Online Mode-Matching Method Countering for Stiffness Nonlinearity in Whole-Angle MEMS Gyroscope

In the whole-angle MEMS gyroscopes, the aniso-stiffness induces a mismatch of the resonant modes and engenders undesired frequency split. The stiffness nonlinearity caused by electrostatic actuation will exacerbate such a mismatch. The model of the stiffness error established in this article demonstrates that the electrostatic stiffness nonlinearity brings an extra 4th harmonic component to the frequency and quadrature control force for the whole-angle MEMS gyroscopes. To improve the performance of the gyroscope, an online mode-matching method based on virtual rotation is proposed to mitigate the impact of both aniso-stiffness and stiffness nonlinearities. Experimental results show that with the self-calibration method, the gyroscope can achieve mode matching with the frequency split of below 1 mHz across the full temperature range from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$- 40~^{\circ }$ </tex-math></inline-formula> C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$60~^{\circ }$ </tex-math></inline-formula> C.