Phase error analysis for MEMS gyroscopes operational modes based on force-to-rebalance rate measurement mode

The force-to-rebalance (FTR) mode is one of the most widely employed measurement schemes in MEMS Coriolis vibratory gyroscopes due to its high precision and stability. However, phase errors distributed across multiple control loops fundamentally constrain the achievable accuracy and robustness of rate measurement. This paper systematically categorizes the phase errors in both the drive modal and sense modal control loops, distinguishing between those arising in the forward and feedback paths, while excluding feedthrough effects. The influence of these phase errors is comprehensively analyzed across three key control loops: the drive modal control loop, the FTR rate control loop, and the quadrature stiffness correction loop. To address phase errors in the drive modal control loop, a dedicated calibration procedure is proposed for both the feedback and forward paths. The effects of phase errors on amplitude regulation, frequency tracking, and FTR rate measurement are quantitatively examined. For the sense modal control loop, an FTR control architecture incorporating phase error characteristics is established, along with a corresponding calibration procedure. Furthermore, the impact of phase errors on the effectiveness of quadrature stiffness correction and FTR rate measurement is investigated in detail. Finally, a comparative analysis of the sensitivity of system performance to various phase errors is conducted, and the relative influence weights of different error sources are determined. The results provide diagnostic insight into the principal mechanisms by which phase errors affect FTR gyroscope performance and lay a foundation for targeted real-time compensation design.