Spatial ϰ₂ 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 ϰ₂ 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 ϰ₂ control has an advantage over the pointwise ϰ₂ control in minimizing the vibration of the entire structure. The spatial ϰ₂ controller minimizes the ϰ₂ norm of the entire structure more uniformly, while the pointwise ϰ₂ controller only has a local effect. The implemented spatial ϰ₂ controller is able to minimize the first six bending modes of the beam effectively. This spatial ϰ₂ control can also be applied to more general structural vibration suppression problems.