Finite dimensional stabilizing controllers for a class of distributed parameter systems this work was supported in part by TUBITAK project no 123E233

Abstract

This paper considers finite dimensional controller design problem for a class of distributed parameter systems. It is assumed that the transfer function of the plant can be written in terms of coprime factors as P=MN/D where M is inner, N is outer and D is rational stable. The proposed controller design can be outlined as follows. First, consider an approximation Nn of the outer part N and design a low order stabilizing controller Kn for Pon=Nn/D. Next, construct a predictor-like internal feedback around Kn; and finally perform rational H∞- approximation of the local predictor feedback in the controller for a finite dimensional implementation. The main idea behind this approach is that it is relatively easy to design simple controllers for rational transfer functions in the form Pon. The inner factor M (which is infinite dimensional) can be treated as a 'time delay', hence the predictor structure. The modeling and controller design steps analyzed here are illustrated on a flexible beam model.