Control system design Thiết kế hệ thống điều khiển

CONTROL SYSTEM
DESIGN
Graham C. Goodwin1
Stefan F. Graebe2
Mario E. Salgado3

Valpara´ıso, January 2000
1 Centre for Integrated Dynamics and Control
University of Newcastle, NSW 2308 AUSTRALIA
2 OMV Aktiengesellschaft
Department of Optimization/Automation
Schwechat, AUSTRIA
3 Departamento de Electr´
onica
Universidad T´ecnica Federico Santa Mar´ıa
Valpara´ıso, CHILE



Dedicated, in thankful appreciation
for support and understanding, to
Rosslyn
Alice
Mariv´ı



CONTENTS OVERVIEW
I

THE ELEMENTS

1
The Excitement of Control Engineering
2
Introduction to the Principles of Feedback
3
Modeling
4
Continuous Time Signals and Systems

II
5
6
7

1
5
21
41
65

SISO CONTROL ESSENTIALS
Analysis of SISO Control Loops
Classical PID Control
Synthesis of SISO Controllers

117
121
157
177

SISO CONTROL DESIGN
Fundamental Limitations in SISO Control
Frequency Domain Design Limitations
Architectural Issues in SISO Control
Dealing with Constraints

195
199
239
263
291

III
8
9
10
11
IV

DIGITAL COMPUTER CONTROL
12
Models for Sampled Data Systems
13
Digital Control
14
Hybrid Control

313
317
351

385

V

ADVANCED SISO CONTROL
15
SISO controller Parameterizations
16
Control Design Based on Optimization
17
Linear State Space Models
18
Synthesis via State Space Methods
19
Introduction to Nonlinear Control

401
405
455
483
515
547

VI

MIMO CONTROL ESSENTIALS
20
Analysis of MIMO Control Loops
21
Exploiting SISO Techniques in MIMO Control

583
587
627

VII MIMO CONTROL DESIGN
22
Design via Optimal Control Techniques
23
Model Predictive Control
24
Fundamental Limitations in MIMO Control

649
653
715
743

VIII ADVANCED MIMO CONTROL
25
MIMO Controller Parameterizations
26
Decoupling

779
783
823

vii

CONTENTS

CONTENTS OVERVIEW

vii

ACKNOWLEDGEMENTS

xxi

PREFACE

xxiii

APPENDICES

xxix

I

THE ELEMENTS

PREVIEW

1
3

1 THE EXCITEMENT OF CONTROL ENGINEERING

1.1 Preview
1.2 Motivation for Control Engineering
1.3 Historical Periods of Control Theory
1.4 Types of Control System Design
1.5 System Integration
1.6 Summary
1.7 Further Reading

5
5
5
9
10
11
18
19

2 INTRODUCTION TO THE PRINCIPLES OF FEEDBACK
2.1 Preview
2.2 The Principal Goal of Control
2.3 A Motivating Industrial Example
2.4 Definition of the Problem
2.5 Prototype Solution to the Control Problem via Inversion

21
21
21
22
27
29

ix


x

Contents Overview

2.6
2.7
2.8
2.9
2.10
2.11

High Gain Feedback and Inversion
From Open to Closed Loop Architectures
Trade-offs Involved in Choosing the Feedback Gain
Measurements
Summary
Further Reading

3 MODELING
3.1 Preview
3.2 The Raison d’ˆ
etre for Models
3.3 Model Complexity
3.4 Building Models
3.5 Model Structures
3.6 State Space Models
3.7 Solution of Continuous Time State Space Models

3.8 High Order Differential and Difference Equation Models
3.9 Modeling Errors
3.10 Linearization
3.11 Case Studies
3.12 Summary
3.13 Further Reading
3.14 Problems for the Reader
4 CONTINUOUS TIME SIGNALS AND SYSTEMS
4.1 Preview
4.2 Linear Continuous Time Models
4.3 Laplace Transforms
4.4 Laplace Transform. Properties and Examples
4.5 Transfer Functions
4.6 Stability of Transfer Functions
4.7 Impulse and Step Responses of Continuous Time Linear Systems
4.8 Poles, Zeros and Time Responses
4.9 Frequency Response
4.10 Fourier Transform
4.11 Frequently Encountered Models
4.12 Modeling Errors for Linear Systems
4.13 Bounds for Modeling Errors
4.14 Summary

32
34
36
36
37
39
41

41
41
42
44
45
45
49
50
50
52
57
58
60
61
65
65
65
66
67
70
74
74
76
85
92
97
99
103
104

