Analysis of Phase Lock Loop Closed-Loop Drive Circuit for Silicon Micromachined Resonant Accelerometer Based on the Average Method

This paper studies the control theory and the methods of the silicon micromachined resonant accelerometers(SMRAs). According to the structure and movement of the resonant accelerometer, the model of its dynamics and the equations of motion are deduced. The model of the closed-loop control is set up with the phase lock loop (PLL). The principle of PLL is expounded in detail. The requirements for phases and gains of the sinusoidal self-drive-oscillation are met by PLL. The average method is to take the average of slowly changing variables within a cycle to find the solutions of nonlinear equations. Using the average method, it analyzes the PLL's phase control methods in depth and derives the system stability condition. The simulation results verify the correctness of the stability condition. It provides a guiding theory for the realization of SMRA's precision control.