Modeling,Error Analysis,and Error Suppression For Force-to-Rebalance Hemispherical Resonator Gyroscopes

Hemispherical resonator gyroscope(HRG)is a high-precision Coriolis vibratory gyroscope,which is known as one of the most ideal inertial sensors in the 21 st century.Because HRG has the advantages of long life,high precision,high reliability,miniaturization,low power consumption,light weight,simple composition and structure,and can adapt to various space physical environments,it has been applied in inertial navigation systems in various fields,such as aerospace,aviation,navigation,and land.Therefore,it is of great significance to study the error mechanism and error compensation and suppression methods of a force-to-rebalance HRG to further improve the precision and performance of a HRG.Based on the proposed dynamic models of a hemispherical shell resonator,this paper deeply analyzes the key error sources restricting the precision and performance of a HRG,clarifies their error mechanisms,and proposes corresponding error compensation and suppression methods.The following key problems are studied,including the high-precision dynamic modeling of a hemispherical shell resonator,the effect of the mass defect of a hemispherical shell resonator on the HRG error,the effect of acceleration on the HRG output error,the effect of uneven capacitance gap on the HRG output error,the thermoelastic modeling of a hemispherical shell resonator and the effect of temperature on the HRG temperature error,and the suppression method of the amplitude jitter of a HRG.The main study contents of the thesis are as follows:1.A dynamic model of a hemispherical shell resonator with multiple mechanical constraints is proposed;the effect of the mass defect of a hemispherical shell resonator and the initial azimuth between its antinode axis and rigid axis on a force-to-rebalance HRG error is clarified.Based on the thin shell theory of elasticity and the Bubnov-Galerkin method,a dynamic model of a perfect hemispherical shell resonator is established by fully considering multiple mechanical constraints such as the dynamic of a entire hemispherical shell resonator,the variation of curvature and torsion,the high-order small quantity,and the actual effect of external loads.Different from the dynamic model of elastic ring resonators,the dynamic model describes the vibration characteristics of a entire hemispherical shell resonator,which is more general.The mass defect of a hemispherical shell resonator is mainly manifested in thickness nonuniformity.By leveraging the modeling method,a dynamic model of an imperfect hemispherical shell resonator with mass defect is established,which enriches the dynamic modeling theory of imperfect hemispherical shell resonators.The effect of the first four harmonics of thickness nonuniformity on frequency split is analyzed,and the effect of frequency split and the initial azimuth on the HRG error is further revealed.The relationship among the HRG error,the mass defect,and the initial azimuth is quantitatively constructed,which provides an important reference for the mass balancing of hemispherical shell resonators and the alignment between their antinode axis and rigid axis.2.A model of the full closed-loop system of a force-to-rebalance HRG is proposed to find the error transmission law of key error sources,and the effects of the error of detecting loop,acceleration,and uneven capacitance gap on the force-to-rebalance HRG error are revealed.Leveraging the established models of exciting and detecting loops,combined with the dynamic model of a hemispherical shell resonator,a model of the full closed-loop system of a force-to-rebalance HRG is proposed to analyze the coupling relationship between multiple loops.The error of the detecting loop is analyzed using the model of the full closed-loop system.The effect of acceleration on the HRG output error is analyzed,and the relationship among acceleration,the hemispherical shell resonator deformation,and the HRG output error is determined using the dynamic model of the hemispherical shell resonator deformation and the model of the full closed-loop system.The accuracy of the proposed compensation model of the HRG output error is verified by tests in gravity field.The effect of uneven capacitance gap on the HRG output error is clarified.The uneven capacitance gap results in the irregular deformation of a hemispherical shell resonator by causing uneven electrostatic force,and further affects the HRG output.Through the model of the full closed-loop system,the effect of the first four harmonics of uneven capacitance gap on the HRG output is analyzed,and the size of the HRG output error caused by different harmonic components is determined,which provides a reference for assembly process.3.Due the effect of temperature on HRGs is unclear,the effect of temperature variation on a force-to-rebalance HRG temperature error is clarified.A relatively perfect thermoelastic model of a hemispherical shell resonator is presented to obtain an analytical solution of the thermal deformation of the hemispherical shell resonator.By comparing with the finite element simulation solution,the accuracy of the analytical solution is evaluated.A HRG temperature error model based on the analytical solution of the thermal deformation of the hemispherical shell resonator is presented,and the effects of two thermal deformations under uniform and nonuniform temperature distributions on the force-to-rebalance HRG temperature error are clarified.The steady-state temperature test of HRGs is done,which verifies the accuracy and practicality of the presented thermoelastic model of the hemispherical shell resonator and HRG temperature error model.The presented thermoelastic model and temperature error model can be used to analyze and compensate the HRG temperature error.4.Aiming at the problem that the jitter of amplitude signals can affect the precision and performance of a force-to-rebalance HRG,a suppression method of the jitter of amplitude signals of a force-to-rebalance HRG is proposed.Due to the coupling relationship among detecting,exciting,and control loops,there is stochastic noise in amplitude voltage signals,which results in the stochastic jitter of amplitude signals.According to the model of the full closed-loop system,the amplitude jitter can affect the angular rate output of a HRG.A doubly-fed tracking control method based on Markov stochastic model is proposed.Combined with hidden Markov model,the method effectively addresses the problem of the stochastic jitter of amplitude and significantly improves the control precision of the amplitude loop,which provides an effective way to improve the precision and performance of the HRG.From the perspective of mechanics,control,machinery and materials,on the basis of the established dynamic models of perfect,imperfect,and thermoelastic hemispherical shell resonators,the thesis deeply analyzes the error transmission law of several key error sources and their effect mechanism and finds the internal quantitative relationship between error sources and the index of the precision and performance of the force-to-rebalance HRG.The corresponding error compensation and suppression methods are proposed to effectively reduce the effect of error sources on the HRG,which improved the precision and performance of the HRG.