Characterization and Compensation of Phase Delay and Modulation Pattern Angle Error for Rate-Integrating Micro-Hemispherical Resonator Gyroscope

This article studies the effect of the control circuit phase delay and modulation pattern angle (MPA) error in micro-hemispherical resonator gyroscope ( $\mu $ HRG) under the rate-integrating (RI) mode. The causes of these errors are initially analyzed. Then, this article establishes a dynamical model of the RI $\mu $ HRG containing phase delay and MPA error for the first time through theoretical derivations, and the error propagation mechanism of these errors in the RI mode is clarified through theoretical analyses and simulations. By utilizing the relationships between the dc biases of the orthogonal control force and amplitude control force with the virtual Coriolis force in the RI mode, this article raises a novel phase delay and MPA error quantitative and simultaneous characterization method. The error characterization and compensation experiments are performed on an RI $\mu $ HRG using this method. The experiment results reveal that after compensation, the RI $\mu $ HRG angular velocity fluctuation error dropped from 1.812°/s to 0.389°/s, dropped by 78.53%; the angle-dependent bias (ADB) error dropped by 76.62% from 0.68° to 0.159°; and the bias instability (BI) dropped by 51.88% from 1.3026°/h to 0.6268°/h. The results confirm the validity of the propounded error characterization approach and the derived RI dynamical model. This research offers practical references and guidance for future RI mode error investigations.