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.
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.