Nonlinear tracking control of vibration amplitude for a parametrically excited microcantilever beam

In this paper, a feedback control algorithm to regulate oscillation amplitude of a microelectromechanical (MEMS) cantilever beam operated at parametric resonances is developed. The control objective is to drive the oscillation amplitude of the micro-beam, which is amplified using parametric excitation, to the desired values. The principle of the control algorithm is to establish an output tracking control based on the nonlinear dynamic model of the micro-beam, where the supply voltage is considered as a control input. The tracking control algorithm is designed to solve the singularities resulting from the zero-deflection state of the micro-beam. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the beam into a set of ordinary differential equations (ODEs). Uniformly ultimate boundedness stability of the control system is proved using Lyapunov method. The effectiveness of the proposed control algorithm is illustrated via numerical simulations.