Fractional-Order Adaptive SMC for the Deployment of STS

In this chapter, a novel FO SMC scheme based on a nonlinear mathematical model in elliptical orbits is presented. A new dimensionless transform based on coordinate translation is constructed to convert input limitation into the form of saturation. With the help of this transform and the Euler-Lagrange mechanical equation, a dynamic model of STS deployment in elliptical orbits is established. To tackle tether tension limitation and thruster saturation, we introduce a quasi-saturated function and a bounded function, with their properties discussed completely. Furthermore, a FO sliding surface is constructed by bringing in a FO derivative operator, reaching higher robustness, smaller overshoots, and shorter settling times. Moreover, we design the controller according to the nonlinear dynamic model, which is a progress than linearized one. Simulation results are presented to evaluate the performance of the proposed methods. To the best of our knowledge, it is the first time in the literature that tether tension limitation and thruster saturation have been considered and handled for nonlinear models in elliptical orbits using a FO sliding mode controller simultaneously.