Linear Modeling and Control of Comb-Actuated Resonant MEMS Mirror With Nonlinear Dynamics

This article presents a novel method to derive and identify an accurate small perturbation model of a comb-actuated resonant microelectromechanical system (MEMS) mirror with highly nonlinear dynamics. Besides the nonlinear stiffness and damping, the comb-drives add nonlinearities due to their electrostatic nature and their effect on the dynamic mirror amplitude over frequency behavior. The proposed model is based on a period to period energy conservation and applies for most nonlinearities present in an oscillator such as MEMS mirrors. It is shown that for specific nominal operation points with square wave excitation, the small perturbation model is linear for a wide range. The full dynamics of the derived linear model are parametrized by three constants, that can be estimated by the phase locked loop (PLL), performing a proposed identification method only based on phase measurements. An analysis of control laws usually applied in a PLL provides important information for the proper design of controllers to meet the desired behavior for individual applications.