# True Digital Control. Statistical Modelling and Non–Minimal State Space Design

• ID: 2561508
• Book
• 360 Pages
• John Wiley and Sons Ltd
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True Digital Control: Statistical Modelling and Non Minimal State Space Design develops a true digital control design philosophy that encompasses data based 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 proportional integral 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
non minimal state variable feedback control systems. Such non minimal 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 manner
Includes practical design case studies and simulation examples
Considers recent research into time variable and state dependent parameter modelling and control, essential  elements of adaptive and nonlinear control system design, and the delta operator (the discrete time equivalent of the differential operator) systems
Accompanied by a website hosting MATLAB® examples

True Digital Control: Statistical Modelling and Non Minimal 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.

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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

9.1 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

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