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Vibration 2018, 1(1), 69-80; https://doi.org/10.3390/vibration1010006

Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada
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Received: 18 May 2018 / Revised: 14 June 2018 / Accepted: 16 June 2018 / Published: 19 June 2018
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Abstract

The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices. View Full-Text
Keywords: gyroscope; stochastic differential equation; dynamic stability; white noise; frequency mismatch; instability; angular rate fluctuation gyroscope; stochastic differential equation; dynamic stability; white noise; frequency mismatch; instability; angular rate fluctuation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Bognash, M.; Asokanthan, S.F. Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations. Vibration 2018, 1, 69-80.

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