.3.3 SMRC dynamics 117

5.3.4 Operating issues 120

5.4 Minimum-phase example 122

5.5 Non-minimum phase examples 124

5.5.1 Revisiting Example 1.3 124

5.5.2 Sugar cane crushing station 125

6 Interaction limits in decentralised control architectures 131

6.1 Introduction to decentralised control 131

6.1.1 Architecture description 131

6.1.2 Interaction measure 132

6.1.3 Control structure selection: the TITO case 134

6.1.4 Decentralised integral controllability 137

6.2 Interaction effects on multiloop strategies 139

6.3 Limiting interactions in decentralised control via SMRC 143

6.3.1 Control scheme 143

6.3.2 Switching law 145

6.3.3 Output dynamics during conditioning 147

6.3.4 Behaviour in presence of output disturbances 148

6.4 Two-degrees of freedom PID controller with adaptive set-point

weighting 149

6.5 Case study: Quadruple tank 150

6.5.1 Plant model analysis 151

6.5.2 Interactions limits in non-minimum phase setting 155

6.6 Delay example: catalytic reactor 161

7 Partial decoupling and non-minimum phase systems 163

7.1 Some introductory comments 163

7.2 Right-half plane zeros directionality and partial decoupling 164

7.2.1 Algebraic interpolation constraint 164

7.2.2 Inverse response on a particular output 167

7.3 Interpolating diagonal and partial decoupling 170

7.4 Partial decoupling with bounded interactions via SMRC 170

7.5 Numerical example 172

7.6 Case study: quadruple tank 175

8 MIMO bumpless transfer 181

8.1 Introduction 181

8.2 Switching at the plant input 182

8.3 A simple SMRC solution for SISO systems 183

8.4 MIMO bumpless transfer 185

8.4.1 Some concepts on collective sliding modes 185

8.4.2 A MIMO bumpless algorithm 188

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Contents ix

8.5 Application to the quadruple tank process 191

8.5.1 Manual–automatic switching 191

8.5.2 Automatic–automatic commutation 193

References 197

Index 207

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x Advanced control for constrained processes and systems

CH001 2 September 2011; 16:22:47

Chapter 1

An introduction to constrained control

1.1 Motivations

In every real control loop, there exist physical limits that affect the achievable

closed-loop performance. Particularly, it is well known that mechanical stops or

technological actuator limitations give rise to unavoidable constraints at the input

to the plant, which must be taken into account to meet performance specifications

or safety operation modes.

In single-input single-output (SISO) systems, these physical limits at the plant

input are the principal cause of highly studied problems like controller and plant

windup. However, there are other types of constraints that have been dealt with to a

much lesser extent but that also have an effect on the achievable performance. For

instance, the few degrees of freedom of industrial controllers (typically PID) or

plants having non-minimum phase features will generally restrict the evolution of

the controlled variables. What is more, some well-known problems such as bumpy

transfers can be attributed to the fact of constraining the controller types and their

switch scheduling. Thus, there also exist structural or dynamic constraints that

together with performance specifications, environmental regulations or safety rules

usually require system states or outputs to be bounded.

Although constrained control problems have been studied primarily in SISO

systems, the majority of the real-world processes have more than one variable to be

controlled and possess more than one control action for this objective. These sys￾tems are called multivariable systems or multiple-input multiple-output (MIMO)

systems. Actually, SISO systems frequently are a given subsystem of an overall

MIMO system.

Multivariable systems can be found almost everywhere. In the bathroom of a

house, the water temperature and flow rate are important variables for a pleasant

shower. In chemical processes, it is commonly required to simultaneously control

pressure and temperature at several points of a reactor. An automated greenhouse

should ensure that the lighting, relative humidity and temperature are adequate for a

given cultivation. A robot manipulator needs six degrees of freedom to have a full

positioning rank, whereas in a plane or a satellite there are dozens of variables to be

controlled.

There are some phenomena that are present only in MIMO systems and do not

occur in SISO systems. For example, the presence of directions associated to

input/output vectors is exclusive to MIMO systems. On this account, a multi￾variable system may have a pole and a zero at the same location that do not cancel

each other, or in a minimum-phase MIMO system the individual elements of the

transfer matrix might have their zeros in the right-half plane (RHP), or vice versa.

Nevertheless, the most distinctive property of a multivariable system is probably

the crossed coupling or interactions between its variables. In effect, in a MIMO

system each input variable affects not only its corresponding output but also all the

remaining controlled variables of the system. This makes controller design a dif￾ficult task, and in most applications precludes one from doing it as if the system

consisted of multiple mono-variable loops, since the gains of a single-loop con￾troller will have impact on the other loops and may even cause instability. This is

the reason why crossed interactions are generally considered the main difficulty of

multivariable control systems [144]. Therefore, in a multivariable process the

effects and demands of the aforementioned system constraints are worsened

because of the directionality and interactions present in this kind of plants. The

search for solutions to such problems has motivated several research works in the

previous years [46,63,123–125,127].

Despite the large number of existing methods to address constrained control

problems, a common practice of engineers is to design control systems using

conventional methods in such a way that they avoid reaching the system limits and,

at the same time, achieve a reasonable performance for a given operating region.

