True Digital Control: Statistical Modelling and NonMinimal State Space Designdevelops atrue digital control design philosophy that encompasses databased model identification, through to control algorithm design, robustness evaluation and implementation. With a heritage from both classical and modern control system synthesis, this book is supported by detailed practical examples based on the authors research into environmental, mechatronic and robotic systems. Treatment of both statistical modelling and control design under one cover is unusual and highlights the important connections between these disciplines.

Starting from the ubiquitous proportionalintegral controller, and with essential concepts such as pole assignment introduced using straightforward algebra and block diagrams, this book addresses the needs of those students, researchers and engineers, who would like to advance their knowledge of control theory and practice into the state space domain; and academics who are interested to learn more about nonminimal state variable feedback control systems. Such nonminimal state feedback is utilised as a unifying framework for generalised digital control system design. This approach provides a gentle learning curve, from which potentially difficult topics, such as optimal, stochastic and multivariable control, can be introduced and assimilated in an interesting and straightforward manner.

Key features:

 Covers both system identification and control system design in a unified mannerIncludes practical design case studies and simulation examplesConsiders recent research into timevariable and statedependent parameter modelling and control, essential elements of adaptive and nonlinear control system design, and the deltaoperator (the discretetime equivalent of the differential operator) systemsAccompanied by a website hosting MATLAB examples

True Digital Control: Statistical Modelling and NonMinimal State Space Design is a comprehensive and practical guide for students and professionals who wish to further their knowledge in the areas of modern control and system identification.

James Taylor received his B.Sc. (Hons.) and Ph.D degrees from Lancaster University, UK, before joining the academic staff of the Engineering Department in 2000. His research focuses on control system design and system identification, with applied work spanning robotics, transport, energy, agriculture and the environment. This has led to over 100 publications in the open literature and widespread impact across a variety of academic and industrybased users. He has pioneered new advances in nonminimal state space design, and coordinates development of the wellknown Captain Toolbox for Time Series Analysis and Forecasting. He is a Fellow of the Institution of Engineering and Technology, and supervises students across a spectrum of mechanical, electronic, nuclear and chemical engineering disciplines.

Peter Young is Emeritus Professor at Lancaster University, UK, and Adjunct Professor at the Australian National University, Canberra. After an apprenticeship in the Aerospace Industry and B.Tech., MSc. degrees from Loughborough University, he obtained his Ph.D degree from Cambridge University in 1970 and became University Lecturer in Engineering and a Fellow of Clare Hall at Cambridge University. After seven years as Professorial Fellow at the Australian National University, he then moved to Lancaster University in 1981 as Professor and Head of the Environmental Science Department. He is well known for his work on optimal identification, databased mechanistic modelling and adaptive forecasting, with applications in areas ranging from the environment, through ecology, biology and engineering to business and macroeconomics.

Until his recent retirement,Arun Chotai was Senior Lecturer in the Lancaster Environment Centre at Lancaster University, UK. He holds a Ph.D in Systems and Control and a B.Sc. (Hons.) in Mathematics, both from the University of Bath, UK. Following his appointment to an academic position at Lancaster in 1984, he taught and developed modules in environmental systems, courses that were then unique to the UK in providing an advanced, quantitative approach to the subject. For many years, he was also joint head (with present coauthor Peter Young) of the Systems and Control Group, which he helped to build into a successful research unit that became known internationally for its research in the areas of system identification, timeseries analysis and control system design.

Preface xiii

List of Acronyms xv

1 Introduction 1

1.1 Control Engineering and Control Theory 2

1.2 Classical and Modern Control 5

1.3 The Evolution of the NMSS Model Form 8

1.4 True Digital Control 11

1.5 Book Outline 12

1.6 Concluding Remarks 13

References 14

2 Discrete-Time Transfer Functions 17

2.1 Discrete-Time TF Models 18

2.2 Stability and the Unit Circle 24

2.3 Block Diagram Analysis 26

2.4 Discrete-Time Control 28

2.5 Continuous to Discrete-Time TF Model Conversion 36

2.6 Concluding Remarks 38

References 38

3 Minimal State Variable Feedback 41

3.1 Controllable Canonical Form 44

3.2 Observable Canonical Form 50

3.3 General State Space Form 53

3.4 Controllability and Observability 58

3.5 Concluding Remarks 61

References 62

4 Non-Minimal State Variable Feedback 63

4.1 The NMSS Form 64

4.2 Controllability of the NMSS Model 68

4.3 The Unity Gain NMSS Regulator 69

4.4 Constrained NMSS Control and Transformations 77

4.5 Worked Example with Model Mismatch 81

4.6 Concluding Remarks 85

References 86

5 True Digital Control for Univariate Systems 89

5.1 The NMSS Servomechanism Representation 93

5.2 Proportional-Integral-Plus Control 98

5.3 Pole Assignment for PIP Control 101

5.4 Optimal Design for PIP Control 110

5.5 Case Studies 116

5.6 Concluding Remarks 119

References 120

6 Control Structures and Interpretations 123

6.1 Feedback and Forward Path PIP Control Structures 123

6.2 Incremental Forms for Practical Implementation 131

6.3 The Smith Predictor and its Relationship with PIP Design 137

6.4 Stochastic Optimal PIP Design 142

6.5 Generalised NMSS Design 153

6.6 Model Predictive Control 157

6.7 Concluding Remarks 163

References 164

7 True Digital Control for Multivariable Systems 167

7.1 The Multivariable NMSS (Servomechanism) Representation 168

7.2 Multivariable PIP Control 175

7.3 Optimal Design for Multivariable PIP Control 177

7.4 Multi-Objective Optimisation for PIP Control 186

7.5 Proportional-Integral-Plus Decoupling Control by Algebraic Pole Assignment 192

7.6 Concluding Remarks 195

References 196

8 Data-Based Identification and Estimation of Transfer Function Models 199

8.1 Linear Least Squares, ARX and Finite Impulse Response Models 200

8.2 General TF Models 211

8.3 Optimal RIV Estimation 218

8.4 Model Structure Identification and Statistical Diagnosis 231

8.5 Multivariable Models 243

8.6 Continuous-Time Models 248

8.7 Identification and Estimation in the Closed-Loop 253

8.8 Concluding Remarks 260

References 261

9 Additional Topics 265

9.1 The -Operator Model and PIP Control 266

9.2 Time Variable Parameter Estimation 279

9.3 State-Dependent Parameter Modelling and PIP Control 290

9.4 Concluding Remarks 298

References 298

A Matrices and Matrix Algebra 301

References 310

B The Time Constant 311

Reference 311

C Proof of Theorem 4.1 313

References 314

D Derivative Action Form of the Controller 315

E Block Diagram Derivation of PIP Pole Placement Algorithm 317

F Proof of Theorem 6.1 321

Reference 322

G The CAPTAIN Toolbox 323

References 325

H The Theorem of D.A. Pierce (1972) 327

References 328

Index 329