Hybrid proportional derivative/repetitive control for active vibration control of smart piezoelectric structures

This paper presents a hybrid control method for active vibration control of smart piezoelectric structures. The proposed controller consists of a proportional derivative (PD) controller for broadband disturbance rejection and a repetitive controller for narrowband disturbance rejection. The proposed design embeds the repetitive controller by solving a Bezout identity satisfying deterministic constraint into an existing PD feedback control loop. The applied method has two main advantages: (1) each controller design is modularized with an "add-on" property for performance improvement; (2) it achieves superior vibration suppression for both impulse and persistent excitation. Experimental results on a piezoelectric cantilever beam demonstrate the effectiveness of the proposed hybrid controller design method.