However, this conservative approach is seldom feasible in complex systems control

or high-performance applications. Moreover, even in relatively simple industrial

problems, the resulting closed-loop performance can be significantly improved if

system constraints are taken into account.

Contrary to what some practising engineers believe, this does not necessarily

require a complete redesign of the control system and abandoning their valuable

experience on nominal control design. Indeed, the basic ideas behind the simplest

anti-windup (AW) schemes highly accepted in industry can be further exploited to

gain robustness, closed-loop performance and design simplicity in more complex

control problems with different kinds of constraints, while preserving conventional

control methods for the nominal controller design. This will be a major topic in the

book: the first part (Chapters 1–3) mainly devoted to SISO constrained systems and

the second part (Chapters 4–8) devoted to some relevant multivariable control

problems.

1.2 Types of constraints

Let us start by giving a classification of system constraints affecting closed-loop

performance. As could be noted from the introductory comments, constraints shall

be understood in a ‘wide sense’. That is, we will refer to system constraints not only

to mention physical limits of the control loop components but also to mention any

other structural constraint or dynamic restriction that affects closed-loop perfor￾mance and can be tackled by delimiting a given signal in the loop.

CH001 2 September 2011; 16:22:48

2 Advanced control for constrained processes and systems

CH001 2 September 2011; 16:22:48

Basically, we broadly classify the constraints from their source type into three

categories:

● Physical limits

● Structural constraints

● Dynamic restrictions

Any of these can be responsible for performance degradation and may conse￾quently generate the necessity of bounding input, output or internal variables of the

process under control (see Figure 1.1).

PERFORMANCE

REQUIREMENTS

Input signal bound

Internal signal bound

Output signal bound

Physical limits

Structural constraints

Dynamic restrictions

Figure 1.1 Types of constraints and their consequent signal bounds requirements

1.2.1 Physical limits

These are directly related to physical or technological limitations of the elements

comprising the control loop. This is the most common type of constraint in the

sense that this is what engineers generally refer to when talking about constrained

systems.

Some examples, although obvious, seem to be opportune:

● Every electrical engine has a voltage limit and a maximum speed that should

not be exceeded.

● A valve can be opened neither more than 100% nor less than 0%.

● The slew rate of a hydraulic actuator will always be limited.

In closed-loop systems, performance requirements frequently lead the control

action to hit these physical limitations at the plant input, i.e. actuator saturation is

reached. Saturation can occur in either amplitude, rate of change or higher-order

signal derivatives, such as acceleration. If the control action exceeds these limits

for any reason, severely detrimental behaviours may occur. Therefore, the control

system design must somehow account for the unavoidable actuator limits by con￾fining the signal at the plant input to adequate values.

However, although physical limits generally appear at the plant input, they do

not exclusively require delimiting the commanded signal to the plant. In effect, we

will see later that this kind of constraint may also demand restricting internal or

output system variables to avoid performance degradation.

In the next section, we briefly present some of the most common effects pro￾duced by this kind of constraints. To emphasise its significance, it is interesting to

An introduction to constrained control 3

recall that physical limits, frequently present in simple industrial control problems,

have also been involved in extremely serious accidents, like various aircraft crashes

and environmental disasters [128].

1.2.2 Structural constraints

We include here the restrictions that are associated with structural limitations of

either the plant or the controller. Some examples are as follows:

● Plants in which pre-existing automation devices and circuitry update are not

feasible, but new specifications should be met.

● Closed-loop systems with a simple and fixed controller structure, such as P or

PI controllers.

● Linear controllers coping with non-linear systems.

● Multiloop or decentralised control structures in multivariable applications.

Although we will deal with many other examples of structural constraints

throughout the book, PID controllers are probably the most illustrative case. Not

only are they highly accepted in industry applications, but the use of any other type

of controller is often turned down. Despite their well-known advantages, it is also

true that they are not able to deal with every type of process and specification.

Thus, if the controller type cannot be changed, it will result in an additional con￾straint for the control designer when trying to achieve quite demanding control

objectives.

1.2.3 Dynamic restrictions

With this term, we refer to those dynamic characteristics of the process to be

controlled (or the controller to be employed) that directly affect the achievable

closed-loop performance and the evolution of the signals in the control loop. For

instance,

● Plants with RHP zeros and poles.

● Systems or controllers with particular combinations of pole and zero locations.

● Non-linear processes in which detrimental dynamic behaviours are excited by

the growth of a given internal variable.

It is well known that RHP zeros produce undesired inverse responses in the

controlled variable. Also, systems with a stable zero closer to the origin than the

dominant poles may give rise to large overshoots in the step response. In complex

processes with non-linear behaviours, the regulation of a variable of interest can

lead auxiliary variables to dangerous or undesirable regions (see the last case study

in Chapter 2).

Consequently, this group of constraints may also translate into bounding

requirements on the loop signals because of performance specifications or safety

operation. This will be pointed out in Section 1.4 and further addressed from

Chapter 3.

CH001 2 September 2011; 16:22:48

4 Advanced control for constrained processes and systems