Zero-Rate-Output Anomaly in Lissajous-FM Gyroscopes With Electrostatic Ring Resonators

This paper investigates the origin of zero-rate-output (ZRO) anomalies observed in Lissajous frequency-modulated (LFM) MEMS gyroscopes employing electrostatic ring resonators. Although LFM detection offers high scale-factor stability through frequency-based angular-rate encoding, residual bias errors often emerge even under zero angular rate. Experimental measurements reveal the presence of a second-harmonic component in the frequency modulation that cannot be explained by conventional linear cross-axis coupling models. To clarify this behavior, a theoretical model is developed considering the inclination of parallel-plate electrostatic transducers under large-amplitude wineglass-mode vibration. The analysis shows that the electrostatic stiffness becomes quadratically dependent on the vibration amplitude of the orthogonal mode, producing a second-order coupling term proportional to$\cos (2\theta)$. Experimental results obtained using an FPGA-based dual-axis control system confirm that the amplitude of the second-harmonic component scales with the square of the drive voltage, validating the proposed model. These findings demonstrate that plate-tilt-induced nonlinear coupling is a major source of ZRO fluctuation in LFM gyroscopes.