Phononic crystals/metamaterials are attracting increasing interest because of their large variety of applications at both the macro and micro scales. In this work, a new metamaterial plate (metaplate) composed of innovative phononic crystal unit-cells is presented, numerically studied, fabricated at the microscale and experimentally tested. Numerical simulations and experimental tests demonstrate a complete 3D phononic bandgap that guarantees a complete vibration isolation in a certain range of frequency. Moreover, its compatibility with Micro Electro Mechanical Systems (MEMS) fabrication processes suggests applications for vibration isolation of MEMS resonant devices. The measured transmission diagram shows a -30 dB attenuation level, which is in good agreement with numerical predictions. The proposed design opens up new perspectives for the development of vibration isolation applications for MEMS resonators. [2020-0069].

For the purpose of direct angle measurement with high accuracy, this paper focuses on the gain self-calibration of operating modes of MEMS disk gyroscope, when it works in the rate-integration mode. The difference of C/V conversion gain, quality factor and front-end amplifier’s gain of gyroscope operating modes will lead to the total gain difference, which causes angle error. Although one-time manual calibration can temporarily reduce the influence of gain difference, environmental factors (e.g. temperature) will interfere with the calibration results. In this paper, a novel self-calibration method is proposed, which detects the gain difference of gyroscope operating modes in real time and compensates it without adding additional circuits. This method is verified using a digital signal processing platform, and the angle dependent bias (ADB) error is reduced from 18 degrees to 2 degrees.

To resolve the problem of frequency split arising from non-uniform circumferential stiffness distribution in the fully symmetrical resonator structure of Micro-Electro-Mechanical systems (MEMS) vibration gyroscopes due to processing errors. In this research, an in-run automatic mode-matching method with amplitude correction and phase compensation is proposed for a MEMS disk resonator gyroscope (DRG). A double-sideband signal negative feedback system is constructed with a double-sideband signal as the input and the sense mode output signal as the output. By comparing the response amplitude difference between the lower sideband signal and the upper sideband signal using the negative feedback system, the identification and measurement of the frequency split between gyroscope modes are realized. In addition, the deterioration of tuning accuracy due to the amplitude asymmetry and circuit phase errors are studied theoretically and by simulation. A response amplitude demodulation method with amplitude correction and phase compensation is proposed to further improve the tuning accuracy. The results of experiments show that the bias instability (BI) and the angle random walk (ARW) of the MEMS DRG are 0.5662 °/h and 0.03935 °/√h, respectively, when adopting the mode-matching method with compensation. Compared with the mode-matching method without compensation, the BI and the ARW of the MEMS DRG are increased by 3.07 and 1.62 times, respectively. The tuning accuracy is controlled within -0.06 Hz in the mode-matching state.

This paper demonstrates an automatic phase error compensation method for a Micro-Electro-Mechanical systems (MEMS) quad mass gyroscope (QMG) operating in Force-to-Rebalance (FRB) mode. First, the mechanical structure and dynamics of the QMG are introduced and analyzed. Then, the main source of phase error is identified, and the impact of phase error on both the gyroscope drive mode and sense mode is analyzed. To address this issue, an automatic phase error compensation method is developed based on identifying the phase value that corresponds to the minimum drive voltage amplitude. Additionally, a phase-compensated Phase-Locked Loop (PC-PLL) is designed to compensate for both the phase error and demodulation phase error. Simulation results validate the analysis of phase error. The experimental results demonstrate the effectiveness of the compensation method. After compensation, the scale factor is reduced from 331.895 LSB/°/s to 321.143 LSB/°/s and the calculated phase error is found to be 14.624°, which closely matches the compensated phase of 15°. Furthermore, the drift of quadrature suppression voltage decreases to less than 1% when the input angular rate range is within ±150 °/s after compensation. This extends the dynamic range of the QMG from ±45 °/s to ±150 °/s. The Allan variance curves shows that the angle random walk (ARW) remains relatively unchanged at 0.06 °/√h. However, the bias instability is improved to 0.147 °/h, representing a 1.25 times enhancement after phase compensation.

This paper demonstrates an in-run automatic mode-matching method for a Micro-Electro-Mechanical systems (MEMS) disk resonator gyroscope (DRG) operating in the n = 3 wineglass mode. In proposed method, two sideband signals whose frequencies are located at both sides of the drive mode symmetrically, are used to excite the gyroscope, and the response of the gyroscope in the Coriolis force channel is demodulated to obtain the indicator of the frequency split for mode-matching. The input angle rate can still be measured when the proposed mode-matching loop works normally. However, due to the asymmetry of the amplitude of the double-sideband response of the sense mode, there is a tuning error, which leads to a shift of the matching frequency. To eliminate the tuning error and achieve perfect mode-matching, a novel compensation method for the amplitude correction is proposed. The theories of electrostatic tuning of the MEMS DRG, the proposed mode-matching method and the compensation method are analyzed and introduced. The simulation results show that this method can achieve in-run automatic closed-loop mode matching for gyroscopes, and the compensation method can effectively eliminate the tuning error and reduce the frequency split from ~0.5 Hz to < 0.01 Hz. The experimental results show that the bias instability (BI) and the angle random walk (ARW) is improved by 5.8 times and 1.7 times, respectively, under mode-matching. After the tuning error is eliminated with compensation method, the BI and ARW are further reduced to 1.36 °/h and 0.1562 °/ $\surd \text{h}$ , respectively.

In this paper, an adaptive fuzzy-PID controller is proposed to make the closed-loop drive system of a MEMS disk gyroscope with a high Q respond faster without overshoot and achieve high stability accuracy. The principle of the MEMS disk gyroscope operating in force-to-rebalanced (FTR) mode is studied. An adaptive fuzzy-PID controller is designed and implemented. The fuzzy controller adjusts the parameters of the PID controller online according to the input error and error change rate. The response time of closed-loop drive of the gyroscope is reduced from 1.09 s to 0.54 s, and the overshoot is reduced from 20% to 0.004%, with no degradation in angle random walk (ARW) and bias instability (BI). The FTR control system is implemented on a field programmable gate array (FPGA) platform. The performance of the n=3 MEMS disk gyroscope with natural frequency of 9,536 Hz and a quality factor of ~20000 using the novel FTR control system revealed an ARW of 0.1667 deg/ √ hr and an in-run BI of 1.177 deg/hr.