Modeling and Simulation of a Parametrically-Excited Micro-Mirror With Duty-Cycled Square-Wave Excitation

Electrostatically-actuated MEMS mirrors are used in a variety of applications involving fast optical scanning, with endoscopic microscopy an area of particular interest for miniaturization of advance optical imaging systems. In this paper, analytical and experimental characterization of the dynamics and stability of a 1D torsional micro-mirror is described. The micro-mirror being studied is intended for use in biomedical imaging, in which operation strictly by duty-cycled square waves at one or more voltages can be convenient for practical mirror operation and/or control. Analysis focuses on a Hill’s equation approach to predicting stability regions of parametric resonance behavior when input is a duty-cycled square wave, using an approximation for nonlinear capacitance behavior of the mirror. An analytical approach is compared to experimental results. In results to date, analytical models show good agreement with stability predictions, particularly at small voltages, over the range of duty cycled excitations. Additionally, the paper explores how phase delay varies over a range of micro-mirror frequencies for a 50% duty cycle, also compared with experimental results, for potential use in feedback control.