Dynamic Control For Deployment And Retrieval Of Tethered Satellite Systems

The concept of Tethered Satellite System (TSS), that is, two or more satellites connected by thin and long cables, promises to revolutionize many aspects of space exploration and exploitation. However, the dynamics and control of any TSS are quite complex. Because of their overall flexibility, the tethers are strongly susceptible to undergoing a complicated set of librations and vibrations when they are placed into a space environment and coupled with flexible satellites. The problem becomes even more challenging when the deployment and retrieval parts of a TSS mission are taken into consideration because the librations and vibrations of tether can grow dramatically due to the effect of the Coriolis accelerations. If not carefully controlled, motions with large amplitudes may result in an excessively high tensional stress beyond the strength of tether material and may lead to the failure of a whole TSS.This dissertation focuses on the dynamics and control problems concerning tether deployment and retrieval, which may be the most important but also delicate parts of a TSS mission. The main themes and contributions of the dissertation include:1. A detailed study is presented on the Legendre-Gauss-Lobatto (LGL) pseudospectral (PS) methods for solving nonlinear optimal control problems. Additionally, a costate estimation scheme is proposed for the Bolza problem of optimal control of a set of dynamic equations of the second order by using the direct LGL PS approach. The presented algorithms are coded into a reusable general optimal control package in C++ language, and the computation efficiency is improved by using a symbolic preprocessor and putting the sparse structures of involved matrices into full use.2. Optimal schemes are presented for controlling the deployment process of a tethered subsatellite model with fixed and free end-time, in which a second-order differential inclusion formulation is exploited to achieve a significant reduction of the number of optimization variables and constraints. The investigation is later extended to control the retrieval process of an electrodynamic tethered satellite system in an inclined orbit, and to achieve the optimal deployment of a three-body tethered satellite formation in the orbital plane. The optimal control is solved by discretizing the original continuous optimal control problem first, based on the LGL PS algorithm, and numerically solving the resulting large-scale optimization problem.3. The idea of direct real-time trajectory generation is exploited to design feedback controller for the deployment process of a TSS subject to perturbations with the aid of a grid adaptation scheme, which contributes a significantly reduction of computation burden. In addition, a model predictive control (MPC) scheme is proposed for stabilizing the retrieval process of an electrodynamic TSS in an inclined orbit, and the performance of the MPC scheme is demonstrated by using a multi-body dynamics model.4. Infinite-horizon optimal control schemes are also explored to stabilize the retrieval process of a TSS. The infinite-horizon optimal control problem is solved individually through two Legendre-Gauss-Radau (LGR) PS algorithms by using a straightforward domain-transformation. A preliminary exploration on feedback controller synthesis is further made about the idea of real-time trajectory generation.5. Furthermore, an innovative experiment design is presented for the ground-based experiments of TSS, where a combination of air-bearing facilities and on-board thrusts are proposed to simulate the microgravity field and the Coriolis forces experienced by a TSS. Additionally, a detailed discussion is presented on the theoretical and technical issues related to the development of some key subsystems, such as satellite simulator, computer vision module, tether reel device, etc.