Reduced Order Controller Design for Discrete Time Systems

Abstract

This paper is concerned with robust discrete control system design techniques and model reduction. A new LQG/LTR † † We follow standard abbreviations: LQR Linear Quadratic Gaussian LTR Loop Transfer Recovery KBF Kalman-Bucy Filter LQR Linear Quadratic Regulator procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has a desired loop shape, and then recovered by a realizable LQG controller. To do this, results that show the effects of the weighting matrices (noise intensities) on LQR (KBF) return difference and inverse-return difference are derived and a procedure to recover the QR loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization where an error bound is discussed. The second is a frequency weighting technique where it is possible to vary the approximation accuracy with frequency. For this method, a bound on the weighted reduction error is derived. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.