Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator 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 and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.