Bifurcation-Based Stability Analysis of Electrostatically Actuated Micromirror as a Two Degrees of Freedom System

Torsional micromirror devices have been widely used in micro displays, RF switches, optical communications, and optical coherence tomography systems. In order to study the stability of electrostatically driven torsional micromirror system with double bottom plates and two voltage sources, a dimensionless, two degrees of freedom (2-DoF) dynamic model was constructed. Governed by the dimensionless phase space model equation, the pull-in and bifurcation phenomena were analyzed using the Hamiltonian method and numerical simulation. In particular, the influence of the damping coefficient and the torsion-bending coupling effect on the phase trajectory was investigated. Furthermore, the conditions that can lead to pull-in were numerically determined for saddle-node, pitchfork and Hopf bifurcations in the framework of 2-DoF system. Result showed that the dynamic pull-in voltage as predicted by the proposed 2-DoF system model is considerably lower than that by the one degree of freedom (1-DoF) system model. It was also confirmed that the pull-in voltage varies with the damping coefficient and/or the ratio of the two voltages applied to the bottom plates of the micromirror. The modelling method and stability analysis presented in this paper shall provide valuable insight to the design and control of electrostatically actuated micromirror systems.