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 reports an in-run automatic mode-matching method of whole-angle (WA) micro-hemispherical resonator gyroscope ( $\mu $ HRG) based on standing wave self-precession. When the standing wave precesses in real-time by self-precession, all information of frequency mismatch contained in the output force of the quadrature suppression loop is identified by the least mean square algorithm (LMS). Then the electrostatic negative stiffness effect is used to realize online real-time mode matching to eliminate the angle bias error of WA $\mu $ HRG caused by the asymmetry of stiffness. Self-precession rate overcomes the limitation of rotation rate requirement so that the LMS algorithm can work without rate turntable. The physical input angular rate can still be measured when the proposed mode matching loop works normally. The mechanical gain loss caused by frequency mismatch is investigated, distorting the measured angle relative to the forced angle. The expression of the angle error caused by mechanical gain loss is derived. The electrostatic tuning theory of WA $\mu $ HRG, the proposed information identification method for frequency mismatch, and the realization principle of mode matching are analyzed and introduced. Experiment results show that the automatic mode-matching method in whole-angle mode is effective. After mode matching, the final mode matching accuracy of 28.7mHz is realized, with a reduction of about 95% from 570.7mHz (original frequency mismatch). And the WA $\mu $ HRG realized the angle-dependent bias (ADB) error decreased from 25.8° to 7.3° after mode matching. For the mode-matched WA $\mu $ HRG, the ADB is improved by nearly 3.5 times.

This paper presents a bias modulation method for the force-to-rebalanced (FTR) micro hemispherical resonator gyroscope ( $\mu $ HRG) based on the mode-rotation, which is achieved by regulating the gyroscope’s drive and sense modes revolving at an assigned rate. The $\mu $ HRG output under the mode-rotation includes the sinusoidally modulated bias and a rotation-induced DC bias. Accordingly, the alternating mode-rotation is proposed to chop the DC rate bias into square waves. By this approach, errors in the DC component from the scale factor drift are also modulated. The open-loop and closed-loop relationships between the rotation actuating force and the mode-rotation rate are investigated by theoretical analyses and numerical simulations. The lower and upper bounds of the rotation rate and the alternating frequency are discussed under the considerations of the error changing rate, the forcer capacity, the maximum voltage, the resonator momentum, and the measurement range. In addition, the controllers in the amplitude, quadrature, and inclination loops utilize the proportional-integral-resonance (PIR) regulating law to suppress the sinusoidal-varying errors introduced by the assigned rotation. The proposed bias modulation method was experimentally verified by a $\mu $ HRG with an FPGA platform. The results suggest the alternating mode-rotation improved the bias temperature coefficient by 12 times over the rotation-free FTR architecture. For a three-hour measurement at room temperature, the rate-integration of the mode alternately rotated FTR was within 50 degrees. In comparison, the rate-integration of the rotation-free FTR diverged over 600 degrees due to the bias drift. The presented bias modulation method can be utilized in axisymmetric gyroscopes, such as hemispherical, ring/disk, quad-mass gyroscopes, etc.

This paper demonstrates a study of a switch-bridge-based readout circuit for differential capacitance measurement in MEMS resonators. The proposed switch-bridge circuit is improved upon a diode-bridge circuit, which is simple, highly sensitive, and environmentally robust. However, the diode-bridge circuit suffers an output limitation due to the requirement of reverse-bias for diodes. The switch-bridge circuit keeps the advantages of the diode-bridge circuit but eliminates its limitation by replacing diodes with switches. As a result, the sensitivity of the switch-bridge circuit can be further improved by increasing the reference voltage. The presented behaviors and characteristics of the switch-bridge circuit are also suitable for the diode-bridge circuit, whose detailed theoretical analyses have not been reported yet. Then, we introduce an error model to investigate the impacts of nonideal switches in practical applications. In addition, the noise feature is discussed by using a power spectral density model. Experimental results show that the switch-bridge-based readout circuit, when applied to a capacitive MEMS gyroscope, achieves a gain of 7.1 V/pF, or equivalently 1.96 V/ $\mu {\mathrm{ m}}$ , and a noise density of 0.077 aF/sqrt(Hz) between 20 Hz to 50 kHz.