时滞控制下的微梳状驱动器动力学研究

Nonlinear dynamics of folded-MEMS comb drive resonators with time-delayed control

在微梳状驱动器的直、交流两种驱动电压中,加入时滞速度反馈,建立了时滞影响下的微梳状驱动器的单自由度模型。假设驱动器以微小振幅振动,将含速度时滞反馈的静电驱动力进行泰勒近似展开,应用多尺度法得到时滞参数影响下系统的幅频响应方程;驱动频率在共振频率附近时,系统非线性振动随时滞参数改变时发生跳跃现象;不同的直流电压等物理参数状态下的系统振动频率和软硬特性不同,可以通过改变时滞参数控制不同物理参数下的系统的振动的稳定范围和幅值。经过计算并使用数值方法验证了结论,正时滞参数引起系统振动失稳,负时滞参数可使振动幅值跳跃现象消失。

A time-delayed velocity feedback was made in use in the DC and AC driving voltage of folded-MEMS comb drive resonators and a single degree of freedom model of the folded-MEMS comb drive resonators under the influence of time-delayed control was presented. The expression of the electricity driving force,recieving the velocity feedback under the condition of small vibration amplitude,was approximated with the Taylor expansion. The method of multiplescales was used to obtain the amplitude-frequency response equation of the system under the influence of time-delay parameters. The change of time-delayed parameters may result in jumping phenomena in the nonlinear vibration of the system when the driving frequency is in the vicinity of resonance frequency. The resonance frequency and nonlinear characteristics of softening or hardening will vary under conditions with different physical parameters such as DC and AC voltages. The stability region and vibration amplitude of the system with different physical parameters can be controlled by changing the time-delay parameters. It is concluded that the positive time-delayed control gain makes the system instable and the negative time-delayed control gain leads to the disappearance of jumping phenomenais,which was verified by the numerical computations.