In this paper, a novel MEMS accelerometer with tuned quasi-zero stiffness stabilized and operated in a closed-loop is proposed. By using the electrostatic softening effect of the double-sided comb-finger capacitors and the triangular capacitors, the effective stiffness of the accelerometer can be adjusted to quasi-zero. The variation of the electrostatic stiffness arising from the thermal drift of the proposed quasi-zero stiffness accelerometer can be greatly reduced when utilizing the double-sided comb-finger capacitors. For a high-sensitivity and high-linearity acceleration measurement, a traditional proportional-integral-derivative (PID) controller and a proportional-integral sliding mode (PISM) controller are designed for the stabilization near the border of pull-in. The parameters of the controller are tuned to ensure that the proof mass is stably positioned at the desired position. Both the simulation and experiment validate the feasibility of two controllers, showing distinct transient characteristics and long-term stability performance. Compared to the open-loop accelerometer with untuned stiffness, the sensitivity of the closed-loop accelerometer is increased over 40 times while the long-term stability of the closed-loop accelerometer with quasi-zero stiffness is remarkably improved for both controllers. The PID-controlled accelerometer with quasi-zero stiffness has an Allan bias instability as low as 22.51 ng and narrow bandwidth of 0.36 Hz. The PISM controlled accelerometer with quasi-zero stiffness has a linearly varied Allan bias instability from 37 ng to $2.02 ~\mu \text{g}$ depending on the switching gain which determines the acceleration input range. However, the bandwidth of the PISM control system exhibits a nonlinear and wide-range variation with respect to the switching gain.

This article proposes a digital control structure for a doubly decoupled gyroscope working in the Lissajous frequency-modulated (LFM) mode based on digital phase-locked loops (PLLs), which demodulates the angular rate signal directly from the readable digital gyroscope resonance frequency, eliminating the need for specific frequency readout circuits. The resonance frequencies of the LFM gyroscope working modes contain a mode mismatch frequency modulated by input angular rate, respectively, which are tracked by two digital PLLs followed by subsequent digital demodulation and filtering. A linearized model of the digital PLL is built to analyze noise and control characteristics for different PI parameters. The impact of different amplitude–phase extraction architectures on the extracted phase signal is also addressed in this article. Contrast experiments are carried out using the same gyroscope with large internal thermal stress due to the silicon-glass bonding process and no stress relief structure around the sensing element, working in the traditional amplitude-modulated (AM) mode and the LFM mode. Overall, the LFM working mode maintains its low-temperature sensitivity and high stability in spite of the large internal thermal stress in the gyroscope compared to AM working modes. The maximum scale factor variation over the temperature range from 10 °C to 50 °C is 1000 ppm for the LFM mode compared to 51 900 ppm for the AM closed mode. The maximum zero rate output drift over the same temperature range is 0.1248 °/s for the LFM mode and 10.7139 °/s for the AM closed mode. The scale factor nonlinearity is 329 ppm with an angular rate input range of ±50 °/s for the LFM mode compared to 1902 ppm for the AM closed mode. The LFM mode zero-bias fluctuation for ten days is less than 0.12 °/s. The angle random walk (ARW) and the bias instability (BI) of the LFM gyroscope are 0.316 °/ $\surd \text{h}$ and 2 °/h, respectively.

We propose a MEMS gyroscope system working with a fixed resonance frequency which combines resonant constant-frequency (RCF) driving and real-time automatic mode-matching technique with the help of linear tuning triangular capacitors. The special tuning capacitors are implemented in both the gyroscope drive mode and sense mode as drive-mode frequency-tuning (DFT) and sense-mode frequency-tuning (SFT), respectively. RCF assures that the drive-mode equivalent resonance frequency after tuned can keep with the given constant excitation frequency, while real-time automatic mode-matching further eliminates mismatches between the drive-mode and sense-mode equivalent resonance frequencies. As a result, the gyroscope system achieves constancy and equality of the excitation frequency and two modal resonance frequencies. Performance evaluations show that the gyroscope with the sense mode quality factor of 26.7k reaches bias instability of 0.09°/h and angle random walk of 0.0087°/ $\surd \text{h}$ under room temperature without any compensation, and is capable of detecting an angular rate as low as 0.001°/s.

This article describes a closed-loop detection MEMS accelerometer for acceleration measurement. This paper analyzes the working principle of MEMS accelerometers in detail and explains the relationship between the accelerometer zero bias, scale factor and voltage reference. Therefore, a combined compensation method is designed via reference voltage source compensation and terminal temperature compensation of the accelerometer, which comprehensively improves the performance over a wide temperature range of the accelerometer. The experiment results show that the initial range is reduced from 3679 ppm to 221 ppm with reference voltage source compensation, zero-bias stability of the accelerometer over temperature is increased by 14.3% on average and the scale factor stability over temperature is increased by 88.2% on average. After combined compensation, one accelerometer zero-bias stability over temperature was reduced to 40 μg and the scale factor stability over temperature was reduced to 16 ppm, the average value of the zero-bias stability over temperature was reduced from 1764 μg to 36 μg, the average value of the scale factor stability over temperature was reduced from 2270 ppm to 25 ppm, the average stability of the zero bias was increased by 97.96% and the average stability of the scale factor was increased by 98.90%.

This paper presents for the first time an improved algorithm for vibration amplitude-phase information extraction of capacitive microelectromechanical systems (MEMS) gyroscopes. Amplitude and phase information resulting from the improved algorithm is insensitive to the phase variation of an interface capacitance-voltage (CV) circuit, thus both long time drift of the gyroscope and bias instability have been improved. Experimental results show that both the phase and amplitude information extracted using this improved algorithm is insensitive to phase variation of CV circuit which is in accordance with theory. Bias instability using this improved configuration is 0.64°/h, which is improved two times more than the configuration using traditional double-side-band (DSB) demodulation configuration, and 4.3 times more than the configuration using single-side-band (SSB) demodulation, respectively. Allan deviation analysis shows that the slow varying drift term using D&S configuration is effectively reduced due to its robustness to CV phase variation compared to test results using DSB or SSB configuration.

In this Letter, the authors theoretically and experimentally investigate the characteristics of phase delay in capacitive pick‐off circuits for micro‐electromechanical systems (MEMS) resonators for the first time in history. An analytical model considering the phase delay for capacitive pick‐off circuits is built up in theory. Only when they use their proposed novel modified double side‐band demodulation configuration for resonators to extract motional amplitude and phase, the phase delay of pick‐off circuits can be eliminated and extracted meanwhile in real time. Experiments show that the changing feature of phase delay primarily depends on temperature rather than drive frequency. Experimental results agree well with the theoretical model and reveal the relatively high correlation between the phase delay and temperature. This work provides a new indicator of temperature for resonators, using this phase delay of the pick‐off interface, to make temperature compensation.