Fractional-order sliding mode control for deployment of tethered spacecraft system

This paper proposes a fractional-order integral sliding mode control with the order 0 < ν < 1 to stabilize the deployment of tethered spacecraft system with only tension regulation. The work in this paper is partially based on integer-order nonlinear sliding mode controller and improves its performance with fractional-order calculus. The proposed scheme makes use of integral sliding surface to obtain smaller convergence regions of state errors, and the fractional derivative is synthesized to enhance the flexibility of controller design by fining parameters for better dynamic and steady-state performance. Fractional-order observers help to eliminate external disturbances while the adaptive law is presented to remove the adverse effect in stability analyses, and fractional-order uniform ultimate boundedness is proved to guarantee the existence of the proposed sliding surface. According to theoretical analyses, the fractional order will indeed affect the dynamic and steady-state performance of control system, and the proposed method will be verified in numerical simulations compared with the nonlinear sliding mode counterpart.