Robust Multivariable Control of Multi-Axis Electrodynamic Shaking System Using .MU.-synthesis

Abstract

The application of a robust multivariable control to an electrodynamic multi-axis shaking system that is not permitted to employ an iteration control method is presented. The influences of a resonant specimen and a cross-coupling term are considered, and the robust controller is designed by using μ-synthesis. Because a redundancy arises from the fact that the 4-degree-of-freedom (DOF) shaking table is composed of five shakers, an undesirable high-gain controller may be obtained. A transformation matrix is then used to eliminate the redundancy. Furthermore, when an uncertainty for the resonant specimen is introduced, a parametric state-space uncertainty is considered because of the improvement in performance and the reduction of an order of the controller. Finally, the good performance of the controller is confirmed with the help of experiments conducted using the actual equipment with the resonant specimen.