This paper reports a novel MEMS accelerometer whose effective stiffness can be adjusted flexibly and even tuned to almost zero by using the electrostatic softening effect of two parallel plate capacitors: the comb-finger capacitor and the triangular capacitor. When applied to a biased voltage, the comb-finger capacitor provides a relatively large and nonlinear negative stiffness in the gap-varying direction, while the triangular capacitor produces a small yet linear negative stiffness in the area-varying direction. The proposed accelerometer is fabricated by using a standard silicon-on-glass manufacturing process and controlled by a customized digital circuit. An analytical model based on the pull-in dynamics as a result of the stiffness tuning is developed and simulated to investigate the dynamic behavior of the nonlinear accelerometer system. The proportion integral differential controller is utilized to improve the performance of the accelerometer while maintaining the stability of the closed-loop system operating with extremely low effective stiffness. The experimental results indicate that a two-fold increase of the sensitivity, a 30% reduction of Allan deviation bias instability, and a 20% reduction of Allan velocity random walk are achieved for the open-loop accelerometer system. A 75% decrease of the standard deviation bias instability and nearly two orders of magnitude improvement of the noise floor at 1 Hz for the closed-loop accelerometer system are realized when the effective stiffness is reduced to almost zero.

This paper investigates the pull-in dynamics of single-sided and double-sided parallel-plate (SSPP and DSPP) structures employed in MEMS devices for acceleration measurement. A lumped electromechanical model considering a variable damping coefficient and external acceleration is developed for studying their pull-in dynamical behavior. The critical pull-in displacement and pull-in voltage for both parallel-plate structures operated with external acceleration are derived based on the static and dynamical analysis of the proposed model, which are in good agreement with the experimental results. The derived closed-form solutions are shown to be capable of predicting the pull-in behavior of both parallel-plate structures in an overdamped system. Two MEMS parallel-plate structures exhibit distinct pull-in characteristics due to their distinct configurations. The commonly used SSPP structure for MEMS devices is shown to have a relatively linear response to the external acceleration in terms of the critical pull-in displacement and pull-in voltage. However, the DSPP structure exhibits much larger yet nonlinear sensitivity of both the critical pull-in displacement and the critical pull-in voltage to a small range of external acceleration, which has the potential of developing high-sensitivity accelerometers whenever the sensitivity nonlinearity is compensated. Moreover, the effects of pressure are characterized for both DSPP and SSPP devices, which affects the difference between the critical static and dynamic pull-in voltages. The SSPP structure is shown to have the critical pull-in voltage proportional to the logarithmic magnitude of the pressure, while that of the DSPP structure do not vary linearly with respect to the logarithmic magnitude of the pressure.

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 work analyses circuit phase delay for carrier-modulation MEMS capacitive gyroscopes. The temperature-dependent circuit phase delay is a major source of gyroscope output drift, which deteriorates the gyroscope bias instability (BI) and angle random walk (ARW). Effects of both drive-mode and sense-mode circuit phase delay on gyroscope performance when using different signal extraction architectures are analyzed in detail. The online suppression method which combines the so-called modified double sideband (MDSB) extraction architecture in the gyroscope drive mode and closed-loop force-rebalance loop in the sense mode can eliminate the impact of residual fluctuation error of circuit phase delay in real time. When drive-mode circuit phase delay equivalently varies from −20° to 20°, using MDSB decreases the fluctuation of the open-loop zero-rate output (ZRO) by 70% compared to using double sideband (DSB) and by 99.7% with respect to using single sideband (SSB). Meanwhile, improvement for the closed-loop ZRO using MDSB is 92.48% and 94% compared to cases using DSB and SSB, respectively. Furthermore, when the equivalent circuit phase delay of the sense-mode alters from −20° to 20°, ZRO variation for the gyroscope with force rebalanced sense loop and quadrature stiffness nulling loop decreases by 80% in contrast to the case with open loop, which demonstrates the effectiveness of online suppression for circuit phase delay of both the drive-mode and sense-mode. Using the online suppression method, the gyroscope has achieved a BI of 0.16° h ⁻¹ and ARW of 0.011° (√h) ⁻¹ . Furthermore, using the MDSB in the drive mode obtains the best stability compared to using the DSB and SSB as the temperature changes.

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 report for the first time an implementable method to identify and suppress the driving force misalignment angle for a MEMS gyroscope working either in amplitude modulated (AM) or Lissajous frequency modulated (LFM) mode using parametric excitation. By introducing driving force misalignment angle into gyroscope dynamic equations, we illustrate that gyroscope angular rate output is affected by driving force misalignment angle and cross-axis damping jointly. We propose parametric excitation as a way to both identify and calculate the driving force misalignment angle. The identification results for a gyroscope working in both AM and LFM mode are similar, which indicates the effectiveness of the proposed identification method. Instead of using traditional amplitude control loop by adjusting the driving force, we do the automatic gain control by adjusting the parametric pump voltage so that a fixed drive voltage can be used, which also indicates fixed force coupling. Experimental results show that after suppression, the bias instability (BI) of AM mode is improved from 4.7° h⁻¹ to 2.3° h⁻¹ and the BI of LFM mode is improved from 1.4° h⁻¹ to 0.9° h⁻¹ which is the lowest result reported for LFM gyroscope.