Bounded input H2-optimal feedback control of linear systems with application to the control of a flexible beam

Abstract

Previous researchers have studied the problem of finding the best possible feedback controller which minimizes the integral-squared tracking error (the so-called H2-norm minimization problem) without considering bounds on the plant input. However, if the plant is strictly proper, such a controller invariably requires plant inputs of unrealizable magnitude. In this paper, we solve the problem of designing H2-optimal controllers in the presence of bounds on the plant input, and show that the problem can be formulated as one of minimizing a quadratic objective function subject to quadratic constraints. The solution of the latter problem is straight-forward, using the Kuhn-Tucker conditions. The method given here is applied to the model of an experimental flex-arm, which has some non-minimum phase zeros and all its poles on the unit circle. Experimental and simulation results on the performance of a fifth order controller thus obtained are presented. The results shown here suggest that this method of controller design ensures good performance of the closed loop system.