Fractional-Order Nonsingular Terminal Sliding Mode Tension Control for the Deployment of Space Tethered Satellite

In this article, a novel fractional-order nonsingular terminal sliding mode (FONTSM) control scheme is developed, which guarantees the desired deployment performance of space tethered satellite (STS) system. The presented control scheme is to stabilize the underactuated deployment mission with only tension regulation. Based on the underactuated model, a practicable integer-order nonsingular terminal sliding mode (IONTSM) controller is designed to realize the deployment of the STS system, with the finite-time stability. Then, to improve the deployment performance, the fractional-order calculus is introduced to raise the FONTSM controller, whose Mittag-Leffler-based uniform ultimate boundedness is proved to ensure the finite-time convergence and steady-state performance. In the FONTSM controller, a fractional-order disturbance observer and a fractional-order adaptive compensation law are proposed, to eliminate the adverse impacts of external disturbances and input saturation, respectively. Moreover, compared to the reported fractional-order sliding mode control strategy of the STS system, a better deployment performance can be obtained by the IONTSM and FONTSM controllers in this work. Finally, the effectiveness of the proposed controllers is verified by groups of deployment simulations of the STS system.