Order Reduction Method of Controller for Structural Control Based on LMIs

Abstract

In this paper, we propose an order reduction of controller for a flexible structure. This method is based upon the combination of the alternating projection method and the weighted balanced realization. The necessary and sufficient condition for the existence of a reduced-order controller leads to a non-convex feasibility problem. To solve the problem, we use an improved computational scheme based on the alternating projection method. The weighted balanced realization is used as the initial values of the alternating projection method. This method is verified by applying it to a control problem of a flexible structure having the transverse-torsional coupled vibration modes. Its performance is compared to that of the reduced-order controller obtained from the modal truncation. From the simulation and the experiment results, it is demonstrated that the reduced-order controller obtained by the proposed method is better than the reduced-order controller obtained by the modal truncation.