Discrete-time Contractive MPC-based Sliding Mode Tension Control for the Deployment of Space Tethered Satellite

This paper develops a novel discrete-time sliding mode tension control strategy based on the contractive MPC scheme, for the deployment of space tethered satellite system with input limitation. By deriving the discrete-time Euler-Lagrange equation, the discrete-time nonlinear model is constructed for space tethered satellite system. Hence, the proposed discrete-time sliding surface is strictly nonlinear and underactuated. Then, the contractive MPC controller is designed to drive the sliding mode asymptotically converge to the sliding surface, which makes it possible to prove the exponential stability of the proposed controller. Furthermore, considering the limited input, a novel control structure with input compensation is raised to obtain a preferable performance. Finally, simulation studies are conducted to investigate the influences of contractive MPC and input compensation on the discrete-time sliding mode, validating the effectiveness of the proposed control strategy.