Experimental implementation of spatial H _∞ control on a piezoelectric-laminate beam

This paper is aimed to develop a feedback controller that suppresses vibration of flexible structures. The controller is designed to minimize the spatial H _∞ norm of the closed-loop system. This technique guarantees average reduction of vibration throughout the entire structure. A feedthrough term is incorporated into the truncated flexible-structure model to compensate for the neglected dynamics in the finite-dimensional model. Adding the feedthrough term reduces the uncertainty associated with the truncated model, which is instrumental in ensuring the robustness of the closed-loop system. The controller is applied to a simply-supported piezoelectric-laminate beam and is validated experimentally to show the effectiveness of the proposed controller in suppressing structural vibration. It is shown that the spatial H _∞ control has an advantage over the pointwise H _∞ control in minimizing the vibration of the entire structure. This spatial H _∞ control methodology can also be applied to more general structural vibration suppression problems.