时滞位移反馈作用下多自由度微陀螺的刚度非线性及控制研究

Stiffness nonlinearity and control of multi-DOF micro-gyroscope under time-delay displacement feedback

为揭示多自由度微陀螺非线性系统中位移反馈项对系统动力学特性的影响规律,探索对非线性的控制方法,以一类四自由度静电驱动微机械陀螺为研究对象,采用多尺度法对微陀螺受控系统在频域和时域中的动力学特性进行了分析。研究发现:时滞量为整周期或半周期时反馈增益可有效的对系统共振频率进行调节;时滞量为四分之一或四分之三周期时,反馈增益主要影响幅值大小,共振频率基本保持不变;反馈控制参数选取得当可消除非线性引起的多稳态解,增加陀螺的灵敏度稳定性,选取不当会导致系统出现复杂的概周期运动使灵敏度稳定性遭到破坏。

To study effects of displacement feedback term on dynamic characteristics of a multi-DOF micro-gyroscope nonlinear system and explore control method for system nonlinearity, a 4-DOF electrostatically driven micromachined gyroscope was taken as the study object. The dynamic characteristics of this controlled micro-gyroscope system in frequency domain and time domain were analyzed with the multi-scale method. Results showed that feedback gain can effectively adjust resonant frequencies of the system if the time delay is a whole period or half one;feedback gain mainly affects the system’s displacement amplitude and its resonant frequencies remain basically unchanged if the time delay is one quarter or three quarters of a period;feedback control parameters selected properly can eliminate multiple steady state solutions caused by the system’s nonlinearity to increase the gyroscope’s sensitivity and stability;feedback control parameters selected improperly can cause the system’s complex quasi-periodic motion to destroy the gyroscope’s sensitivity and stability.