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This paper presents a detailed study on the transient response and stability of the automatic gain control (AGC) with a proportion-integral (PI) controller for a MEMS vibratory gyroscope, which constructs a closed-loop control system to make the gyroscope achieve a constant amplitude vibration at its resonant frequency. The nonlinear mathematical model for the control system is established by applying the averaging and linearization method, which is evaluated through numerical simulations. The stability and convergence characteristics of the whole loop are investigated by using the phase plane method and Routh–Hurwitz criterion. The analysis provides a quantitative methodology for selecting the system parameters to approach stability and an optimal transient response. The negative impact induced by drift of the resonant frequency and Q-factor is also discussed. Simulation results predicted by the model are shown to be in close agreement with the experimental results carried out on a doubly decoupled bulk micromachined gyroscope. By optimizing the control parameters, the measured rising time is less than 100 ms without obvious overshoot. The setting time of the whole loop is less than 200 ms with the relative fluctuation of velocity amplitude within approximately 16 ppm for an hour. The resulting overall performance of the gyroscope is tested under atmospheric pressure. The resonant frequencies and the Q-factor of the drive mode and sense mode are 2.986 kHz, 213 and 3.199 kHz, 233, respectively. The gyroscope achieves a scale factor of 27.6 mV/deg/s with nonlinearity less than 120 ppm in the full-scale range of 800° s−1. The threshold of sensitivity is measured to be about 0.005° s−1 with noise equivalent angular rate evaluated to be 0.001°/s/Hz1/2.

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