ISBN-10:
1848216068
ISBN-13:
9781848216068
Pub. Date:
08/12/2013
Publisher:
Wiley
Control of Switching Systems by Invariance Analysis: Applcation to Power Electronics / Edition 1

Control of Switching Systems by Invariance Analysis: Applcation to Power Electronics / Edition 1

by Laurent Fribourg, Romain Soulat
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Product Details

ISBN-13: 9781848216068
Publisher: Wiley
Publication date: 08/12/2013
Series: FOCUS Series
Pages: 144
Product dimensions: 6.10(w) x 9.30(h) x 0.70(d)

About the Author

Laurent Fribourg is head of the LSV (LaboratoireSpécification et Vérification) and Scientific Coordinatorof the Institut Farman, Institut Fédératif de RechercheCNRS, which brings together the expertise of five laboratories fromENS Cachan, in France, in the fields of modeling, simulation andvalidation of complex systems. He has published over 70 articles ininternational journals and reviewed proceedings of internationalconferences, in the domain of the theory of formal methods andtheir applications.

Romain Soulat is in the third year of his doctorate atthe LSV at ENS Cachan in France, under the supervision of LaurentFribourg. He is working on the modeling and verification of hybridsystems. In particular, his interests concern robustness inscheduling problems – especially as part of a collaborativeproject with EADS Astrium on the verification of a component in thelauncher for the future Ariane 6 rocket. He has published 5articles in reviewed proceedings of international conferences.

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Table of Contents

PREFACE ix

ACKNOWLEDGMENTS xi

INTRODUCTION xiii

CHAPTER 1. CONTROL THEORY: BASIC CONCEPTS  1

1.1. Model of control systems 1

1.2. Digital control systems 3

1.2.1. Digitization 3

1.2.2. Quantization 6

1.2.3. Switching 6

1.3. Control of switched systems using invariant sets 8

1.3.1. Controlled invariants 9

1.3.2. Safety control problem 9

1.3.3. Stability control problem 10

1.3.4. Other controllers 11

1.4. Notes 11

CHAPTER 2. SAMPLED SWITCHED SYSTEMS 13

2.1. Model 13

2.2. Illustrative examples 18

2.3. Zonotopes 21

2.4. Notes 23

CHAPTER 3. SAFETY CONTROLLERS 25

3.1. Backward fixed point computation (directapproach) 26

3.2. Approximate bisimulation (indirect approach) 29

3.3. Application to a three-cell Boost DC–DCconverter 35

3.3.1. Model 35

3.3.2. Direct method 37

3.3.3. Indirect method 37

3.4. Notes 40

CHAPTER 4. STABILITY CONTROLLERS 41

4.1. Motivation 42

4.2. Preliminaries 42

4.2.1. Control induced by the decomposition 45

4.3. Decomposition function 46

4.3.1. Basic procedure 46

4.3.2. Enhancement for safety 48

4.4. Limit cycles 52

4.4.1. Discussion of the assumptions H1 and H2 53

4.4.2. Illustrative examples 54

4.5. Implementation 58

4.6. Notes 59

CHAPTER 5. APPLICATION TO MULTILEVEL CONVERTERS 61

5.1. Multilevel converters 62

5.2. Application of the decomposition procedure 62

5.2.1. Five-level converter 63

5.2.2. Seven-level converter 67

5.3. Physical experimentations 70

5.4. Notes 73

CHAPTER 6. OTHER ISSUES: REACHABILITY, SENSITIVITY,ROBUSTNESS AND NONLINEARITY 75

6.1. Reachability control 75

6.2. Sensitivity 78

6.3. Robust safety control 79

6.4. Nonlinearity 82

6.5. Notes 87

CONCLUSIONS AND PERSPECTIVES 89

APPENDIX 1. SUFFICIENT CONDITION OF DECOMPOSITION 93

APPENDIX 2. APPLICATIONS OF THE ENHANCED DECOMPOSITION PROCEDURE97

APPENDIX 3. PROOF OF THEOREM 4.3 103

APPENDIX 4. EXAMPLE WITH |R∗Δ| = ∞ 107

APPENDIX 5. CODE 109

BIBLIOGRAPHY 121

INDEX 127

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