Contents Overview

4.15 Further Reading
4.16 Problems for the Reader

II

SISO CONTROL ESSENTIALS

xi
108
109

115

PREVIEW

117

5 ANALYSIS OF SISO CONTROL LOOPS
5.1 Preview
5.2 Feedback Structures
5.3 Nominal Sensitivity Functions
5.4 Closed Loop Stability Based on the Characteristic Polynomial
5.5 Stability and Polynomial Analysis
5.6 Root Locus (RL)
5.7 Nominal Stability using Frequency Response
5.8 Relative Stability: Stability Margins and Sensitivity Peaks
5.9 Robustness

5.10 Summary
5.11 Further Reading
5.12 Problems for the Reader

119
119
119
123
125
126
132
136
141
143
148
150
152

6 CLASSICAL PID CONTROL
6.1 Preview
6.2 PID Structure
6.3 Empirical Tuning
6.4 Ziegler-Nichols (Z-N) Oscillation Method
6.5 Reaction Curve Based Methods
6.6 Lead-lag Compensators
6.7 Distillation Column
6.8 Summary
6.9 Further Reading
6.10 Problems for the Reader

157
157
157
160
160
164
167
169
172
172
174

7 SYNTHESIS OF SISO CONTROLLERS
7.1 Preview
7.2 Polynomial Approach
7.3 PI and PID Synthesis Revisited using Pole Assignment
7.4 Smith Predictor

177
177
177
185
187


xii

Contents Overview

7.5

7.6
7.7

III

Summary
Further Reading
Problems for the Reader

SISO CONTROL DESIGN

188
190
191

195

PREVIEW

197

8 FUNDAMENTAL LIMITATIONS IN SISO CONTROL
8.1 Preview
8.2 Sensors
8.3 Actuators
8.4 Disturbances
8.5 Model Error Limitations
8.6 Structural Limitations
8.7 Remedies
8.8 An Industrial Application (Reversing Mill)

8.9 Design Homogeneity Revisited
8.10 Summary
8.11 Further Reading
8.12 Problems for the Reader

199
199
200
201
203
204
205
220
225
229
230
233
235

9 FREQUENCY DOMAIN DESIGN LIMITATIONS
9.1 Preview
9.2 Bode’s Integral Constraints on Sensitivity
9.3 Integral Constraints on Complementary Sensitivity
9.4 Poisson Integral Constraint on Sensitivity
9.5 Poisson Integral Constraint on Complementary Sensitivity
9.6 Example of Design Trade-offs
9.7 Summary
9.8 Further Reading
9.9 Problems for the Reader

239
239
240
244
246
252
254
257
258
261

10 ARCHITECTURAL ISSUES IN SISO CONTROL
10.1 Preview
10.2 Models for Deterministic Disturbances and Reference Signals
10.3 Internal Model Principle for Disturbances
10.4 Internal Model Principle for Reference Tracking

263
263
263
265
269


Contents Overview

10.5 Feedforward
10.6 Reference Feedforward
10.7 Disturbance feedforward
10.8 Industrial Applications of Feedforward Control

10.9 Cascade Control
10.10Summary
10.11Further Reading
10.12Problems for the reader
11 DEALING WITH CONSTRAINTS
11.1 Preview
11.2 Wind-Up
11.3 Anti-Windup Scheme
11.4 State Saturation
11.5 Introduction to Model Predictive Control
11.6 Summary
11.7 Further Reading
11.8 Problems for the Reader

IV

DIGITAL COMPUTER CONTROL

xiii
269
270
272
277
279
283
286
288
291
291
292

293
299
304
304
305
307

313

PREVIEW

315

12 MODELS FOR SAMPLED DATA SYSTEMS
12.1 Preview
12.2 Sampling
12.3 Signal Reconstruction
12.4 Linear Discrete Time Models
12.5 The Shift Operator
12.6 Z–Transform
12.7 Discrete Transfer Functions
12.8 Discrete Delta Domain Models
12.9 Discrete Delta Transform
12.10Discrete Transfer Functions (Delta Form)
12.11Transfer Functions and Impulse Responses
12.12Discrete System Stability
12.13Obtaining Discrete Models for Sampled Continuous Systems

317
317

317
319
320
320
321
322
326
329
333
334
334
335


xiv

Contents Overview

12.14Using Continuous State Space Models
12.15Frequency Response of Sampled Data Systems
12.16Summary
12.17Further Reading
12.18Problems for the Reader

