Active vibration control of micro-cantilever beam in MEMS

This paper proposes a dynamical model and governing equations of the motion of the micro-cantilever beam with piezoelectric actuator (PZT). The Rayleigh-Ritz method is used to reduce the order of the system and the state equations is presented in modal space. The lirst ten mode frequencies and mode shapes of the micro-cantilever beam with and without PZT are studied. The effects of PZT on the modal frequencies and shapes of beam system can be ignored for the reason that the beam holds higher nature frequencies and Q values in microscale. A rational linearizing feedback controller with a high gain observer is designed to eliminate the unwanted vibration of the beam system. The open-loop step response and the effects of situated places of PZT on the frequency responses of the system are discussed. Various frequency responses of the beam system, subject to different applied control voltages and feedback gains, are illustrated. The four resonances are well controlled, while the anti-resonance has no change. Computer simulations are provided to demonstrate the performance of the designed control scheme.