一类静电驱动微结构谐振传感器的吸合不稳定性研究及控制

摘要

以一类静电驱动微结构谐振传感器为研究对象,基于安全域思想研究了系统直流偏置电压和交流激励电压幅值引起的结构吸合不稳定现象.运用Melnikov函数法得到引起微结构吸合不稳定的系统参数门槛值,且运用四阶Rung-Kutta方法和点映射方法数值地验证了交流电压幅值对系统的吸合区域的影响规律.结果表明,直流偏置电压的增大均易引起微结构的吸合效应,而交流电压幅值的增大则会导致微结构的吸合不稳定.通过实施时滞位移反馈控制来抑制系统的吸合不稳定,数值结果验证了该控制方法的有效性.所得结果在静电驱动微机电系统的设计领域有潜在的应用价值.%A model of electrostatically actuated MEMS resonant sensor was considered.Based on the theory of safe basin,the dynamical pull-in instability caused by the DC bias voltage and the amplitude of AC voltage was discussed in detail.The thresholds of the system parameters at the happening of dynamical pull-in were obtained by using the Melnikov method.The 4th Runge-Kutta and the point mapping methods were employed to verify numerically the effect of the amplitude of AC voltage on the attraction basin of pull-in of the system.It is found that the increasing of DC bias voltage may cause the pull-in phenomena,and the increasing of AC voltage may induce pull-in instability of the structure.The delayed position feedback was applied to reduce the pull-in instability and the numerical results verify the effectiveness of the control approach.The results provide some potential reference to the design of electrostatically actuated resonant MEMS sensors.