Quasi-Periodic Motion And Optimal Control Of Tethered Satellite System

The analysis of dynamics of in-plane tethered subsatellite moving in a circular orbit during station-keeping phase by methods based on nonlinear dynamics and ground-based experiment is made in this dissertation. The nonlinear optimal control for deployment and retrieval of a tethered subsatellite is also studied. The contents and contributions of the dissertation are as follows:A detailed survey of dynamics, control, and ground-based experiment of tethered satellite systems is given first. Then, the motion and dynamics of in-plane tethered subsatellite with attitude during station-keeping phase are studied, including equilibrium configuration and stability analysis. The established mechanical model shows that there exist the coupled fast and slow motions related to the attitude of the subsatellite and the pitch motion of the tether in the case of small ratio of radius of subsatellite to tether length. In order to gain an understanding of the coupled fast and slow motions, a two variable perturbation method in conjunction with multiple scales of time is proposed to obtain the asymptotic analytical solutions. The analytical and numerical results show that the coupled fast and slow motions of in-plane tethered subsatellite system in a circular orbit would fall into a quasi-periodic oscillation. With the help of the on-board thrusts, a ground-based experiment with an artificial dynamics support was carried out to verify the quasi-periodic oscillation. The experiment indicates the quasi-periodic properties which results in coincide with the numerical simulation.Afterwards, the nonlinear receding horizon control based on the indirect Legendre-Gauss pseudo-spectral method is presented for controlling the retrieval process of a tethered subsatellite model, which accounts for the attitude motion of the sub-satellite. In order to obtain the numerical scheme for the controlled tethered subsatellite, the nonlinear receding horizon control problem is simplified into a set of linear optimal control by using the quasi-linearization method and discretization technique at the corresponding Legendre-Gauss points. The numerical results show that the subsatellite can be retrieved by adjusting the tether tension and moment applied to the subsatellite. The proposed control scheme can effectively work for the retrieval process of the tethered subsatellite in the presence of modeling errors, initial state perturbations, and external disturbances.At last, the optimal control for the deployment and retrieval processes of a tethered subsatellite system with free flying time is proposed, which takes in-plane and out-of-plane motions into account. The quasi-linearization and the truncated Chebyshev expansions are adopted to approximate the system state variables so that the constrained nonlinear optimal control can be transformed into a linear quadratic programming problem. The case studies not only support the new method, but also show that the controlled trajectories of the deployment process and the retrieval process are geometrically symmetric to each other with respect to the local vertical axis.The studies in the dissertation have revealed the some dynamics of tethered satellite systems with highly nonlinear behavior and developed the optimal control method for deployment and retrieval.