Deployment trajectory tracking control of tethered satellite system based on fast model predictive control

The stable deployment is one of the key problems for the tethered satellites system (TSS). The deployment of TSS has properties of strong nonlinearity and under-actuated, which is susceptible to external disturbance and parameters uncertainty. This paper proposes the fast model predictive control (FMPC) for the process of deployment with inputs and states constraints. Firstly, the mathematical model of TSS is derived by Lagrange mechanics theory. The nominal deployment trajectory is obtained by using the typical tension control law while parameters in the law are optimized. A fast online controller developed by the model predictive control (MPC) is designed to ensure the precision. To reduce the computation time, the system model is linearized along the nominal trajectory, obtaining a set of linear time varying (LTV) model to be the prediction models. Then, the problem of nominal trajectory tracking with nonlinear model predictive control (NMPC) is transformed into the optimization problem of LTV-MPC scheme by simplifying a nonlinear programming (NP) problem to quadratic programming (QP) problem in each sampling period. The feasibility and rapidity of the proposed controller is verified through numerical case for the deployment of TSS.