Optimal Fixed-Order Compensation of Distributed Parameter Systems

r. Gary Rosen * * Department of Mathematics University of Southern California Los Angeles, CA 90089 In controlling distributed parameter systems it is often desirable to obtain low-order, finitedimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. Our approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. We illustrate the technique by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, RitzGalerkin, finite element approximation. Our numerical studies indicate convergence of the feedback gains with less than 2% performance degradation over full-order LQG controllers for the parabolic system and 10% degradation for the hereditary system. * This research supported in part by the Air Force Office of Scientific Research under contract F 49620-86-C-0002 ** This research supported in part by the Air Force Office of Scientific Research under grant AFOSR-87-0351. Part of this research was carried out while this author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE) at the NASA Langley Research Center in Hampton, VA which is operated under NASA contract NAS1-18107.