Adaptive vibration control of micro-cantilever beam in MEMS

In this paper, the dynamical model and governing equations of motion of the micro-cantilever beam with piezoelectric actuator (PZT) are proposed. The Rayleigh-Ritz method is used to reduce the orders of the system and the state equations is presented in modal space. The effects of PZT on the modal frequencies and shapes of beam system can be ignored, the reason is that the beam holding higher nature frequencies and Q values in micro-scale. 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 show the operation of the designed control methods.