Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero momentum mode. Three axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories. Two approaches are proposed and compared to achieve three axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque.