Robust Modal Control with a Toolbox for Use with MATLAB®

Robust control theory has received much attention in the past decades. The most popular approaches are based on frequency domain analysis and design. Early work in this field can be found in [Rosenbrok, 1974], or [Horowitz, 1991]. The most representative modern frequency domain techniques are Loop Transfer Recovery [Doyle and Stein, 1979, Ma­ciejowski, 1989],H_∞-synthesis [Doyle et al., 1989, McFarlane and Glover, 1990], µ-synthesis [Zhou and Doyle, 1999] and their LMI-based (Linear Matrix Inequality) extensions. Unfortunately, these techniques are not very efficient for problems with respect to real pa­rameter variations. Alternative techniques which are involving robustness more appropriate for dealing with real uncertainties have also been considered, for exam­ple: quadratic stability [Garcia et al., 1997, Khargonekar et al., 1990], adaptation of µ-synthesis [Young, 1996] value set and parameter space techniques [Barmish, 1994, Ackermann, 1993] and so on. But for various reasons (such as: conservatism — special requirements relative to the de­pendency on uncertainties — limitations on the number of uncertainties — very large controller orders) these techniques do not really solve the general problem. As we shall see in this book, multi-model control design based on modal approaches, despite some more or less heuristic features, is very efficient, especially in the case of real uncertainties.

This chapter gives an overview of basic theory for eigenstructure assignment. Proofs are not given.

This section summarizes recommendations and gives some general guidelines for modal control design. It is also useful for diagnosis in case of problems.

It is assumed in this book that, any time non-real eigenvalues and eigenvectors are assigned, the corresponding complex conjugate eigenval­ues and eigenvectors are also assigned. It is also assumed that assigned eigenvalues are never repeated.

The following models are considered for demonstration

A selection of modal control design techniques were presented including some original contributions ,as eigenvector selection, observer design and dynamic feedforward design.