There is mutual coupling between amplitude control and frequency tracking control in the closed-loop control of micromechanical resonant sensors, which restricts sensor performance. This paper introduces the principle of an in-plane vibration micromechanical resonant accelerometer with electrostatic stiffness. The characteristic parameters of the microaccelerometer were obtained through computer-aided dimension measurement and an open-loop frequency sweep test of the fabricated microstructure. An accurate numerical model was established based on the accelerometer’s dynamic principle and characteristic parameters. We established the double closed-loop driving analysis model of amplitude automatic gain control and resonant frequency phase-locked tracking. We used the averaging method to analyze the steady-state equilibrium point and the stable condition. We concluded that the integral coefficient can improve the startup overshoot when the amplitude automatic gain control loop satisfies the stability condition. Under the constraint of frequency tracking, the sizeable coefficient of the integrator can improve the system instability of the amplitude control loop. The theoretical analysis and simulation were helpful in the design and debugging of the system circuit.