A systematic method for tuning the dynamics of electrostatically actuated vibratory gyros

High-performance vibratory gyroscopes require two degenerate modal frequencies for maximizing the rate-induced signals relative to noise produced by signal conditioning electronics. The present paper introduces a systematic approach for tuning these modes in vibratory gyros that employ electrostatic actuation. The key contribution shows how a parametric model, which captures the dependence of the sensor dynamics on the bias electrodes´ potentials, can be fit to empirical frequency response data by solving a generalized eigenvalue problem. The models typically have 20 to 30 parameters for which the frequency response data imposes up to several hundred constraints. Subsequent analysis of the identified model enables the direct computation of the bias potentials which yield degenerate modal frequencies. The results are illustrated on a JPL-Boeing MEMS gyro prototype.