Analysis and Compensation of Phase Error for the Butterfly Gyroscope

X/y axis gyroscope's output error induced by demodulation phase variation with temperature becomes a limit to improve the temperature-dependent performance, which appears periodic and can not be compensated well by common polynomial fitting. This paper reports a method of the temperature-dependent bias instability improvement of butterfly gyroscope based on phase compensation. The zero-bias output change of the modal mismatched gyroscope caused by modal frequency, quality factor and phase response with temperature variation were theoretically derived. The in-plane butterfly gyroscope with its control and compensation scheme was introduced. The theoretical and the tested demodulation phase error change with temperature match well. And the phase compensation was achieved. The maximum error of zero bias output of the butterfly gyroscope drops from 0.026°/s to 0.012°/s after phase error and polynomial temperature compensation, which was tested over the temperature range from 233.15K to 333.15K. Furthermore, the temperature-dependent bias instability has also improved from 1.33°/h to 0.86°/h, behaving a high level performance in state of the art x/y axis MEMS gyroscopes.