Gyro Motion Boundedness under Uncertain Vehicle Spin and Acceleration

An analysis is presented of the motion of a single axis rate gyroscope mounted in a space vehicle, which is simultaneously accelerating and spinning about the output and spin axis, respectively, of the gyro. The time-varying acceleration and deceleration ωx(t) and the spin rate ωz(t) of the vehicle are unknown but bounded functions of time t. It is shown that the motion of the gyro remains bounded if the bound ρ*2 on the uncertainty in ωz(t) does not exceed some threshold *2 and that this threshold depends on the various parameters of the gyro. Furthermore, by a proper selection of the gyro parameters, its motion can be forced to remain in a small neighborhood (called region of ultimate boundedness) of the origin in θ-θ plane after a certain finite interval of time for any bounded uncertain ωx(t) and ωz(t). Analytical relations are derived for the selection of gyro parameters to keep the error caused in the measurement of the input rate due to ωx and ωz within any given limit.