Control of Switching Systems by Invariance Analysis
Applcation to Power Electronics
Published on 5. August 2013
144 pages
978-1-118-79162-2 (ISBN)
Description
This book presents correct-by-design control techniques forswitching systems, using different methods of stability analysis.Switching systems are increasingly used in the electronics andmechanical industries; in power electronics and the automotiveindustry, for example. This is due to their flexibility andsimplicity in accurately controlling industrial mechanisms. Byadopting appropriate control rules, we can steer a switching systemto a region centered at a desired equilibrium point, while avoiding"unsafe" regions of parameter saturation.
The authors explain various correct-by-design methods for controlsynthesis, using different methods of stability and invarianceanalysis. They also provide several applications of these methodsto industrial examples of power electronics.
Contents
1. Control Theory: Basic Concepts.
2. Sampled Switched Systems.
3. Safety Controllers.
4. Stability Controllers.
5. Application to Multilevel Converters.
6. Other Issues: Reachability, Sensitivity, Robustness andNonlinearity.
About the Authors
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 industrial applications.
Romain Soulat is in the third year of his doctorate at the LSV atENS Cachan in France, under the supervision of Laurent Fribourg. Heis working on the modeling and verification of hybrid systems. Inparticular, his interests concern robustness in scheduling problems- especially as part of a collaborative project with EADSAstrium on the verification of a component in the launcher for thefuture Ariane 6 rocket. He has published 5 articles in reviewedproceedings of international conferences.
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08/2013
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Control of Switching Systems by Invariance Analysis
Applcation to Power Electronics
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Persons
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.
Content
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*Delta| = infinity 107
APPENDIX 5. CODE 109
BIBLIOGRAPHY 121
INDEX 127
