An analytical model is developed for structure vibration suppression with collocated piezoelectric sensor/actuator in optimal placement and optimal feedback gain. Two different control algorithms-active damping control and output feedback control-are applied to obtain the control law, and the optimal set of sensor/actuator location and feedback gain is determined by the modified method of feasible direction. Analytical results show that a collocated piezoelectric actuator/sensor can lead to instability of the closed loop system. In active damping control, the optimal sensor/actuator location is not at the root of a cantilever beam as commonly believed. However, for LQ formulation of output feedback control, the optimal location is at the beam root with the feedback gain determined by the Ricatti equation. The analytical predictions are verified by experiments.
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