Automatic calibration and nonlinearity optimization for scale factor of micro-electromechanical system gyroscopes under force rebalanced operation

Abstract

The paper focuses on automatic temperature sensitivity calibration and nonlinearity optimization of scale factor (SF) for MEMS gyroscopes under force rebalanced operation. Calibration of SF temperature sensitivity is done based on stiffness modulation by injecting a cosine calibration signal to modulate the resonance frequency of gyroscope drive mode. Parameters affecting gyroscope scale factor is reciprocal proportional to the loop gain of the demodulated calibration signal, enabling a calibrated temperature insensitive SF. Implementing this real time SF calibration algorithm in an FPGA platform results in a decreased SF error from 42416 ppm to 12141 ppm over temperature range of 0°C to 50°C, which is further reduced to 3526 ppm by calibrating the temperature coefficient of the gain ratio of drive and sense mode front-end excitation circuits with experiment. Additionally, we reveal that force misalignment angle is a major error source for SF nonlinearity, which is verified experimentally with the result that SF residual error within the range of 0.1deg/s-200deg/s decreases from 8550 ppm to 3963 ppm by force misalignment angle compensation with force rotation matrixes. Owing to the elimination of parameters affecting both the SF calibration loop and the real angular readout loop and further calibration of gain ratio temperature sensitivity of discrete boards, the SF error over temperature is reduced by 12 times, while the maximum SF residual error is optimized by 2 times as a result of the force misalignment angle compensation.
Keywords: MEMS gyroscope, force-to-rebalance (FTR), stiffness modulation, force misalignment angle, scale factor calibration