MEMS vibratory angular rate sensors: stability considerations for design

Stability of a class of vibratory angular rate sensors that are subject to periodic fluctuations in input angular rates is investigated. Two typical configurations are considered in the present paper: a single-axis ring-type and a dual-axis disk-type. For the purpose of acquiring stability conditions, when the angular rate input is subject to small intensity periodic fluctuations, dynamic stability behaviour of periodically perturbed linear gyroscopic systems are studied in detail. An asymptotic approach based on the method of averaging has been employed for this purpose, and closed-form conditions for the onset of instability due to parametric resonances have been obtained for these two types of vibrating gyroscopes. Stability predictions have been illustrated via plots in the excitation amplitude–frequency space. Damping is considered and in general it has been demonstrated that the introduction of damping tends to stabilize the sensor systems. Furthermore, for characterizing the effect of input angular rate on the stability, an in-depth natural frequency analysis has been performed for the disk-type angular rate sensor. In addition, the effect of mass mismatch on the stability region has been presented for the ring-type angular rate sensor. Copyright © 2005 John Wiley & Sons, Ltd.