Loop-shaping Robust Control (ePub)

The loop-shaping approach consists of obtaining a specification
in relation to the open loop of the control from specifications
regarding various closed loop transfers, because it is easier to
work on a single transfer (in addition to the open loop) than on a
multitude of transfers (various loopings such as set point/error,
disturbance/error, disturbance/control, etc.). The simplicity and
flexibility of the approach make it very well adapted to the
industrial context.

This book presents the loop-shaping approach in its entirety,
starting with the declension of high-level specifications into a
loop-shaping specification. It then shows how it is possible to
fully integrate this approach for the calculation of robust and
efficient correctors with the help of existing techniques, which
have already been industrially tried and tested, such as H-infinity
synthesis. The concept of a gap metric (or distance between models)
is also presented along with its connection with the prime factors
of a set of systems shaping a ball of models, as well as its
connections with robust synthesis by loop-shaping, in order to
calculate efficient and robust correctors. As H-infinity
loop-shaping is often demanding in terms of the order of
correctors, the author also looks at loop-shaping synthesis under
an ordering constraint. Two further promising lines of research are
presented, one using stochastic optimization, and the other
non-smooth optimization. Finally, the book introduces the concept
of correction with two degrees of freedom via the formalism of
prime factorization.

Avenues for future work are also opened up by the author as he
discusses the main drawbacks to loop-shaping synthesis, and how
these issues can be solved using modern optimization techniques in
an increasingly competitive industrial context, in accordance with
ever more complex sets of functional specifications, associated
with 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 Robust
Stabilization with Order Constraint

Appendix 2. Establishment of Real LMIs for the Quasi-Convex Problem
of Optimization of the Weighting Functions

About the Authors

Philippe Feyel is an R&D Engineer for the high-tech company
Sagem Défense Sécurité, part of the defence and
security business of the SAFRAN group, in Paris, France.