Accurate Analytic Model of a Parametrically Driven Resonant MEMS Mirror With a Fourier Series-Based Torque Approximation

Abstract

An accurate analytic model of a parametrically driven resonant MEMS mirror is proposed using a Fourier series based approximation for out-of-plane comb drive torque. The analytic model consists of slow evolution equations of the amplitude and phase derived by the averaging theorem of perturbation theory. Based on the model, analytic expressions of the primary frequencies and Jacobian are derived, which are computationally efficient and provide additional information on the steady state solutions and local dynamics. Measurement results of frequency response show less than ±0.04 % in frequency errors from the model for various input voltages, i.e. less than ±0.8 Hz for the case of a mirror with 2 kHz natural frequency. The eigenfrequency and damping of the Jacobian matrix show a good agreement with measured local dynamics as well. This verifies the high accuracy of the proposed model, which can be used for improvement of the MEMS mirror design parameters and control design for large amplitude operation.