Tension control of space tether via online quasi-linearization iterations

The paper presents how to stabilize the deployment and retrieval processes of a space tether system via the tension control, where the model predictive control is exploited to optimize the control performance while the nonlinear dynamics and tension constraint are explicitly taken into account. A new scheme of online quasi-linearization iteration is proposed to transfer the nonlinear optimal control problem into a series of linear optimal control problems that can be solved in sequence at a series of sampling instants. Consequently, it avoids the complete solution of the nonlinear optimal control problem at each sampling interval such that the computational load can be greatly alleviated. Furthermore, the scheme extends the conventional quasi-linearization schemes by distributing the iterative process across sampling instants and online updating the initial condition of the linear optimal control problem. The problems of linear optimal control are discretized using a pseudo-spectral algorithm and then solved by a solver of linear quadratic programming. Numerical case studies indicate that successful deployment and retrieval of the system can be achieved using the proposed control scheme without violating the positive tension constraint. The time cost for each online optimization in the proposed scheme is on the order of 10 ms and far below the sampling interval under consideration.