The loop-shaping approach consists of obtaining a specificationin relation to the open loop of the control from specificationsregarding various closed loop transfers, because it is easier towork on a single transfer (in addition to the open loop) than on amultitude of transfers (various loopings such as set point/error,disturbance/error, disturbance/control, etc.). The simplicity andflexibility of the approach make it very well adapted to theindustrial context.
This book presents the loop-shaping approach in its entirety,starting with the declension of high-level specifications into aloop-shaping specification. It then shows how it is possible tofully integrate this approach for the calculation of robust andefficient correctors with the help of existing techniques, whichhave already been industrially tried and tested, such as H-infinitysynthesis. The concept of a gap metric (or distance between models)is also presented along with its connection with the prime factorsof a set of systems shaping a ball of models, as well as itsconnections with robust synthesis by loop-shaping, in order tocalculate efficient and robust correctors. As H-infinityloop-shaping is often demanding in terms of the order ofcorrectors, the author also looks at loop-shaping synthesis underan ordering constraint. Two further promising lines of research arepresented, one using stochastic optimization, and the othernon-smooth optimization. Finally, the book introduces the conceptof correction with two degrees of freedom via the formalism ofprime factorization.
Avenues for future work are also opened up by the author as hediscusses the main drawbacks to loop-shaping synthesis, and howthese issues can be solved using modern optimization techniques inan increasingly competitive industrial context, in accordance withever more complex sets of functional specifications, associatedwith increasingly broad conditions of usage.
Contents
Introduction
1. The Loop-shaping Approach
2. Loop-shaping H-infinity Synthesis
3. Two Degrees-of-Freedom Controllers
4. Extensions and Optimizations
Appendix 1. Demonstrative Elements on the Optimization of RobustStabilization with Order Constraint
Appendix 2. Establishment of Real LMIs for the Quasi-Convex Problemof Optimization of the Weighting Functions
About the Authors
Philippe Feyel is an R&D Engineer for the high-tech companySagem Défense Sécurité, part of the defence andsecurity business of the SAFRAN group, in Paris, France.
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ISBN-13
978-1-118-57475-1 (9781118574751)
Schweitzer Klassifikation
Introduction ix
Chapter 1 The Loop-shaping Approach 1
1.1 Principle of the method 1
1.2 Generalized phase and gain margins 14
1.3 Limitations inherent to bandwidth 17
1.4 Examples 18
1.5 Conclusion 30
Chapter 2 Loop-shaping H infinity Synthesis 33
2.1 The formalism of coprime factorizations 33
2.2 Robustness of normalized coprime factor plant descriptions42
2.3 Explicit solution of the problem of robust stabilization ofcoprime factor plant descriptions 54
2.4 Robustness and upsilon-gap 77
2.5 Loop-shaping synthesis approach 82
2.6 Discrete approach 120
Chapter 3 Two Degrees-of-Freedom Controllers 135
31 Principle 135
3.2 Two-step approach 143
3.3 One-step approach 156
3.4 Comparison of the two approaches 165
3.5 Example 166
3.6 Compensation for a measurable disturbance at themodel's output 174
Chapter 4 Extensions and Optimizations 187
4.1 Introduction 187
4.2 Fixed-order synthesis 188
4.4 Towards a new approach to loop-shaping fixed-ordercontroller synthesis, etc242
APPENDICES 245
Appendix 1 247
Appendix 2 251
Bibliography 255
Index 259
