The work is devoted to the study of a MEMS resonator dynamics under the action of phase-locked and automatic gain control loops. Particular attention is directed to the study of the nonlinearity factor of the resonator elastic restoring force. It was found that the determination of control system parameters based on the stability analysis of the operating resonant mode, in the general case, does not provide the required phase adjustment and stabilization of the oscillation amplitude. Stable multifrequency modes of oscillations are found, and an analytical study of the mechanisms of their appearance and evolution is carried out under variation of the key parameters of the system. The real regions of the control system stable operation are determined (which do not coincide, as was found, with the regions of stability of the operating resonant mode, due to the presence of hidden attractors in the phase space of the system). A methodology has been developed for identifying such areas of stable operation. A significant complication of the structure of possible motions in the system with an increase in the Q-factor of the resonator is revealed.

这项工作致力于研究在锁相和自动增益控制环作用下的 MEMS 谐振器动力学。特别注意研究谐振器弹性恢复力的非线性因素。发现基于工作谐振模式的稳定性分析的控制系统参数的确定，在一般情况下，不能提供所需的相位调整和振荡幅度的稳定。发现了稳定的多频振荡模式，并在系统关键参数的变化下对其出现和演化的机制进行了分析研究。确定控制系统稳定运行的实际区域（如发现的那样，与运行谐振模式的稳定区域不一致，由于系统相空间中存在隐藏的吸引子）。已经开发了一种方法来确定这些稳定运行的区域。随着谐振器的 Q 因子的增加，系统中可能运动的结构显着复杂化。