Instabilities due to Electrostatic Tuning of Frequency-Split in Coriolis Vibratory Gyroscopes

In order to improve the angular rate sensitivity in Coriolis Vibratory Gyroscopes (CVG), an electrostatic frequency tuning mechanism is often used to reduce the split in the resonant frequency of gyroscopes. In this paper, the effect of the amplitude-frequency coupling, as a ramification of the electrostatic frequency tuning, on gyroscope operation in the open-loop angular rate mode is studied. We demonstrate that the amplitude-frequency coupling results in instability in the resonant frequency along the drive axis which degrades the noise performance of a CVG. We present a model that describes the non-linear dynamics of a gyroscope along the drive axis, including the amplitude-frequency coupling terms beyond the Duffing and quintic nonlinearity. Analytical equations were derived to estimate the correlation between frequency noise and amplitude noise. The non-linear electrostatic spring stiffness and the frequency noise in a Dual Foucault Pendulum (DFP) gyroscope were characterized and a good agreement with the predictive analytical model was observed. Our study suggests that as the required tuning voltage for mode-matching is increased, the frequency stability in the gyroscope degrades and the quadrature noise limits the noise performance of the gyroscope. In the case of the DFP gyroscope, we demonstrated that a reduction of the drive amplitude, which reduces the amplitude-frequency coupling, resulted in a 3 times improvement in the Angle Random Walk (ARW) and Bias Instability (BI).