An Automatic Phase Error Compensation Method for MEMS Quad Mass Gyroscope

This article demonstrates an automatic phase error compensation method for a micro-electromechanical systems (MEMS) quad mass gyroscope (QMG) operating in the force-to-rebalance (FRB) mode. First, the mechanical structure and dynamics of the QMG are introduced and analyzed. Then, the main source of phase error is identified, and the impact of phase error on both the gyroscope drive mode and sense mode is analyzed. To address this issue, an automatic phase error compensation method is developed based on identifying the phase value that corresponds to the minimum drive voltage amplitude. Additionally, a phase-compensated phase-locked loop (PC-PLL) is designed to compensate for both the phase error and demodulation phase error. Simulation results validate the analysis of phase error. The experimental results demonstrate the effectiveness of the compensation method. After compensation, the scale factor is reduced from 331.895 LSB/degrees/s to 321.143 LSB/degrees/s, and the calculated phase error is found to be 14.624 degrees, which closely matches the compensated phase of 15 degrees. Furthermore, the drift of quadrature suppression voltage decreases to less than 1% when the input angular rate range is within +/- 150 degrees/s after compensation. This extends the dynamic range of the QMG from +/- 45 degrees/s to +/- 150 degrees/s. The Allan variance curves show that the angle random walk (ARW) remains relatively unchanged at 0.06 degrees/root h. However, the bias instability is improved to 0.147 degrees/h, representing a 1.25x enhancement after phase compensation.