Optimal delayed control of primary and second resonances of an electrostatic driving double-sided micro-actuator

Abstract

Abstract In this paper, an electrostatic driving double-sided micro-actuator was studied based on the fully clamped micro-beam with a uniform thickness. An analysis of primary, superharmonic and subharmonic resonances with two distinct time delays was investigated. The multiple scales perturbation method was used to solve the nonlinear equation without large deformation. Steady-state solutions and their stabilities under each resonance conditions were studied. The optimal time delay was obtained for controller design. The effect of the feedback gains and time delays on the nonlinear response of the system was discussed and the analysis shows that a suitable choice of the feedback gains and time delayed quantity can reduce the nonlinearity, resonance region and unstable multi-solutions, also improve the efficiency of the vibration control. It is believed that the results of this paper will be valuable in the design of optimal controllers.