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.
Keywords: gyroscopes; micro-electro-mechanical system (MEMS); nonlinear PLL (NPLL); nonlinearity; phase-locked loop (PLL).