Finite Dimensional Stabilizing Controllers for a Class of Distributed Parameter Systems

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 whereM is inner, N is outer and D is rational stable. The proposed controller design can be outlined as follows. First, consider an approximation N-n of the outer part N and design a low order stabilizing controller K-n for P-on = N-n/D. Next, construct a predictor-like internal feedback around K-n; and finally perform rational H-infinity-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.