Precise Synchronization Control of Parametrically Driven Resonant MEMS Mirrors for Lissajous Scanning with a Fixed Frequency Ratio

Synchronized operation of multiple micro-electromechanical systems (MEMS) scanning axes is crucial for applications such as Lissajous scanning. This paper presents a precise linear model and a synchronization control with a fixed frequency ratio for two electrostatically actuated MEMS mirrors driven in parametric resonance. The precise linearized model of the nonlinear resonant mirror is extended for the two-axis synchronization. Based on a master-slave architecture, each mirror is controlled by an individual independent phase-locked loop (PLL) with the displacement current self-sensing, while the duty cycles of the square wave driving signals are either used for amplitude control or phase synchronization to keep a fixed frequency ratio between both mirrors. The dynamics of the controlled nonlinear MEMS mirror at the nominal operation point are analyzed based on a period-to-period energy conservation method, leading to a simple linear model for control design. The derived model and the synchronized operation of the proposed system are verified by measurements, demonstrating an RMS center pixel synchronization error of 0.09 mrad for the master and 0.13 mrad for the slave and providing good maintenance of the high-resolution scanning pattern under environmental influences.