Robust active control of a vibrating plate

Abstract

This paper addresses several aspects of designing robust controllers for active control of vibration in a plate with piezo actuators and acceleration sensors. The discussion ranges over identification of the plant, design and implementation of controllers, and evaluation of their robustness and performance. All the concepts are tested on an experimental setup. Robustness issues are prominent, since in practice the plant differs from models obtained through identification, and moreover changes in ambient conditions induce variation over time in the plant’s characteristics such as modal frequencies and damping ratios. Consequently, a controller designed for a nominal plant model may yield a poor performance or even result in an unstable system if robustness issues are not considered properly. Several H∞ controllers are compared here. Besides using the usual multiplicative and additive uncertainty models, controllers are also designed using the eigenvalue perturbation approach. It is found that controllers designed using this approach are more robust than those obtained using conventional methods. Furthermore, the performance does not degrade severely (which usually occurs due to the robustness performance tradeoff). Hence, it is concluded that the approach is suitable for active vibration control of a plate or similar plants. a)Previously with Fac. Mathematical Sciences, Univ. Twente, The Netherlands.