Full Symmetric MEMS Rate Gyroscope Automatic Mode-Matching Method Based on Pendulum Variable Demodulation and Phase-Shifted Virtual Coriolis Force Modulation

Full symmetric micro-gyroscopes, such as MEMS Hemispherical Resonator Gyroscopes (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>HRGs) and nested-rings disk resonator gyroscopes (DRGs), offer advantages in terms of smaller size, lower cost, and reduced power consumption compared to traditional MEMS gyroscopes. However, the mode mismatch caused by MEMS processing errors limits the performance improvement of these gyroscopes. This article presents an automatic mode-matching technique for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>HRG utilizing pendulum variable demodulation and phase-shifted virtual Coriolis force modulation. Initially, a force-to-rebalance (FTR) control loop scheme based on pendulum-variable demodulation is designed. Through an analysis of FTR mode performance optimization, it is concluded that suppressing stiffness errors can significantly reduce zero bias error, suppress circuit noise, and improve dynamic performance. Therefore, this study utilizes negative stiffness effects and phase-shifted virtual Coriolis force modulation to design an automatic identification, decoupling, and compensation (AIDC) process for stiffness errors based on phase-shifted virtual Coriolis force modulation to realize mode-matching. The experimental findings indicate that this method achieves a tuning accuracy of 1.04 MHz. After eliminating the stiffness error using the AIDC process, the bias instability (BI) improves to 0.195°/h, and the angle random walk decreases to 0.036°/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula>h. Compared to the mode mismatch condition, the BI and angle random walk (ARW) of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>HRG are improved by 61.91 and 50.53 times, respectively.