Improving Nonlinear Control for Underactuated Satellite Orientation

Improvement of orientation control laws for an underactuated satellite, is attemted using a nonlinear optimal control algorithm derived by Beard, et al. 1. A control law for an underactuated satellite would be used when the spacecraft is damaged during it's mission. Because of the immense cost in accessing space, recovery and repair is uncommon. Also, for this reason, it is necessary to maximize the performance of an underactuated satellite so that the decrease in mission performance is kept at a minimum. This paper builds upon previous work to establish a control law which is optimal in a least-squares sense with respect to an energy cost function. Three control laws are attempted to be optimized, a smooth time-periodic control law developed by Walsh, et al. 2 , and a non-smooth control law developed by Sordalen, et al. 3 , and the time-independent portion of a control law developed by Morin et al. 4. Since three inherently diierent control laws are analyzed in this paper, three models for a satellite are used.