By Vladislav Apostolyuk
This publication offers the most recent theoretical research and layout methodologies of alternative kinds of Coriolis vibratory gyroscopes (CVG). jointly, the chapters examine varieties of delicate point designs and their kinematics, derivation of movement equations, research of delicate parts dynamics in modulated and demodulated signs, calculation and optimization of major functionality features, and sign processing and keep an eye on. crucial facets of numerical simulation of CVG utilizing Simulink® also are coated. this is often an excellent ebook for graduate scholars, researchers, and engineers operating in fields that require gyroscope program, together with yet now not constrained to: inertial sensors and platforms, car and client electronics, small unmanned airplane keep an eye on platforms, own cellular navigation structures and comparable software program improvement, and augmented and digital truth systems.
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Extra info for Coriolis Vibratory Gyroscopes: Theory and Design
Solution of this problem by means of proper choice of natural frequency split and damping will be considered later in this book. 4 Stability and Transient Process Optimisation Both stability and unit-step transient process quality depend on position of the system poles in the real–imaginary plane. 11). 21), it is easy to see that CVGs are inherently stable. 21) are zero. One pole has large imaginary part Àx2 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 À f22 À x\0; which is always way below zero, and corresponds to high frequency oscillations in the envelope.
3 Modelling Proof Mass Motion Trajectory 41 Fig. 5 Relative error of the big half-axis approximation One should note that the sensitive element trajectory parameters depend on the phase shift u ¼ u2 À u1 between primary and secondary phases. 17), phases do not depend on the angular rate. 37) can now be used to analyse parameters of the actual trajectory of the CVG sensitive element. 39) is apparent that small half-axis is absent in either of two cases: perfect match of the natural frequencies (dk ¼ 1) or absence of the external angular rate (dX ¼ 0).
Apparently, motion Eq. 28) are quite similar to the translational sensitive element equations in case when there is no decoupling frame. 5 Generalised Motion Equations It is no coincidence that motion equations of all considered above sensitive element designs look so similar, since they are all based on the same principle—Coriolis acceleration measurement by vibrating structures. Let us now write down CVG sensitive element motion equations in a form that is applicable to all designs: ( _ 2; €x1 þ 2f1 x1 x_ 1 þ ðx21 À d1 X2 Þx1 ¼ q1 À g1 X_x2 À d3 Xx _ 1: €x2 þ 2f2 x2 x_ 2 þ ðx2 À d2 X2 Þx2 ¼ q2 þ g2 X_x1 þ d4 Xx ð2:29Þ 2 Here x1 and x2 are the generalised displacements describing primary and secondary motion of the sensitive element, either translational or rotational; x1 and x2 are the natural frequencies, f1 and f2 are the damping factors of the primary and secondary motions correspondingly; q1 and q2 are the accelerations (either translational or rotational) from external forces/torques, X is the external angular rate, orthogonal to the primary and secondary motions.
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