New Startup Method Using Internal Momentum Management of Variable-Speed Control Moment Gyroscopes

An initial startup method for a spacecraft actuated by a pyramidal arrangement of variable-speed control moment gyroscopes is developed. The method provides closed-loop internal momentum tracking control to enable the flywheels to start from rest and reach desired wheel speeds. The proposed controller functioning as a variable-speed control moment gyroscope steering law is developed in terms of the gimbal rates and the flywheel accelerations, which are weighted by a singularity measure. Specifically, using null motion, a strategy is developed to simultaneously perform gimbal reconfiguration for singularity avoidance and internal momentum management for flywheel startup. A Lyapunov-based stability analysis is used to prove asymptotic attitude tracking and exponential internal momentum tracking despite the effects of uncertain, time-varying satellite inertia properties and uncertain actuator inertia properties. Numerical simulations illustrate the performance of the adaptive controller as a variable-speed control moment gyroscope steering law.