On the determination of the optimal feedback gains for multivariable linear systems incorporating integral action

Abstract

In this paper we present a technique of obtaining the optimal feedback gains for multivariabe linear systems incorporating integral action. Unlike the methods proposed up to now, a performance index in this paper is the practical quadratic one which does not penalize either the integration of output error or the time derivative of control, therefore giving a reasonable solution. The necessary condition for the solution is given by the non-linear simultaneous matrix equations which can be solved by a gradient technique. Also we suggest a minimax solution which minimizes the worst case in order to get practical feedback gains.