Vibration Sensing and Control of a Flexible Beam Using Piezoelectric Films

Abstract

Multimodal vibration control of a cantilever beam using bonded piezoelectric film sensors and actuators is studied both theoretically and experimentally. Equations of motion of the Bernoulli-Euler beam with collocated bonded piezoelectric sensors / actuators are derived. Then, direct velocity feedback control is employed as the vibration control law, and applying Lyapunov's direct method, it is shown that this control law is stable for arbitrary vibration mode. Transient responses of the beam, with control and without control, are studied for the cases in which an impact force is applied to the tip of the beam. Numerical results and experimental results show good agreement, which shows the validity of the proposed control scheme. It is also shown that first three bending modes are efficiently controlled, and that in order to achieve more broadband vibration control, it is necessary to consider the dynamics such as extensional vibrations of the beam which is not considered in the present study.