Zhipeng Ma's research while affiliated with Nanjing University of Aeronautics & Astronautics and other places

This paper presents a high-performance MEMS accelerometer with a DC/AC electrostatic stiffness tuning capability based on double-sided parallel plates (DSPPs). DC and AC electrostatic tuning enable the adjustment of the effective stiffness and the calibration of the geometric offset of the proof mass, respectively. A dynamical model of the proposed accelerometer was developed considering both DC/AC electrostatic tuning and the temperature effect. Based on the dynamical model, a self-centering closed loop is proposed for pulling the reference position of the force-to-rebalance (FTR) to the geometric center of DSPP. The self-centering accelerometer operates at the optimal reference position by eliminating the temperature drift of the readout circuit and nulling the net electrostatic tuning forces. The stiffness closed-loop is also incorporated to prevent the pull-in instability of the tuned low-stiffness accelerometer under a dramatic temperature variation. Real-time adjustments of the reference position and the DC tuning voltage are utilized to compensate for the residue temperature drift of the proposed accelerometer. As a result, a novel controlling approach composed of a self-centering closed loop, stiffness-closed loop, and temperature drift compensation is achieved for the accelerometer, realizing a temperature drift coefficient (TDC) of approximately 7 μg/°C and an Allan bias instability of less than 1 μg.

We report a digital control architecture which demodulates both amplitude modulated (AM) and frequency modulated (FM) rate information simultaneously from gyroscope working in Lissajous frequency modulated (LFM) mode. The angular rate information is derived from both quadrature (X and Y) resonance modes of the gyroscope simultaneously. Noise model for the AM signal processing channel of the LFM gyroscope is built, analyzed and compared with that of conventional AM gyroscope, which shows that methods to improve performance of conventional AM gyroscope also applies to the AM signal processing channel of LFM gyroscope. The angular rate output obtained from the AM information of LFM gyroscope has better noise characteristics which therefore supplements the low precision inadequacy of the FM signal channel of LFM mode. Test results for the same gyroscope working in different control architectures are conducted. The ARW and BI of the AM channel of the proposed architecture is 0.51 deg/√h and 1.8 deg/h respectively, which is better than the results obtained from the FM channel in the same architecture with value of 0.99 deg/√h and 4.3 deg/h respectively. Also the AM output of the proposed architecture is better than the result of 0.50 deg/√h and 5.2 deg/h respectively using the same gyroscope working in conventional AM mode.

This paper reports an approach of in-operation temperature bias drift compensation based on phase-based calibration for a stiffness-tunable MEMS accelerometer with double-sided parallel plate (DSPP) capacitors. The temperature drifts of the components of the accelerometer are characterized, and analytical models are built on the basis of the measured drift results. Results reveal that the temperature drift of the acceleration output bias is dominated by the sensitive mechanical stiffness. An out-of-bandwidth AC stimulus signal is introduced to excite the accelerometer, and the interference with the acceleration measurement is minimized. The demodulated phase of the excited response exhibits a monotonic relationship with the effective stiffness of the accelerometer. Through the proposed online compensation approach, the temperature drift of the effective stiffness can be detected by the demodulated phase and compensated in real time by adjusting the stiffness-tuning voltage of DSPP capacitors. The temperature drift coefficient (TDC) of the accelerometer is reduced from 0.54 to 0.29 mg/°C, and the Allan variance bias instability of about 2.8 μg is not adversely affected. Meanwhile, the pull-in resulting from the temperature drift of the effective stiffness can be prevented. TDC can be further reduced to 0.04 mg/°C through an additional offline calibration based on the demodulated carrier phase representing the temperature drift of the readout circuit.

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 AM or 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 deg/h to 2.3 deg/h and the BI of LFM mode is improved from 1.4 deg/h to 0.9 deg/h which is the lowest result reported for LFM gyroscope.

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.

This paper presents characterization and compensation of the thermal bias drift of a MEMS accelerometer whose effective stiffness is electrostatically tuned to a low value with the help of the single-sided parallel plates (SSPP) capacitors. A temperature drift model for the proposed accelerometer is built and the temperature effect on the mechanical stiffness and the circuit gains is characterized. The characterization reveals that the variations of the feedforward coefficient including the mechanical stiffness and the readout gain due to the temperature change play a significant role in the bias drift of output of the proposed closed-loop accelerometer. On the other hand, the variations of both feedback gain and tuning gain as a function of temperature are one-order-of-magnitude less than that of the feedforward coefficient. To calibrate the feedforward coefficient, an excitation signal as a form of AC reference displacement is introduced to drive the proof mass and the readout response is demodulated to calibrate the variance of the feedforward coefficient correspondingly. An open-loop compensation scheme for the temperature-induced bias drift using the variance of the calibrated response is proposed accordingly. Alternatively, the calibrated response can be controlled to a preset value by a new proportion integral derivative (PID) controller by the adjustment of the SSPP tuning voltage. The output of the PID controller is used for the calibration of the introduced bias from the electrostatic tuning force. Therefore, a closed-loop compensation of the thermal bias drift is achieved by remaining the feedforward coefficient while eliminating the calibrated bias. Experiments under a temperature cooling process and different tuning voltages are carried out to verify two proposed compensation schemes. The temperature drift coefficients of both compensated outputs exhibit at least one-order-of-magnitude reduction in response to the temperature change. When the effective stiffness of the accelerometer is tuned to about 4.19 N/m, the temperature drift coefficient (TDC) of the compensated output using the proposed open-loop or closed-loop compensation schemes is reduced to about 0.1136 mg/°C or 0.0391 mg/°C, respectively and meanwhile, the Allan bias instability (BI) is slightly increased to 48.63 μg or 56.14 μg, respectively.

In this paper, an improved area-varying tuning electrode with better immunility to fringe capactor is proposed, analyzed and tested, which is mainly used for frequency tuning of micromechanical gyroscopes. Based on the existing area-varying tuning electrode[23], this paper firstly analyzes the capacitance of the tuning electrode, and obtains the relationship between the capacitance and the displacement using both the analytic formula and finite element analysis, verifying that the fringe capacitance in area-varying tuning electrode decreases the tuning ability of both up-tuning electrode and down-tuning electrode. Then, parametric scanning method is used to optimize the geometry parameter of the tuning electrode, which reduces the influence of fringe capacitance and increases the tuning ability of the tuning electrode. Contrast experiments and tests are carried with gyroscope samples with tuning electrodes before and after optimizing. The tested mean value of tuning ability of the improved tuning electrode is improved by 95.7% after opimization.