A comparative study of sliding mode control and time-optimal control

A comparative study of sliding mode control and time-optimal control for spacecraft attitude control using thrusters is presented. The on-off type thrusters are assumed to be attitude control actuators. Application of time-optimal control theory to the kinematic and dynamic equations of motion leads to a nonlinear two-point boundary value problem. The solution can be computed by iterative numerical methods, but typically, the computing method is not compatible with real-time computing constraints. In this paper, sliding mode control is used for the input of PWPF (Pulse Width and Pulse Frequency) modulator thrusters. The settling times are minimized by tuning the gains of sliding mode control. The sliding mode control is derived using modified Rodrigues parameters. We also derive the upper bound of sliding function for inertia uncertainty and external disturbances. Disturbance accommodating sliding mode control with PWPF is derived to minimize the settling time with inertia uncertainty and external disturbance. Simulation results show that the settling times are shorter than the ones of the sliding mode control with PWPF.