338
340
343
346
347

13 DIGITAL CONTROL
13.1 Preview
13.2 Discrete Time Sensitivity Functions
13.3 Zeros of Sampled Data Systems
13.4 Is a Special Theory of Digital Control Design Really Necessary?
13.5 Approximate Continuous Designs
13.6 At-Sample Digital Design
13.7 Internal Model Principle for Digital Control
13.8 Fundamental Performance Limitations
13.9 Summary
13.10Further Reading
13.11Problems for the Reader

351
351
351
353
355
356
360
371
375
379
380
381

14 HYBRID CONTROL
14.1 Preview
14.2 Hybrid Analysis
14.3 Models for Hybrid Control Systems

14.4 Analysis of Intersample Behavior
14.5 Repetitive Control Revisited
14.6 Poisson Summation Formula
14.7 Summary
14.8 Further Reading
14.9 Problems for the Reader

385
385
385
385
389
391
392
394
395
396

V

ADVANCED SISO CONTROL

401

PREVIEW

403

15 SISO CONTROLLER PARAMETERIZATIONS
15.1 Preview

15.2 Open Loop Inversion Revisited
15.3 Affine Parameterization. The Stable Case

405
405
405
406


Contents Overview

15.4 PID Synthesis using the Affine Parameterization
15.5 Affine Parameterization for Systems having Time Delays
15.6 Undesirable Closed Loop Poles
15.7 Affine Parameterization: The Unstable Open Loop Case
15.8 Discrete Time Systems
15.9 Summary
15.10Further reading
15.11Problems for the reader

xv
416
425
428
437
444
445
449
451

16 CONTROL DESIGN BASED ON OPTIMIZATION
16.1 Preview
16.2 Optimal Q (Affine) Synthesis
16.3 Robust Control Design with Confidence Bounds
16.4 Summary
16.5 Further Reading
16.6 Problems for the Reader

455
455
456
462
476
476
479

17 LINEAR STATE SPACE MODELS
17.1 Preview
17.2 Linear Continuous Time State Space Models
17.3 Similarity Transformations
17.4 Transfer Functions Revisited
17.5 From Transfer Function to State Space Representation
17.6 Controllability and Stabilizability
17.7 Observability and Detectability
17.8 Canonical Decomposition
17.9 Pole Zero Cancellation and System Properties
17.10Summary
17.11Further Reading
17.12Problems for the Reader

483
483
483
484
486
488
489
499
505
507
511
513
514

18 SYNTHESIS VIA STATE SPACE METHODS
18.1 Preview
18.2 Pole Assignment by State Feedback
18.3 Observers
18.4 Combining State Feedback with an Observer
18.5 Transfer Function Interpretations

519
519
519
523
529
531


xvi

Contents Overview

18.6 Reinterpretation of the Affine Parameterization of all Stabilizing Controllers
18.7 State Space Interpretation of Internal Model Principle
18.8 Trade-Offs in State Feedback and Observers
18.9 Dealing with Input Constraints in the Context of State Estimate
Feedback
18.10Summary
18.11Further Reading
18.12Problems for the Reader

537
538
543
544
545
547
548

19 INTRODUCTION TO NONLINEAR CONTROL
551
19.1 Preview
551
19.2 Linear Control of a Nonlinear Plant
551
19.3 Switched Linear Controllers
556
19.4 Control of Systems with Smooth Nonlinearities
559

19.5 Static Input Nonlinearities
559
19.6 Smooth Dynamic Nonlinearities for Stable and Stably Invertible Models560
19.7 Disturbance Issues in Nonlinear Control
567
19.8 More General Plants with Smooth Nonlinearities
572
19.9 Non-Smooth Nonlinearities
575
19.10Stability of Nonlinear Systems
577
19.11Summary
581
19.12Further Reading
583
19.13Problems for the Reader
585

VI

MIMO CONTROL ESSENTIALS

587

PREVIEW

589

20 ANALYSIS OF MIMO CONTROL LOOPS
20.1 Preview

20.2 Motivational Examples
20.3 Models for Multivariable Systems
20.4 The Basic MIMO Control Loop
20.5 Closed Loop Stability
20.6 Steady State Response for Step Inputs
20.7 Frequency Domain Analysis
20.8 Robustness Issues

591
591
591
593
603
605
609
610
620


Contents Overview

20.9 Summary
20.10Further Reading
20.11Problems for the Reader
21 EXPLOITING SISO TECHNIQUES IN MIMO CONTROL
21.1 Preview
21.2 Completely Decentralized Control
21.3 Pairing of Inputs and Outputs
21.4 Robustness Issues in Decentralized Control
21.5 Feedforward Action in Decentralized Control

