Dynamic Behaviour of a MEMS-Gyroscope Subjected to Stochastic Angular Rate Perturbations

Abstract

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. For the purpose of acquiring stability conditions, when the angular rate input is subject to small intensity stochastic fluctuations, dynamic behaviour of stochastically perturbed linear gyroscopic systems is studied in detail. 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. Further, to illustrate the applicability of the results in practice, conditions for varying input angular rates are mapped. Although, the above conditions are predicted for the spring-mass type gyroscope, the predictions can be easily translated to other vibratory gyroscope designs.