Discrete-time pure-tension sliding mode predictive control for the deployment of space tethered satellite with input saturation

A novel discrete-time pure-tension sliding mode predictive control scheme is presented to realize the deployment of space tethered satellite system in consideration of saturated input, which inherits the property of explicitly handling constraints from model predictive control, and the remarkable robustness from sliding mode control. Considering the digital control characteristics of the practical engineering, a discrete-time nonlinear model of space tethered satellite system is derived based on the discrete-time Euler-Lagrange theorem. Then, a discrete-time underactuated sliding manifold and a sliding mode predictive equation are raised to guarantee a more stable and faster tension control. Meanwhile, given the input saturation, an auxiliary controller is involved in the proposed controller to compensate saturated tension. By using Lyapunov stability theory, the accessibility of the discrete-time sliding manifold and the asymptotic stability of the deployment process are certificated. Finally, groups of numerical simulations for the deployment are demonstrated to verify the effectiveness of the proposed control scheme.