In this paper, we study a phase locked loop system operating in conjunction with an automatic gain control system to control the primary oscillations of high-quality micromechanical resonators using an RR-type gyroscope as an example. In order to measure the angular velocity of an object with high accuracy, it is necessary to ensure the stability of the amplitude and frequency of the primary oscillations of the sensitive element. Automatic gain control (AGC) is necessary to maintain the amplitude of the primary oscillations at the initially set level.The task of the phase-locked loop (PLL) system is to maintain the frequency of the voltage-controlled oscillator at a value equal to the resonant frequency of the primary oscillations. A complete system of equations of motion of the sensing element was written, taking into account the control loops of the PLL and AGC. Separately, the axis of primary oscillations in control loops is considered, to which the averaging method is applied to obtain the evolution of motion in slow variables for verification of direct numerical simulation. Stability conditions for the resulting stationary regime are obtained in the linear approximation. The questions of accuracy of various methods of numerical solution of differential equations in Matlab are considered. The output characteristics of control systems are presented, as well as the dynamics of the sensitive element along the primary axis of motion. A study of the PLL system was carried out in terms of such characteristics as: speed, delay area in the operating mode, as well as resistance to changes in the parameters of the control system.