Su Yan, Xu Pengfei, Han Guowei, Si Chaowei, Ning Jin, Yang Fuhua
Engineering Research Center for Semiconductor Integrated Technology, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China.
College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China.
Micromachines (Basel). 2020 Feb 24;11(2):233. doi: 10.3390/mi11020233.
With the miniaturization of micro-electro-mechanical system (MEMS) gyroscopes, it is necessary to study their nonlinearity. The phase-frequency characteristics, which affect the start-up time, are crucial for guaranteeing the gyroscopes' applicability. Nevertheless, although the amplitude-frequency (A-f) effect, one of the most obvious problems in nonlinearity, has been well studied, the phase response of nonlinear gyroscopes is rarely mentioned. In this work, an elaborate study on the characteristics and locking process of nonlinear MEMS gyroscopes is reported. We solved the dynamic equation using the harmonic balance method and simulated the phase-locked loop (PLL) actuation process with an iterative calculation method. It was shown that there existed an apparent overhanging and multi-valued phenomenon in both the amplitude-frequency and phase-frequency curves of nonlinear gyroscopes. Meanwhile, it was ascertained by our simulations that the locking time of PLL was retarded by the nonlinearity under certain conditions. Moreover, experiments demonstrating the effect of nonlinearity were aggravated by the high quality factor of the drive mode due to the instability of the vibration amplitude. A nonlinear PLL (NPLL) containing an integrator was designed to accelerate the locking process. The results show that the start-up time was reduced by an order of magnitude when the appropriate integral coefficient was used.
随着微机电系统（MEMS）陀螺仪的小型化，研究其非线性特性变得十分必要。相位频率特性会影响启动时间，对于保证陀螺仪的适用性至关重要。然而，尽管作为非线性中最明显问题之一的幅频（A-f）效应已得到充分研究，但非线性陀螺仪的相位响应却很少被提及。在这项工作中，我们报告了对非线性MEMS陀螺仪的特性和锁定过程的详细研究。我们使用谐波平衡法求解了动力学方程，并采用迭代计算方法模拟了锁相环（PLL）的驱动过程。结果表明，非线性陀螺仪的幅频和相频曲线中均存在明显的悬垂和多值现象。同时，我们的模拟结果确定，在某些条件下，锁相环的锁定时间会因非线性而延迟。此外，由于振动幅度的不稳定性，驱动模式的高品质因数加剧了证明非线性效应的实验难度。我们设计了一种包含积分器的非线性锁相环（NPLL）来加速锁定过程。结果表明，当使用合适的积分系数时，启动时间缩短了一个数量级。
