Experiments in spatial H infinity control of 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-infinity norm of the closed-loop system, which guarantees average reduction of vibration throughout the entire structure. The spatial H-infinity control problem can be solved by finding an equivalent system representation that allows the solution to a standard H-infinity control problem to be used. Feedthrough terms are incorporated into the flexible-structure model to correct the locations of the in-bandwidth zeros. 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-infinity control has an advantage over the pointwise H-infinity control in minimizing the vibration of the entire structure. This spatial H-infinity control methodology can also be applied to more general structural vibration suppression problems.