Stability and chaotic dynamics of a perturbed rate gyro

An analysis of stability and chaotic dynamics is presented by a single-axis rate gyro subjected to linear feedback control loops. This rate gyro is supposed to be mounted on a space vehicle which undergoes an uncertain angular velocity ωZ(t) around its spin axis and simultaneously acceleration occurs with respect to the output axis. The necessary and sufficient conditions of stability and degeneracy conditions for the autonomous case, whose vehicle undergoes a steady rotation, were provided by Routh–Hurwitz theory. The stability of the nonlinear nonautonomous system was investigated by Liapunov stability and instability theorems. As the electrical time constant is much smaller than the mechanical time constant, the singularly perturbed system can be obtained by the singular perturbation theory. The Liapunov stability of this system by studying the reduced and boundary-layer systems was also analyzed. Using the Melinikov technique, we can give criteria for the existence of chaos in the gyro motion when the vehicle undergoes perturbed harmonic rotation about its spin and output axes.