Characteristic locus method robustness improvement through optimal static normalizing pre‐compensation

Abstract

AbstractControlled systems designed by using the characteristic locus method can be very sensitive to small perturbations in the plant input and output at the frequencies where the plant transfer matrix is far from normal. In order to improve the closed‐loop system robustness, previous work proposes the design of a dynamic normalizing pre‐compensator followed by the design of a commutative controller for the pre‐compensated plant. The restriction on its structure and the need for approximation by a stable rational transfer matrix were among the limitations of the dynamic pre‐compensator. This paper shows that it suffices to design a static pre‐compensator that makes the pre‐compensated plant as closely as possible to a normal matrix in a frequency band containing the crossover frequency. The pre‐compensator is found by solving an optimization problem, whose solution is obtained directly by computing either a singular value decomposition of a real matrix or the spectral decomposition of a symmetric matrix, depending on whether normalization is to be achieved in one or more frequencies. Numerical examples illustrate the theoretical results of the paper. Copyright © 2009 John Wiley & Sons, Ltd.