21.6 Converting MIMO Problems to SISO Problems
21.7 Industrial Case Study (Strip Flatness Control)
21.8 Summary
21.9 Further Reading
21.10Problems for the Reader

VII

MIMO CONTROL DESIGN

xvii
622
625
627
631
631
631
635
638
641
643
644
648
649
650

653

PREVIEW

655

22 DESIGN VIA OPTIMAL CONTROL TECHNIQUES
22.1 Preview
22.2 State Estimate Feedback
22.3 Dynamic Programming and Optimal Control
22.4 The Linear Quadratic Regulator (LQR)
22.5 Properties of the Linear Quadratic Optimal Regulator
22.6 Model Matching Based on Linear Quadratic Optimal Regulators
22.7 Discrete Time Optimal Regulators
22.8 Connections to Pole Assignment
22.9 Observer Design
22.10Linear Optimal Filters
22.11State Estimate Feedback
22.12Transfer Function Interpretation
22.13Achieving Integral Action in LQR Synthesis
22.14Industrial Applications
22.15Summary
22.16Further Reading

657
657
657
660
663
665
669
672
674
676

677
690
691
693
695
709
712


xviii

Contents Overview

22.17Problems for the Reader

715

23 MODEL PREDICTIVE CONTROL
23.1 Preview
23.2 Anti-Windup Revisited
23.3 What is Model Predictive Control?
23.4 Stability
23.5 Linear Models with Quadratic Cost Function
23.6 State Estimation and Disturbance Prediction
23.7 Rudder Roll Stabilization of Ships
23.8 Summary
23.9 Further Reading
23.10Problems for the Reader

719

719
720
724
728
731
734
736
740
741
743

24 FUNDAMENTAL LIMITATIONS IN MIMO CONTROL
24.1 Preview
24.2 Closed Loop Transfer Function
24.3 MIMO Internal Model Principle
24.4 The Cost of the Internal Model Principle
24.5 RHP Poles and Zeros
24.6 Time Domain Constraints
24.7 Poisson Integral Constraints on MIMO Complementary Sensitivity
24.8 Poisson Integral Constraints on MIMO Sensitivity
24.9 Interpretation
24.10An Industrial Application: Sugar Mill
24.11Non-Square Systems
24.12Discrete Time Systems
24.13Summary
24.14Further Reading
24.15Problems for the Reader

747
747

748
749
749
750
751
756
758
760
762
773
776
777
778
780

VIII

ADVANCED MIMO CONTROL

783

PREVIEW

785

25 MIMO CONTROLLER PARAMETERIZATIONS
25.1 Preview
25.2 Affine Parameterization: Stable MIMO Plants

787

787
787


Contents Overview

25.3 Achieved Sensitivities
25.4 Dealing with Model Relative Degree
25.5 Dealing with NMP Zeros
25.6 Affine Parameterization: Unstable MIMO Plants
25.7 State Space Implementation
25.8 Summary
25.9 Further Reading
25.10Problems for the Reader

xix
789
789
800
817
820
823
824
826

26 DECOUPLING
829
26.1 Preview
829
26.2 Stable Systems

830
26.3 Pre and post Diagonalization
837
26.4 Unstable Systems
839
26.5 Zeros of Decoupled and Partially Decoupled Systems
848
26.6 Frequency Domain Constraints for Dynamically Decoupled Systems 852
26.7 The Cost of Decoupling
854
26.8 Input Saturation
858
26.9 MIMO Anti Wind-Up Mechanism
859
26.10Summary
867
26.11Further Reading
869
26.12Problems for the Reader
871
NAME INDEX

873

SUBJECT INDEX

877

ACKNOWLEDGEMENTS

The authors wish to thank the large number of colleagues and friends who have
worked with us in the area of control over the years. This book is really a synthesis
of ideas that they helped us to formulate. All three authors spent time together
in the Centre for Industrial Control Science at the University of Newcastle, Australia. This was a fertile breeding ground for many discussions on the principles of
control. Financial support from the Australian Government for this centre under
the Commonwealth Special Centres program is gratefully acknowledged. Also, financial and other support was provided by the Universidad T´ecnica Federico Santa
Mar´ıa covering, amongst other things, several visits to Chile by the first author
during the writing of this book. Many students and colleagues read drafts of the
book ranging over a five year period. The authors accept full responsibility for
the views expressed in the book (and all remaining errors). Nonetheless, they wish
to particularly acknowledge suggestions from Thomas Brinsmead, Arthur Conley,
Sam Crisafulli, Jose De Don´a, Arie Feuer, Jaime Glar´ıa, William Heath, Kazuo Komatsu, David Mayne, Trisan Perez, Mar´ıa Seron, Gustavo Vergara, Liuping Wang
and Steve Weller. The book was composed and typed by many people, including
the authors. However, in the final stages of producing the book, Jayne Disney
gave considerable help. Also, Tim Wylie and Adrian Bastiani kindly produced the
Engineering Drawings shown in the text.

