High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

中文翻译：

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具有占空比激励的参数谐振微镜的建模与仿真

高频大扫描角静电驱动微机电系统 (MEMS) 反射镜用于涉及快速光学扫描的各种应用。此处分析了用于生物医学成像的一维参数谐振扭转微镜，该微镜通过占空比方波进行操作。占空比方波激励对于实际反射镜调节和/或控制具有显着优势。在这种激励下反射镜的非线性动力学以希尔方程的形式进行分析。这种形式用于使用反射镜非线性电容行为的迭代近似来预测大扫描角度上参数谐振行为的稳定区域（电压-频率关系）。还进行了数值模拟以获得镜子' s 对不同占空比的几个电压的频率响应。将分析和仿真方法的频率扫描、稳定性结果和占空比趋势与实验结果进行比较。在测试的占空比激励范围内，分析模型和模拟都与实验结果非常吻合。本文讨论了随占空比改变幅度和相位对稳健开环操作和未来闭环操作策略的影响。