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. [2020-0158]

中文翻译：

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具有基于傅立叶级数的扭矩近似的参数驱动谐振 MEMS 反射镜的精确分析模型

使用基于傅立叶级数的面外梳状驱动扭矩近似值，提出了参数驱动的谐振 MEMS 反射镜的精确解析模型。解析模型由幅度和相位的慢演化方程组成，由微扰理论的平均定理导出。基于该模型，推导出主频率和雅可比矩阵的解析表达式，这些表达式具有计算效率，并提供有关稳态解和局部动力学的附加信息。频率响应的测量结果表明，对于各种输入电压，模型的频率误差小于 ±0.04%，即对于具有 2 kHz 固有频率的反射镜，小于 ±0.8 Hz。雅可比矩阵的特征频率和阻尼也显示出与测得的局部动力学非常吻合。这验证了所提出模型的高精度，可用于改进MEMS反射镜设计参数和大振幅操作的控制设计。[2020-0158]