Adaptive Terminal Sliding Mode Fault-Tolerant Control of Spacecraft Based on the Left Attitude Error Function of SO(3)

For the problem of spacecraft attitude actuator failure, an adaptive terminal sliding mode fault-tolerant controller (ATSMFTC) based on the differential manifold SO(3) modelling is designed in this paper. First, SO(3) is used to provide a global and unique description of the spacecraft attitude dynamic model. This modelling method not only avoids the problems of singularity and unwinding that exist in traditional modelling methods but also the SO(3) modelling has a simple formulation of the dynamic equations. Then a left attitude error descriptor function is constructed on SO(3) to design an ATSMFTC. This controller is capable of fast and accurate tracking of the time-varying desired attitude. At the same time, it can react quickly to maintain system stability in case of spacecraft attitude actuator failure. The controller designed based on the left attitude error description system of SO(3) has the features of small computational effort and simple design process. Finally, the numerical simulation of the attitude tracking error verifies the feasibility and high efficiency of the controller designed in this paper.