Spatial 𝒽2 control of a piezoelectric laminate beam: experimental implementation

This paper designs and experimentally evaluates the performance of a feedback controller to suppress vibration of a flexible beam. The controller is designed to minimize the spatial /spl Hscr//sub 2/ norm of the closed-loop system to ensure average reduction of vibration throughout the entire structure. Vibrations of the first six bending modes of the beam are controlled using a collocated piezoelectric actuator-sensor pair attached to the beam. Feedthrough terms are incorporated into the flexible-structure model to correct the locations of the in-bandwidth zeros. It is shown that the spatial /spl Hscr//sub 2/ control has an advantage over the pointwise /spl Hscr//sub 2/ control in minimizing the vibration of the entire structure. The spatial /spl Hscr//sub 2/ controller minimizes the /spl Hscr//sub 2/ norm of the entire structure more uniformly, while the pointwise /spl Hscr//sub 2/ controller only has a local effect. The implemented spatial /spl Hscr//sub 2/ controller is able to minimize the first six bending modes of the beam effectively. This spatial /spl Hscr//sub 2/ control can also be applied to more general structural vibration suppression problems.

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