Dynamic instabilities in a single-axis gyroscope subjected to stochastic angular rate perturbations

Instabilities in a vibratory MEMS gyroscope that is subject to stochastic fluctuations in input angular rates are investigated. The vibratory-type gyroscope considered in the present study is of the spring-mass type. An asymptotic approach based on the method of stochastic averaging has been employed for this purpose, and closed-form conditions for mean square stability of dynamic response are obtained for the case of exponentially correlated noise. Results are shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the system. The presented results remain valid if the stochastic parametric excitation has a small correlation time compared with the system relaxation time. Stability predictions have been illustrated via stability diagrams in the power-spectral-density–damping-ratio space.