Effect of Electrostatic Nonlinearity on Force-to-Rebalance Mode of Operation in CVG

In Micro Electro-Mechanical (MEM) Coriolis Vibratory Gyroscopes (CVG), the electrostatic frequency tuning mechanism is often used to match the resonant frequencies along the drive and sense axes of the gyroscope. However, the electrostatic frequency tuning results in nonlinearity in the dynamics of the CVG and a large amplitude-frequency coupling is introduced. In this paper, we present a comparative study of the effect of electrostatic nonlinearity on the noise performance of a CVG in the open-loop angular rate mode and the Force-to-Rebalance (FRB) angular rate mode of operation. Based on the experimental noise characterization of a Dual Foucault Pendulum (DFP) gyroscope, it is demonstrated that the amplitude-frequency coupling adversely affects the stability of the resonant frequency along the drive axis of the gyroscope. In the case of the open-loop operation modality, it is shown that noise in the oscillation frequency along with an uncompensated quadrature coupling between the sense and drive modes causes noise degradation and scale-factor instability. In the FRB mode, however, by using Quadrature Nulling Control (QNC) and Rate Control (RC) loops, the zero-rate output and scale-factor were observed to have much lower sensitivity to frequency instability along the drive axis, caused by the amplitude-frequency coupling. In the case of the DFP gyroscope, we demonstrated that the FRB mode provides a 20-times lower Angle Random Walk (ARW), as compared to the open-loop mode of operation. In this work, by operating the DFP gyroscope in the FRB mode, an ARW better than 0.0068 deg/√hr and a Bias Instability (BI) better than 0.09 deg/hr were demonstrated at a vibration amplitude of 0.8 microns, equivalent to half of the capacitive gap size.