This paper proposes a modeling method for 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, dynamic equations of driving loop are derived to obtain vibration differential equations of a hemispherical resonator driven by electrostatic forces, further obtain accurate output models of wave amplitude and angular rate, which establishes a model of driving loop. Next, the output model of wave amplitude is analyzed to clarify the relationship between amplitude voltage and wave amplitude. Simultaneously, influences of interference factors on 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 deformation equations of the hemispherical resonator. A model of detecting loop is established to analyze its performance and precision. Finally, by tests of amplitude voltage and resonant frequency, accuracy of the models of driving loop and detecting loop is proved. A model of fully closed-loop system of the HRG is proposed based on the models of driving loop and detecting loop. The HRG output errors caused by resonator’s deformation, detecting error and nonuniformity of quality factor are identified and compensated accurately by the proposed model. It is verified by simulations and tests that the proposed model of 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.

In this article, a novel ultrahigh precision mass balancing method for fused quartz hemispherical resonator based on the ion beam etching process is proposed from the perspective of vibration mechanics. First, the motion equations of resonator with mass defect are established to reveal the quantitative relationship between the amplitude of defective mass and frequency split, and the geometrical relationship between the distribution of defective mass and eigenfrequency axis, which is the equivalent morphology of mass defect. Second, according to the motion equations, the radial vibration model of resonator lip edge is deduced, then a new identification model for the vibration parameters composed of the frequency split, mechanical time constant, and azimuth of eigenfrequency axis based on the vibration envelope and spectral analysis is established. The vibration parameters are identified by nonlinear optimization method. After that, the mass removal function and etching efficiency function of ion beam acting on the resonator are calibrated by experimental data, then the etching trajectory is planned and the etching time is calculated. Finally, the experimental result of mass balancing indicates that the frequency split is reduced from 0.2354 to 0.0006 Hz, and the quality factor is greater than 2.2 × 10 ⁷ , which can significantly improve the vibration performance of resonator.

Vibratory gyroscopes are the most ideal inertial sensors in the 21st century. The amplitude is an important index of vibratory gyroscopes. This article investigates an asynchronous tracking control approach for amplitude signals in vibratory gyroscopes. Since the manufacturing error of vibratory gyroscopes can result in the stochastic signal of the amplitude, Markov stochastic systems are adopted to approximate vibratory gyroscopes. Because the stochastic signal results in the amplitude jitter, a novel doubly fed tracking controller with the stochastic stability performance is proposed for reducing the amplitude jitter. In the practical application, regarding the known degree of the stochastic process, the partially unknown mode information is approximately given. By considering the asynchronous phenomenon between the system mode and controller mode, a hidden Markov model is constructed to name the resultant tracking error system. It is proved that the tracking error system is stochastically stable. Furthermore, the presented asynchronous tracking controller can well track the reference amplitude signal and significantly reduce the amplitude jitter. Finally, comparative results show the control precision of amplitude signals is significantly improved such that the better precision and performance of vibratory gyroscopes are achieved, which demonstrates the effectiveness and practicability of the proposed control approach.

The Hemispherical Resonator Gyro (HRG) is a solid-state and widely used vibrating gyroscope, especially in the field of deep space exploration. The flat-electrode HRG is a new promising type of gyroscope with simpler structure that is easier to be fabricated. In this paper, to cover the shortage of a classical generalized Coriolis Vibration Gyroscope model whose parameters are hard to obtain, the model of flat-electrode HRG is established by the equivalent mechanical model, the motion equations of unideal hemispherical shell resonator are deduced, and the calculation results of parameters in the equations are verified to be reliable and believable by comparing with finite element simulation and the reported experimental data. In order to more truthfully reveal the input and output characteristics of HRG, the excitation and detection models with assemble errors and parameters are established based on the model of flat-electrode capacitor, and they convert both the input and output forms of the HRG model to voltage changes across the electrodes rather than changes in force and capacitance. An identification method of assemble errors and parameters is proposed to evaluate and improve the HRG manufacturing technology and adjust the performance of HRG. The average gap could be identified with the average capacitance of all excitation and detection capacitors; fitting the approximate static capacitor model could identify the inclination angle and direction angle. With the obtained model, a firm and tight connection between the real HRG system and theoretical model is established, which makes it possible to build a fully functional simulation model to study the control and detection methods of standing wave on hemispherical shell resonator.

Compensation for the hemispherical resonator gyroscope detection error significantly improves gyroscope performance as well as provides a basis for the implementation of high precision control algorithms. In this paper, an identification method is proposed in which the precession factor and the detection error parameters including gain error, non-orthogonal angle error, and phase error can be identified simultaneously in a single test. Firstly, we analyze the detection error caused by gyroscope manufacturing as well as the inconsistency in circuit device parameters. Secondly, the detection error is modeled, and the impact of the error on the standing wave azimuth detection and the control system is discussed. Thirdly, a method is presented for identifying the error parameters based on the nonlinear least squares. Finally, experiments are conducted to verify the effectiveness of the identification and compensation method. As a result of compensation, the bias instability decreases by 33 times from 5.08°/h to 0.15°/h, and the scale factor nonlinearity decreases by 4 times from 50.26ppm to 10.23ppm.