Structure and performance of discreteH∞ optimal control

Abstract

In recent years a good deal of attention has been focused on the development of model-based controllers optimizing infinity-norm performance objectives. The motivation behind this is a perceived need for controllers which are more robust to modelling errors than those which result from conventional LQ designs. At the present time, however, numerical solution of the H∞ problems remains very much an open issue. This paper examines Grimble's approach to the design of discrete-time H∞ control laws for univariate plants subject to stationary stochastic disturbances. The structure of the controller is analysed using the internal model control concept of Garcia and Morari and is compared with that obtained for a polynomial LQ scheme. Simulation results are presented for both minimum phase and non-minimum phase systems in which the H∞ technique is seen to be inferior to LQ in terms of performance, robustness to parametric mismatch and computational complexity.