Stability of Gyro with Harmonic Nonlinearity in Spinning Vehicle

A stability analysis of a single-axis rate gyroscope mounted in a space vehicle which is spinning with uncertain angular velocity ωz about the spin axis of the gyro is presented. The complete nonlinear equation of motion, which includes the fundamental and second harmonic nonlinear terms, arising due to ωz, is considered. For time-varying ωz(t), using the circle criterion, it is shown that the gimbal motion is globally asymptotically stable if the Nyquist plot of the linear transfer function of the gyro lies in the interior of a certain disk. For the case of uncertain constant ωz, using the Lyapunov approach, conditions for global asymptotic stability (GAS) and asymptotic stability are derived. Stable regions in parameter space of the gyro and state space are obtained. Analytical relations for the selection of gyro parameters are derived.