Characterization and compensation of thermal bias drift of a stiffness-tunable MEMS accelerometer

Abstract

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.