Dynamic Modeling and Error Analysis of MEMS Ring Gyroscope Based on FTR Mode: Principle and Structural Errors

This paper presents a unified dynamic-modeling and error-analysis framework for an FTR (force-to-rebalanced)-operated MEMS ring gyroscope. Starting from an equivalent mass-point representation of the ring resonator, a dynamic model including stiffness and damping errors is first established. Principle-related inertial-acceleration errors and structural errors are then analyzed within the same framework. The results show that, under practical rate-measurement conditions, inertial-acceleration errors have negligible effects on both the drive and sense modes. In contrast, structural errors, including modal-frequency perturbation, damping-decay-time mismatch, mass-distribution mismatch, and electrode angular misalignment, impair drive-mode amplitude control and frequency tracking, introduce in-phase bias components into the sense-mode output, and produce quadrature signals through frequency coupling. The analysis further indicates that electrostatic mode matching should be implemented in two steps: quadrature-stiffness correction followed by modal-frequency tuning. The proposed model provides a concise and physically transparent basis for resonator design, parameter identification, and control compensation in high-performance MEMS ring gyroscopes.