Rejecting multiple-period disturbances: active vibration control of a two degree-of-freedom piezoelectric flexible structure system

In this study, an active vibration suppression control is presented for use in a two degree-of-freedom piezoelectric flexible structure system containing a rectangular plate driven by dc motors. A mathematical model involving a clamped-free-free-free cantilever flexible plate, piezoelectric transducer, and motor dynamics is derived for modal analysis and control design. To simplify the control design of this multivariable system, a two-stage design strategy is proposed because the plate motion exerts a comparatively small effect on the dc motors. Both the plate vibration and coupling effect in the motors are considered when designing a centralized motor tracking controller. Given a well-designed two-axis motor control system, piezoelectric actuators are used on the plate to perform efficient active vibration suppression control. Hybrid proportional-derivative and repetitive control methods are extended to manage the multiple-period disturbances and resonant excitation. Three sets of simulation experiments were conducted, focusing on suppressing the plate vibration response and demonstrating the effectiveness of the proposed method.