Reverse Engineering in Control Design

NOMENCLATURE ix

INTRODUCTION xi

CHAPTER 1. OBSERVER-BASED REALIZATION OF A GIVEN CONTROLLER 1

1.1. Introduction 1

1.2. Principle 3

1.3. A first illustration 9

1.4. Augmented-order controllers 12

1.5. Discussion 16

1.6. In brief 19

1.7. Reduced-order controllers case 20

1.8. Illustrations 23

1.8.1. Illustration 1: plant state monitoring 24

1.8.2. Illustration 2: controller switching 26

1.8.3. Illustration 3: smooth gain scheduling 29

1.9. Reference inputs in observer-based realizations 31

1.9.1. General results 31

1.9.2. Illustration 33

1.10. Disturbance monitoring and rejection 36

1.10.1. General results 36

1.10.2. Illustration 40

1.11. Minimal parametric description of a linear system 44

1.12. Selection of the observer-based realization 47

1.12.1. Luenberger observer dynamics assignment 47

1.12.2. State-estimator dynamics assignment 48

1.13. Conclusions 49

1.14. Bibliography 49

CHAPTER 2. CROSS STANDARD FORM AND REVERSE ENGINEERING 53

2.1. Introduction 53

2.2. Definitions 55

2.3. Low-order controller case (nK ? n) 56

2.3.1. Uniqueness condition 58

2.3.2. Existence of a CSF 59

2.4. Augmented-order controller case (nK > n) 61

2.5. Illustration 61

2.5.1. Solving the inverse H?-optimal control problem 61

2.5.2. Improving K0 with frequency-domain specification 64

2.5.3. Improving K0 with phase lead 66

2.6. Pseudo-cross standard form 69

2.6.1. A reference model tracking problem 69

2.6.2. Illustration 70

2.6.3. Comment 72

2.7. Conclusions 72

2.8. Bibliography 73

CHAPTER 3. REVERSE ENGINEERING FOR MECHANICAL SYSTEMS 77

3.1. Introduction 77

3.2. Context 78

3.3. Model, specifications and initial controller 79

3.4. H? design based on the acceleration sensitivity function 81

3.4.1. General results 81

3.4.2. Illustration 84

3.4.3. Analysis on an augmented model 88

3.4.4. Illustration 88

3.4.5. Synthesis on an augmented model 89

3.4.6. Illustration 91

3.4.7. Taking into account a roll-off specification 94

3.4.8. Illustration 96

3.4.9. Taking into account an integral term 98

3.4.10. Illustration 100

3.5. Mixed H2/H? design based on the acceleration sensitivity function 102

3.5.1. The one degree of freedom case 103

3.5.2. First-order optimality conditions 106

3.5.3. Numerical solution using Matlab® 118

3.5.4. Multi-variable case 120

3.6. Aircraft lateral flight control design 121

3.6.1. Model and specifications 121

3.6.2. Basic H2/H? control problem 123

3.6.3. Augmented H? control problem 126

3.7. Conclusions 130

3.8. Bibliography 131

CONCLUSIONS AND PERSPECTIVES 135

APPENDICES 139

Appendix 1. A Preliminary Methodological Example 141

Appendix 2. Discrete-time Case 149

Appendix 3. Nominal State-feedback for Mechanical Systems 153

Appendix 4. Help of Matlab® Functions 159

LIST OF FIGURES 169

INDEX 175