H ∞ Control with μ-analysis of a Piezoelectric Actuated Plate

Abstract

This paper presents the development of a multimodal H ∞ controller for piezoelectric actuated plates designed to simultaneously suppress vibrational components of the first two modes. The controller is developed for a reduced structural model. The closed-loop control scheme is subject to both uncertainties due to control and observation spillover in the unmodeled residual modes and to parametric errors in the structural model. The closed-loop stability and performance robustness is analyzed using μ-analysis, and numerical investigations indicate that the controller tolerates uncertainties of significant size.