Analyzing MEMS resonator static pull-in and dynamics under electric excitation via position feedback controller

Abstract

Abstract The micro-electromechanical systems (MEMS) have efficacious and widespread use in several applications such as signal filtering, time referencing, sensing, and more. This paper’s aim is to study the effect of a position feedback controller on a clamped-clamped MEMS resonator. The resonator’s dynamics are modeled and studied to establish both the mode shape function and temporal function. Then, the method of multiple scales (MMS) is applied to generate analytical formulas for the resonator response, capturing nonlinearities and stability regions across various voltage levels. Several response plots are shown to clarify the controller’s impact on the dynamical behavior of the resonator. The general behavior of the analyzed model is verified numerically using the fourth order Rung-Kutta technique. Incorporating the position feedback controller delayed static pull-in by increasing the DC pull-in voltage threshold. In addition, the analysis of the frequency and voltage response curves of different feedback settings indicates small vibration changes and reveals that the nonlinear behavior of the resonator changes from softening to hardening with the increase of the gap distance.