以一类典型的静电驱动双边电容型微谐振器为研究对象，基于全局分岔理论，研究微结构吸合不稳定的机理；在此基础上，在系统直流偏置电压上引入线性时滞速度反馈，对系统复杂动力学行为实施控制。通过引入独立参数，得出系统异宿轨道的精确解析表达，进而利用Melnikov方法预测微结构的异宿分岔条件，从而获得引起微结构吸合不稳定的交流电压阈值。数值算例与理论解析结果的吻合验证了时滞速度反馈控制能有效抑制该类双边电容型微结构吸合不稳定以及混沌等复杂动力学行为，该研究在优化控制微谐振器性能方面具有潜在的应用价值。
Abstract
Based on the global bifurcation theory, the mechanism of pull-in instability of a typical electrostatic driven bilateral capacitive micro-resonator was studied. Then, a linear time-delay velocity feedback was introduced into the system’s DC bias voltage to control complex dynamic behavior of the system. By introducing independent parameters, the exact analytical expression of the system’s heteroclinic orbit was obtained. Furthermore, Melnikov method was used to predict heteroclinic bifurcation conditions of the microstructure to obtain its AC voltage threshold causing its pull-in instability. It was shown that the numerical results agree well with the theoretical analytical ones to verify the time-delay velocity feedback control being able to effectively suppress pull-in instability, chaos and other complex dynamic behaviors of this kind of bilateral capacitive micro structures; the study results have potential application value for optimal controlling the performance of micro resonators.
关键词
微谐振器 /
吸合不稳定 /
时滞速度反馈控制 /
异宿分岔 /
安全盆
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Key words
micro-resonator /
pull-in instability /
time delay velocity feedback /
heteroclinic bifurcation /
safe basin
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