General problems of dynamics and control of vibratory gyroscopes

Abstract

A general model of operation of vibratory gyroscopes, which is applicable to a broad class of instruments, including cylindrical, disc and micro-machined gyros, is formulated on the basis of analysis of dynamics and control of a hemispherical resonator gyroscope. The foundations of feedback control in the gyroscopes are considered and classification of the main operational regimes is given in terms of the integral manifolds and new classes of nonlinear parametric excitation forces are added. Qualitative effects of different classes of forces are analysed and conclusions about the structure of nonlinear control forces are proposed. Specific imperfections of the vibratory gyroscopes, operating in the whole regime, force-to-rebalance, travelling wave and combined regimes, are considered. The cumulative effects of errors are represented as superposition of the effects of particular classes. A closed set of integral manifolds is formulated, in terms of which the dynamics of a vibratory gyroscope is considered.