This paper proposes an analytic model of a resonant MEMS mirror with electrostatic actuation based on a Fourier series approximation for both the comb drive torque and the input waveform and verifies the model by measurements using rectangular input waveforms with various duty cycles. The analytic model is derived by the perturbation method, results in slow flow evolution in amplitude and phase with dynamic influence matrices and vectors and also provides the local dynamics for each equilibrium described by a Jacobian matrix. An analysis of the dynamic influence matrices and vectors provides understanding of the mirror dynamics by frequency components of the input waveform and the comb drive capacitance. The asymptotic behavior at zero amplitude provides the transition curve in an extended dynamic model, which corresponds to the well-known Mathieu’s equation solely with the constant and fundamental frequency components of the input waveform. The measurement results verify the proposed model, showing less than ±0.06 % frequency error for large amplitudes and ±0.47 % for small amplitudes, which corresponds to ±1.2 Hz and ±9.6 Hz for the case of a mirror with 2 kHz natural frequency, respectively. Measurements of local dynamics and transition curves also show a good agreement with the proposed model, which can be used for a fast and accurate analysis of resonant MEMS mirrors for high precision applications. [2020-0387]

中文翻译：

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用于一般电压输入的基于傅立叶级数的谐振 MEMS 反射镜的分析模型

本文提出了基于梳状驱动扭矩和输入波形的傅立叶级数近似的静电驱动谐振 MEMS 反射镜的分析模型，并通过使用具有各种占空比的矩形输入波形的测量来验证该模型。解析模型是通过扰动方法推导出来的，导致具有动态影响矩阵和向量的幅度和相位的缓慢流动演变，并且还提供了由雅可比矩阵描述的每个平衡的局部动态。动态影响矩阵和向量的分析通过输入波形的频率分量和梳状驱动电容提供了对镜像动态的理解。零振幅处的渐近行为提供了扩展动态模型中的过渡曲线，它对应于众所周知的 Mathieu 方程，仅具有输入波形的恒定和基频分量。测量结果验证了所提出的模型，大振幅的频率误差小于 ±0.06 %，小振幅的频率误差小于 ±0.47 %，这分别对应于具有 2 kHz 固有频率的反射镜的情况的 ±1.2 Hz 和 ±9.6 Hz . 局部动力学和过渡曲线的测量也显示出与所提出模型的良好一致性，可用于对高精度应用的谐振 MEMS 反射镜进行快速准确的分析。[2020-0387] 小振幅为 47 %，对于具有 2 kHz 固有频率的反射镜，分别对应于 ±1.2 Hz 和 ±9.6 Hz。局部动力学和过渡曲线的测量也显示出与所提出模型的良好一致性，可用于对高精度应用的谐振 MEMS 反射镜进行快速准确的分析。[2020-0387] 小振幅为 47 %，对于具有 2 kHz 固有频率的反射镜，分别对应于 ±1.2 Hz 和 ±9.6 Hz。局部动力学和过渡曲线的测量也显示出与所提出模型的良好一致性，可用于对高精度应用的谐振 MEMS 反射镜进行快速准确的分析。[2020-0387]