Fractional-Order SMC for the Deployment of STS

This chapter proposes a FO integral sliding mode control with the order \(0<\nu <1\) to stabilize the deployment of tethered spacecraft system with only tension regulation. The work 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 derivate is synthesized to enhance the flexibility of controller design by fining parameters for better dynamic and steady-state performance. FO observers help to eliminate external disturbances while the adaptive law is presented to remove the adverse effect in stability analyses, and FO uniform ultimate boundedness is proved to guaranteed the existence of proposed sliding surface. According to theoretical analyses, the FO 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.