Delayed feedback controller for microelectromechanical systems resonators undergoing large motion

Abstract

In this paper, we study the effect of a delayed feedback controller on stabilizing microelectromechanical systems (MEMS) resonators when undergoing large amplitude motion. A delayed feedback velocity controller is implemented through modifying the parallel plate electrostatic force used to excite the resonator into motion. A nonlinear single-degree-of-freedom model is used to simulate the resonator response. Long-time integration is used. Then, a finite difference technique to capture periodic motion combined with the Floquet theory is utilized to capture the stable and unstable periodic responses. We show that applying a suitable positive gain can stabilize the MEMS resonator near or inside the dynamic pull in instability bands. We also study the stability of the resonator by tracking its basins of attraction while sweeping the controller gain and the frequency of excitations. We notice significant enhancement in the safe area of the basins of attraction in the cases of positive delayed gains.