xxi



PREFACE

Control Engineering plays a fundamental role in modern technological systems. The
benefits of improved control in industry can be immense. They include improved
product quality, reduced energy consumption, minimization of waste materials, increased safety levels and reduction of pollution.
However, a difficulty with the subject is that some of the more advanced aspects
depend on sophisticated mathematical background. Arguably, mathematical systems theory is one of the most significant achievements of twentieth century science.

However, its practical impact is only as good as the benefits it can bring. Thus, in
this book, we aim to strike a balance which places strong emphasis on design.
It was the author’s involvement in several industrial control system design
projects that provided part of the motivation to write this book. In a typical
industrial problem, we found ourselves investigating fluid and thermal dynamics,
experiencing the detrimental effects of non-constant PLC scan rates, dealing with
system integration and network communication protocols, building trust with plant
operators and investigating safe bumpless transfer schemes for testing tentative
control designs on potentially dangerous plants. In short, we experienced the dayto-day excitement, frustration, set-backs and progress in getting advanced control
to contribute to a commercial company’s bottom line. This is not an easy task.
Moreover, success in this type of venture typically depends on the application of a
wide range of multidisciplinary skills. However, it is rewarding and exciting work
for those who do it.
One of the main aims of this book is to share this excitement with our readers.
We hope to contribute to the development of skills and attitudes within readers
and students that will better equip them to face the challenges of real-world design
problems. The book is thus intended to contribute to the ongoing reform of the
Control Engineering curriculum. This topic is receiving considerable international
attention. For example, a recent issue of IEEE Control Systems Magazine features
an entire special section devoted to this theme.
However, reforming the curriculum will not be done by books alone - it will be
done by people; by students, by teachers, by researchers, by practitioners, by publication and grant reviewers; and by market pressures. Moreover, for these efforts to
xxiii


xxiv

PREFACE

be efficient and sustainable, the control engineering community will need to communicate their experiences via a host of new books, laboratories, simulations and

web-based resources. Thus, there will be a need for several different and complementary approaches. In this context, the authors believe that this book will have
been successful if it contributes, in some way, to the revitalization of interest by
students in the exciting discipline of control engineering.
We stress that this is not a how-to book. On the contrary, we provide a comprehensive, yet condensed, presentation of rigorous control engineering. We employ,
and thus require, mathematics as a means to model the process, analyze its properties under feedback, synthesize a controller with particular properties and arrive at a
design addressing the inherent trade-offs and constraints applicable to the problem.
In particular, we believe that success in control projects depends on two key
ingredients: (i) having a comprehensive understanding of the process itself, gained
by studying the relevant physics, chemistry, etc.; and (ii) by having mastery of the
fundamental concepts of signals, systems and feedback. The first ingredient typically occupies more than fifty per cent of the effort. It is an inescapable component
of the complete design cycle. However, it is impractical for us to give full details
of the processes to which control might be applied since it covers chemical plants,
electromechanical systems, robots, power generators, etc. We thus emphasize the
fundamental control engineering aspects that are common to all applications and
leave readers to complement this with process knowledge relevant to their particular
problem. Thus, the book is principally aimed at the second ingredient of control
engineering. Of course, we do give details of several real world examples so as to
put the methods into a proper context.
The central theme of this book is continuous-time control. However we also
treat digital control in detail, since most modern control systems will usually be
implemented on some form of computer hardware. This approach inevitably led
to a book of larger volume than originally intended but with the advantage of
providing a comprehensive treatment within an integrated framework. Naturally,
there remain specialized topics that are not covered in the book. However, we trust
that we provide a sufficiently strong foundation so that the reader can comfortably
turn to the study of appropriate complementary literature.
Thus, in writing this book we chose our principal goals as:
• providing accessible treatment of rigorous material selected with applicability
in mind,
• giving early emphasis to design including methods for dealing with fundamental trade-offs and constraints,

• providing additional motivation through substantial interactive web-based
support, and
• demonstrating the relevance of the material through numerous industrial case
studies.


