Nonlinear dynamics and control of a dual-capacitively driven torsional MEMS scanning mirror

Dual capacitively driven MEMS mirrors, when driven with a sinusoidally varying voltage, will experience a nonlinear torque. Nonlinearities arise from the nonlinear relationship between voltage and torque and the fact that the capacitor gap is a function of the angular displacement of the mirror. At high maximum scan angles, the dynamics of the mirror exhibit behavior similar to that of a nonlinear harmonic oscillator with a softening spring. This behavior is characterized by amplitude instability relative to frequency and results in the need to implement additional control algorithms to achieve stable operation. In this work we present experimental results demonstrating the effects of the nonlinearities and the implications of these nonlinearities for high fidelity image rendering using these scanning mirrors. We then present an analysis of the nonlinearities in the system showing significant nonlinearities up to the 10th order. We present numerical results consistent with the observed behavior of the MEMS scanning mirror. Next, we present an analysis showing that the nonlinearities can be significantly reduced applying a non-sinusoidal voltage signal. Finally, we discuss control issues, solutions and implications for high fidelity image rendering using these scanning mirrors.