Reverse Engineering in Control Design

Reverse Engineering in Control Design proposes practical approaches to building a standard H-infinity problem taking into account an initial controller. Such approaches allow us to mix various control objectives and to initialize procedures for a fixed-structure controller design. They are based on the Observer-Based Realization (OBR) of controllers. The interest of OBR from the controller implementation point of view is detailed and highlighted in this book through academic examples. An open-source toolbox is available to implement these approaches in Matlab.
Throughout the book academic applications are proposed to illustrate the various basic principles. These applications have been chosen by the author for their pedagogic contents and demo files and embedded Matlab functions can be downloaded so readers can run these illustrations on their personal computers.

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