Reduced-Order Controller of Transverse-Torsional Coupled Vibration Based on Linear Matrix Inequalities

Abstract

This paper is concerned with the application of reduced-order controller to a flexible structure hav ing the transverse-torsional coupled vibration modes. The dynamical model of the structure is first presented and then the robust controller for the structure is designed by using the H ∞-control theory. Furthermore, the order of the controller is reduced by using the combination of the alternating-projection method and the weighted-balanced realization. The performance of the reduced-order controller is examined through simu lation and experiment. To verify its robustness and validation in the transverse-torsional coupled vibration condition, the lumped mass is added on the right side at the 3rd story. From these results, it is made clear that the reduced-order controller obtained by the proposed method is effective in reducing the vibration of the structure, where the order of the controller can be reduced to 8th order from 30th order.