Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

One of the methods of force/moment exertion to micro beams is utilizing piezoelectric actuators. In this paper the problem of vibration boundary control of a clamped-free Timoshenko micro-cantilever considering effects of the piezoelectric actuator to achieve asymptotic stability is addressed. To achieve this purpose, the dynamic equations of the beam actuated by a piezoelectric layer laminated on one side of the beam are extracted. The control law has been made to decay vibrations of the beam. This control law is achieved from the feedback of time derivatives of boundary states of the beam. The obtained control is applied in the form of voltage of the piezoelectric. To illustrate the impact of the proposed controller to the micro beam, the finite element method and Timoshenko beam element have been used and then the simulation has been performed. The simulation shows that not only does this control voltage decay the vibration of the beam, but also the mathematical proofs proposed in this article are precise and implementable.