A Novel Model for Fully Closed-Loop System of Hemispherical Resonator Gyroscope Under Force-to-Rebalance Mode

Abstract

This article proposes a modeling method for the fully closed-loop system of hemispherical resonator gyroscope (HRG) under force-to-rebalance mode. A fully closed-loop system consists of two parts: driving loop and detecting loop. First, the dynamic equations of the driving loop are derived to obtain the vibration differential equations of a hemispherical resonator driven by the electrostatic forces, to further obtain accurate output models of the wave amplitude and angular rate, which establishes a model of the driving loop. Next, the output model of the wave amplitude is analyzed to clarify the relationship between the amplitude voltage and wave amplitude. Simultaneously, the influences of interference factors on the amplitude voltage and angular rate voltage are analyzed, which can result in the HRG output error. Then, a model of detecting capacitance is built based on the deformation equations of the hemispherical resonator. A model of the detecting loop is established to analyze its performance and precision. Finally, by tests of amplitude voltage and resonant frequency, the accuracy of the models of the driving loop and detecting loop is proven. A model of the fully closed-loop system of the HRG is proposed based on the models of the driving loop and detecting loop. The HRG output errors caused by the resonator's deformation, detecting error, and nonuniformity of the quality factor are identified and compensated accurately by the proposed model. It is verified by simulations and tests that the proposed model of the fully closed-loop system is effective, which can not only identify the main errors of the HRG accurately but also provide an accurate model for error analysis.