In-Run Automatic Mode-Matching of Whole-Angle Micro-Hemispherical Resonator Gyroscope Based on Standing Wave Self-Precession

This paper reports an in-run automatic mode-matching method of whole-angle (WA) micro-hemispherical resonator gyroscope (
$\mu $
HRG) based on standing wave self-precession. When the standing wave precesses in real-time by self-precession, all information of frequency mismatch contained in the output force of the quadrature suppression loop is identified by the least mean square algorithm (LMS). Then the electrostatic negative stiffness effect is used to realize online real-time mode matching to eliminate the angle bias error of WA
$\mu $
HRG caused by the asymmetry of stiffness. Self-precession rate overcomes the limitation of rotation rate requirement so that the LMS algorithm can work without rate turntable. The physical input angular rate can still be measured when the proposed mode matching loop works normally. The mechanical gain loss caused by frequency mismatch is investigated, distorting the measured angle relative to the forced angle. The expression of the angle error caused by mechanical gain loss is derived. The electrostatic tuning theory of WA
$\mu $
HRG, the proposed information identification method for frequency mismatch, and the realization principle of mode matching are analyzed and introduced. Experiment results show that the automatic mode-matching method in whole-angle mode is effective. After mode matching, the final mode matching accuracy of 28.7mHz is realized, with a reduction of about 95% from 570.7mHz (original frequency mismatch). And the WA
$\mu $
HRG realized the angle-dependent bias (ADB) error decreased from 25.8° to 7.3° after mode matching. For the mode-matched WA
$\mu $
HRG, the ADB is improved by nearly 3.5 times.