Fractional-order robust fixed-time sliding mode control for deployment of tethered satellite

Tether deployment of the space tether system is the first step of related on-orbit experiments, which requires an advanced and reliable control scheme to realize rapid deployment without overshoot. In this paper, we propose a fractional-order fixed-time controller based on hierarchical sliding mode control to be applied to the deployment process of the tether system. The application of fractional calculus improves the local effect of the controller. Through strict mathematical derivation, we prove that the proposed control law satisfies the global fixed-time stability. So the closed-loop system has the performance of fixed-time convergence. Part of the simulation uses a fractional sliding mode control law for comparison, which further illustrates the superiority of the control law proposed in this paper. In view of the uniqueness of tether system dynamics, the research ideas in this paper are also of reference value to similar under-actuated systems.