PREFACE

xxv

Design is a complex process, which requires judgment and iteration. The design
problem is normally incompletely specified, sometimes ill-defined, and many times
without solution. A key element in design is an understanding of those factors which
limit the achievable performance. This naturally leads to a viewpoint of control
design which takes account of these fundamental limitations. This viewpoint is a
recurring theme throughout the book.
Our objective is not to explore the full depth of mathematical completeness but
instead to give enough detail so that a reader can begin applying the ideas as soon as
possible. This approach is connected to our assumption that readers will have ready
access to modern computational facilities including the software package MATLABSIMULINK. This assumption allows us to put the emphasis on fundamental ideas
rather than on the tools. Every chapter includes worked examples and problems
for the reader.
The book is divided into eight parts. A brief summary of each of the parts is
given below:
Part 1: The Elements
This part covers basic continuous time signals and systems and would be suitable
for an introductory course on this topic. Alternatively it could be used to provide
revision material before starting the study of control in earnest.
Part II: SISO Control Essentials
This part deals with basic SISO control including classical PID tuning. This,

together with part 1, covers the content of many of the existing curricula for basic
control courses.
Part III: SISO Control Design
This part covers design issues in SISO Control. We consider many of these ideas
to be crucial to achieving success in practical control problems. In particular, we
believe the chapter dealing with constraints should be mentioned, if at all possible,
in all introductory courses. Also feedforward and cascade structures, which are
covered in this part, are very frequently employed in practice.
Part IV: Digital Computer Control
This part covers material essential to the understanding of digital control. We
go beyond traditional treatments of this topic by studying inter-sample issues.
Part V: Advanced SISO Control
This part could be the basis of a second course on control at an undergraduate
level. It is aimed at the introduction of ideas that flow through to multi-input
multi-output (MIMO) systems later in the book.
Part VI: MIMO Control Essentials
This part gives the basics required for a junior level graduate course on MIMO
control. In particular, this part covers basic MIMO system’s theory. It also shows
how one can exploit SISO methods in some MIMO design problems.


xxvi

PREFACE

Part VII: MIMO Control Design
This part describes tools and ideas that can be used in industrial MIMO design. In particular, it includes linear quadratic optimal control theory and optimal
filtering. These two topics have major significance in applications. We also include
a chapter on Model Predictive Control. We believe this to be important material
because of the widespread use of this technique in industrial applications.

Part VIII: Advanced MIMO Control
This final part of the book could be left for private study. It is intended to
test the readers understanding of the other material by examining advanced issues.
Alternatively instructors could use this part to extend parts VI and VII in a more
senior graduate course on MIMO Control.
Two of the authors (Goodwin and Salgado) have taught undergraduate and
postgraduate courses of the type mentioned above using draft versions of this book
in both Australia and South America.
The material in the book is illustrated by several industrial case studies with
which the authors have had direct involvement. Most of these case studies were
carried out, in collaboration with industry, by the Centre for Integrated Dynamics
and Control (CIDAC) (a Commonwealth Special Research Centre) at the University
of Newcastle.
The projects that we have chosen to describe include:
• Satellite tracking
• pH control
• Control of a continuous casting machine
• Sugar mill control
• Distillation column control
• Ammonia synthesis plant control
• Zinc coating mass estimation in continuous galvanizing line
• BISRA gauge for thickness control in rolling mills
• Roll eccentricity compensation in rolling mills
• Hold-up effect in reversing rolling mills
• Flatness control in steel rolling
• Vibration control
Many of the case studies have also been repeated, and further embellished, on
the book’s web page where Java applets are provided so that readers can experiment
with the systems in the form of a “virtual laboratory”. A secondary advantage of

PREFACE

xxvii

having the case studies gathered in one place on the web page is that real control
problems usually bring together many aspects and thus it is difficult to localize them
in the book. The web page thus gives a more holistic view of the issues involved in
the case studies.
In addition, we refer to several laboratory scale control problems including a
ball and plate mechanism, coupled tanks apparatus, and inverted pendulum. Each
of these is the basis of a laboratory experiment within our universities to illustrate
control principles.
The book has substantial Internet support — this was designed and built by
Nathan Clement and can be accessed at:
/>Alternatively see the authors’ home-pages for a link.
Newcastle, Australia
Valpara´ıso, Chile
Vienna, Austria