Due to the micro hemisphere structure’s small anchor point area, the micro hemisphere resonator and the Pyrex7740 glass electrode substrate are prone to tilt during the assembly process. The inclination angle of the assembly makes the electrode gap uneven, which will affect the control of the resonator and the detection of vibration signals, thereby reducing the accuracy of the gyroscope. In this paper, the formation mechanism of assembly inclination angle error of micro hemispherical resonator gyroscope ( $\mu $ HRG) is analyzed in detail. The influence of assembly inclination error on electrostatic driving ability, capacitance detection ability, and electrostatic stiffness adjustment ability is revealed. Then, the dynamic model of second-order resonant state vibration with inclination error parameters is established. By measuring the capacitance when the resonator is still, the assembly inclination angle and inclination azimuth angle are identified by combining genetic algorithm with Nelder-Mead simplex. The correctness and effectiveness of the assembly inclination error parameter identification method are verified by experiments. The experimental results show that, compared with the uncompensated case, the bias instability of the $\mu $ HRG is reduced from 2.470 °/h to 2.322 °/h and the angle random walk (ARW) is reduced from $0.233~^{\circ }/\sqrt {h}$ to $0.226~^{\circ }/\sqrt {h}$ by using the gain compensation method.

An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 ${}^{°}$ /h to 2.8331 ${}^{°}$ /h, and the Angle Random Walk (ARW) decreases from 1.0208 ${}^{°}/\sqrt{h}$ to 0.0524 ${}^{°}/\sqrt{h}$ . Compared with the mode mismatch condition, the ARW is improved by 19.48 times.

This paper investigates the influence of gain mismatches in whole-angle (WA) micro hemispherical resonator gyroscope (μHRG) and proposes a gain mismatch identification method based on modal reversal. The gain mismatches considered here contain detection and actuation gain mismatches in X/Y channels of the μHRG. The operational principle of WA mode is introduced in this paper, followed by an analysis of the factors contributing to the gain mismatches. A dynamical model of WA μHRG encompassing gain mismatches is established for the first time through theoretical derivation. The influence of the gain mismatches on angle bias error and closed-loop control of WA μHRG is investigated by theoretical analyses and numerical simulations. By using the proposed modal reversal method, the gain mismatches of the μHRG are identified, and the gain mismatch compensation experiments are conducted accordingly. The experimental results suggest that after compensation, the peak-to-peak value of the angular rate fluctuation error of the WA μHRG decreased from 39.072°/s to 4.22°/s, a reduction of 9.26 times, and the peak-to-peak value of the angle bias error decreased from 19.05° to 1.124°, a reduction of 16.95 times. The results demonstrate the effectiveness of the proposed gain mismatch identification method based on modal reversal and the correctness of the established gain mismatch theoretical model, providing practical, theoretical guidance for error analysis of the WA mode in subsequent studies.

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the $n=2$ wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the $n=2$ mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.

Aiming at the excitation coupling error caused by assembly eccentricity error in micro-hemispherical resonator gyroscope ( $\mu$ HRG), this paper proposes a method to identify excitation coupling coefficients by using the relationship between input angular velocity and excitation forces during mode reverses. Firstly, this paper studies the influence mechanism of eccentricity error on displacement detection and electrostatic excitation under force-to-rebalanced (FTR) mode. Furthermore, theoretical derivation and simulation results show that the coupling error of excitation force will lead to the mutual coupling between the driving and the sensing loops, which reduces the stability of the driving force and introduces additional zero-bias drift into the sensing mode. According to the proposed identification method of the coupling coefficient of excitation force, the coupling coefficients are calibrated, and the principle of direct compensation in the FPGA system is given. The experimental results show that in the FTR mode, the driving force amplitudes at different input angular rates and the zero-bias drift at room temperature before and after error compensation are compared, which verifies the effectiveness of the proposed error calibration and compensation method. At room temperature, under the FTR mode, compared with the uncompensated test results, the average value of the measured bias stability (1 $\sigma$ ) of the three groups is reduced from 74.667 $^\circ$ /h to 9.670 $^\circ$ /h, which is improved by nearly 7.72 times. When at 40 $^\circ$ C, the $\mu$ HRG’s bias stability (1 $\sigma$ ) is reduced from uncompensated 177.151 $^\circ$ /h to compensated 9.256 $^\circ$ /h. 2022-0174

Accurately modeling, characterizing, and compensating for detection and actuation coupling errors is essential for enhancing the performance of micro hemispherical resonator gyroscopes (μHRGs) under whole-angle (WA) mode. This article proposes a novel coupling error simultaneous and quantitative characterization method by utilizing the relationships between amplitude control force and force balance control force with input angular velocity during mode inversion under force-to-rebalance (FTR) mode. The sources causing detection and actuation coupling errors in μHRG are analyzed first. Subsequently, through theoretical derivation, this article, for the first time, establishes a dynamic model of WA μHRG incorporating detection and actuation coupling errors, and the impact of the coupling errors in the WA mode is investigated thoroughly based on the derived model. The coupling error characterization is carried out by utilizing the presented coupling error characterization method, and the compensatory experiments are implemented using the characterization results. The results demonstrate that the oscillation error of the WA μHRG’s angular velocity reduced from 5.61°/s to 0.55°/s after compensation, decreased by 90.2%; the angle-dependent bias (ADB) reduced from 2.635° to 0.2142°, decreased by 91.87%. Experimental findings confirm the efficacy of the presented coupling error characterization method and the accuracy of the established coupling error model for the WA mode. The proposed coupling error characterization and compensation method can be applied to the gyroscopes with symmetric structures operating in the WA or FTR mode.