Comparison of two magnetic damping laws for the attitude acquisition of a dual spin satellite

Dual spin satellite motion in the attitude acquisition phase is considered. Starting from the arbitrary rotation state, the satellite should end up with its angular momentum aligned with the orbit normal. The satellite is equipped with magnetorquers that provide the angular velocity damping. Two control strategies are compared, that is the simple exponential damping and 'weighted' damping arising from the classical sliding control implementation. The time response of the control system depending on the satellite inertia moments is analysed. Simple damping is proven to provide better results for the low control authority even for the significantly elongated satellite. This result is proved with the analytical solution for the characteristic exponents approximations. Weighted damping is shown to provide better results for significant control authority through numerical simulation.