Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems presents a comprehensive introduction to the use of frequency domain and polynomial system design techniques for a range of industrial control and signal processing applications. The solution of stochastic and robust optimal control problems is considered, building up from single-input problems and gradually developing the results for multivariable design of the later chapters. In addition to cataloguing many of the results in polynomial systems needed to calculate industrial controllers and filters, basic design procedures are also introduced which enable cost functions and system descriptions to be specified in order to satisfy industrial requirements. Providing a range of solutions to control and signal processing problems, this book: * Presents a comprehensive introduction to the polynomial systems approach for the solution of H_2 and H_infinity optimal control problems. * Develops robust control design procedures using frequency domain methods. * Demonstrates design examples for gas turbines, marine systems, metal processing, flight control, wind turbines, process control and manufacturing systems. * Includes the analysis of multi-degrees of freedom controllers and the computation of restricted structure controllers that are simple to implement. * Considers time-varying control and signal processing problems. * Addresses the control of non-linear processes using both multiple model concepts and new optimal control solutions. Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems is essential reading for professional engineers requiring an introduction to optimal control theory and insights into its use in the design of real industrial processes. Students and researchers in the field will also find it an excellent reference tool.

Professor Michael Grimble, Director of the Industrial Control Centre and Past Chairman of the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, UK

Preface xix

Acknowledgements xxi

1 Introduction to Optimal and Robust Control 1

1.1 Introduction 1

1.1.1 Optimality, Feedback and Robustness 2

1.1.2 High-integrity and Fault-tolerant Control Systems 3

1.1.3 Self-healing Control Systems 4

1.1.4 Fault Monitoring and Detection 5

1.1.5 Adaptive versus Robust Control 5

1.1.6 Artificial Intelligence, Neural Networks and Fuzzy Control 5

1.1.7 Discrete-time Systems 7

1.2 The H₂ and H8 Spaces and Norms 8

1.2.1 Graphical Interpretation of the H8 Norm 9

1.2.2 Terms Used in H8 Robust Control Systems Design 9

1.3 Introduction to H8 Control Design 9

1.3.1 Properties of H8 Robust Control Design 11

1.3.2 Comparison of H8 and H₂ /LQG Controllers 12

1.3.3 Relationships between Classical Design and H8 Robust Control 13

1.3.4 H₂ and H8 Design and Relationship to PID Control 13

1.3.5 H8 Polynomial Systems Synthesis Theory 13

1.4 State-space Modelling and Synthesis Theory 14

1.4.1 State-space Solution of Discrete-time H8 Control Problem 14

1.4.2 H8 Control Design Objectives 15

1.4.3 State-feedback Control Solution 15

1.4.4 State-feedback Control Problem: Cross-product Costing Case 18

1.4.5 State-space Solution of Discrete-time H8 Filtering Problem 19

1.4.6 Bounded Real Lemma 21

1.4.7 Output Feedback H8 Control Problem 24

1.5 Introduction to H₂ or LQG Polynomial Synthesis 29

1.5.1 System Description 29

1.5.2 Cost Function and Solution 31

1.5.3 Minimisation of the Performance Criterion 31

1.5.4 Solution of the Diophantine Equations and Stability 34

1.5.5 H₂ /LQG Design Examples 35

1.6 Benchmarking 40

1.6.1 Restricted Structure Benchmarking 41

1.6.2 Rules for Benchmark Cost Function Selection 42

1.7 Condition Monitoring 44

1.8 Combining H₂ , H8 and ' 1 Optimal Control Designs 45

1.9 Linear Matrix Inequalities 46

1.10 Concluding Remarks 47

1.11 Problems 48

1.12 References 51

2 Scalar H₂ and LQG Optimal Control 57

2.1 Introduction 57

2.1.1 Industrial Controller Structures 58

2.1.2 The 2 -DOF Structure 59

2.1.3 Restricted Structure Control Laws 60

2.2 Stochastic System Description 60

2.2.1 Ideal Response Models 62

2.2.2 System Equations 62

2.2.3 Cost Function Weighting Terms 63

2.3 Dual-criterion Cost-minimisation Problem 64

2.3.1 Solution of the Dual-criterion Minimisation Problem 66

2.3.2 Theorem Summarising LQG Controller 71

2.3.3 Remarks on the Equations and Solution 73

2.3.4 Design Guidelines 76

2.3.5 Controller Implementation 77

2.3.6 LQG Ship-steering Autopilot Application 78

2.4 LQG Controller with Robust Weighting Function 82

2.4.1 Youla Parameterisation 82

2.4.2 Cost Function with Robust Weighting Function 83

2.4.3 Solution of the Dual-criterion Problem with Robust Weighting 84

2.4.4 Summary of H₂ /LQG Synthesis Problem with Robust Weighting 86

2.4.5 Comments on the Solution 88

2.5 Introduction to the Standard System Model 89

2.5.1 Standard System Model 89

2.6 The Standard System Model Structure 91

2.6.1 Polynomial System Models 92

2.6.2 Reference Model 93

2.6.3 Cost Function Signals to be Weighted 94

2.7 Generalised H₂ Optimal Control: Standard System Model 95

2.7.1 Optimal Control Solution of the Standard System Model Problem 96

2.7.2 Summary of H₂ /LQG Controller for Standard System Results 102

2.7.3 Remarks on the Solution 104

2.8 Concluding Remarks 105

2.9 Problems 105

2.10 References 109

3 H8 Optimal Control of Scalar Systems 113

3.1 Introduction 113

3.1.1 Links Between LQG and H8 Solutions 114

3.1.2 Reference and Feedback Controller Designs 115

3.2 System Description 115

3.3 Lemma Linking H8 and LQG Control Problems 115

3.4 Calculation of the H8 Optimal Controller 116

3.4.1 Simple H8 Controller Structures and Calculations 117

3.4.2 Zero Measurement Noise Case 117

3.4.3 Solution for the H8 Optimal Controller 118

3.4.4 Stability Robustness of Mixed-sensitivity H8 Designs 121

3.4.5 One-block H8 Control Problems 122

3.5 The GH8 Control Problem 123

3.5.1 GH8 Cost Function Definition 124

3.5.2 Youla Parameterised Form of the GH8 Controller 126

3.5.3 Calculation of the GH8 Controller 128

3.6 Stability Robustness of GH8 Designs 136

3.6.1 Structure of the Uncertain System 136

3.6.2 Rational Uncertainty Structure 137

3.6.3 Stability Lemma 139

3.6.4 Influence of the Uncertainty Model 140

3.6.5 Design Procedure for Uncertain Systems 140

3.6.6 H8 Self-Tuning Controller for Systems with Parametric Uncertainty 147

3.7 Standard System and Cost Function Description 147

3.8 Calculation of H8 Controller for the Standard System 147

3.8.1 F-iteration Method of Solving the Robust Weighting Equation 148

3.8.2 H₂ / H8 Trade-off 149

3.9 Probabilistic System Descriptions and H8 Control 150

3.9.1 Uncertain System Model 151

3.9.2 Cost Function Definition 153

3.9.3 Uncertain System and Polynomial Equation Representation 155

3.9.4 Discussion of Probabilistic Uncertainty Modelling and Control 158

3.10 Concluding Remarks 158

3.11 Problems 159

3.12 References 163

4 Multivariable H₂ /LQG Optimal Control 167

4.1 Introduction …