Multivariable feedback design. (English) Zbl 0691.93001

Maciejowski, J. M.

Electronic Systems Engineering Series. Wokingham etc.: Addison-Wesley Publishing Company. xvii, 424 p. (1989).

This book forms an advanced textbook on the present day available design methods for linear multivariable control systems. One of the basic problems in controller design consists of determining some feedback mechanism that satisfies a number of design requirements like for instance stability, gain and phase shaping, disturbance rejection. Classically, one uses for a single input single output system tools like the generalized Nyquist stability criterion, Bode plots, Nyquist arrays and Gershgorin bands, and several of these methods have been generalized to multivariable systems. Each method ultimately replaces a multivariable design problem by a set of single input single output controller problems. An important problem in the controller design is how to combat with uncertainties in the given model. This forms in fact the essential question of the book. Several methods for determining a desirable feedback are given, and subsequently a discussion about robustness of each of the methods is given. The methods discussed in the book are the Nyquist-like techniques, multivariable LQG methods, the H-infinity optimal control method (using a Youla-parametrization) and parameter optimization design. The last chapter of the book is devoted to computer- aided design and describes some of the available numerical algorithms that are available for solving design problems. A number of detailed worked examples illustrate each of the design techniques.

Reviewer: H.Nijmeijer

MSC:

93-02	Research exposition (monographs, survey articles) pertaining to systems and control theory
93B50	Synthesis problems
93D15	Stabilization of systems by feedback
93C35	Multivariable systems, multidimensional control systems
93C05	Linear systems in control theory
93B17	Transformations
93B35	Sensitivity (robustness)
93B40	Computational methods in systems theory (MSC2010)

Keywords:

linear multivariable control systems; controller design; stability; gain and phase shaping; disturbance rejection; uncertainties; robustness; Nyquist-like techniques; multivariable LQG methods; H-infinity optimal control; computer-aided design