Spatial resonant control of flexible structures - application to a piezoelectric laminate beam

This paper introduces a class of resonant controllers that can be used to minimize structural vibration using collocated piezoelectric actuator-sensor pairs. The proposed controller increases the damping of the structure so as to minimize a chosen number of resonant responses. The controller can be tuned to a chosen number of modes. This results in controllers of minimal dimension. The controller structure is chosen such that closed-loop stability is guaranteed. Moreover, the controller can be designed such that the spatial H ₂ norm of the system is minimized. This will guarantee average reduction of vibration throughout the entire structure. Experimental validation on a simply supported beam is presented showing the effectiveness of the proposed controller.