Abstract
In this paper we present an exact solution for the attitude control of a satellite with a twin Control Moment Gyros (CMG) system. A method is described to design feedback gains and/or size the CMGs such that the closed-loop response of the system with the exact steering law gives the fastest possible manoeuvre without hitting a singularity. Moreover, the effect of gimbal rate saturation on feedback control synthesis is also analysed and the steering law shown to give rise to a near-optimal control.