Spatial resonant control with collocated piezoelectric actuator/sensor pairs

This paper introduces a class of resonant controllers for minimizing vibrations of flexible structures using collocated piezoelectric actuator-sensor pairs. The controller minimize the resonant responses of a chosen number of vibration modes. The controller structure is chosen such that the closed loop stability is guaranteed. The controller is designed to minimize the spatial H₂ norm of the closed loop system, so that it guarantees average reduction of vibration throughout the entire structure. Controller parameters are determined via Lagrange multipliers optimization technique. The proposed controller is validated experimentally to a simply-supported beam to show the controller effectiveness in controlling selected vibration modes.