Nonlinear Proportional-Derivative Control Incorporating Closed-Loop Control Allocation for Spacecraft

A novel saturated proportional-derivative control law incorporated with closed-loop control allocation is proposed for spacecraft attitude stabilization in this paper. More specifically, a saturated proportional-derivative-based baseline nonlinear controller is designed to guarantee the globally asymptotic stability under control input/signal constraints. Then, a closed-loop constrained optimal control allocation scheme is employed to distribute the moments synthesized by the baseline controller over the redundant actuators in the presence of constraints due to actuator amplitude and rate constraints. The optimal control solution is to be found by penalizing the control allocation errors and rates using optimal quadratic programming algorithms. A significant feature of this work is that the asymptotic stability with the closed-loop control allocation is guaranteed theoretically. Simulation results are presented to illustrate the performance of the proposed scheme.