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UBC Theses and Dissertations

Planar dynamics and control of tethered satellite systems Pradhan, Satyabrata


A mathematical model is developed for studying the inplane dynamics and control of tethered two-body systems in a Keplerian orbit. The formulation accounts for: • elastic deformation of the tether in both the longitudinal and inplane trans- verse directions; • inplane libration of the flexible tether as well as the rigid platform; • time dependent variation of the tether attachment point at the platform end; • deployment and retrieval of the point mass subsatellite; • generalized force contributions due to various control actuators (e.g. momentum gyros, thrusters and passive dampers); • structural damping of the tether; • shift in the center of mass of the system due to the tether deployment and retrieval. The governing nonlinear, nonautonomous and coupled equations of motion are obtained using the Lagrange procedure. They are integrated numerically to assess the system response as affected by the design parameters and operational disturbances. Attitude dynamics of the system is regulated by two different types of actuators, thruster and tether attachment point offset, which have advantages at longer and shorter tether lengths, respectively. The attitude controller is designed using the Feedback Linearization Technique (FLT). It has advantages over other control methods, such as gain scheduling and adaptive control, for the class of time varying systems under consideration. It is shown that an FLT controller based on the rigid system model, can successfully regulate attitude dynamics of the original flexible system. A hybrid scheme, using the thruster control at longer tether lengths and the offset control for a shorter tether, is quite attractive, particularly during retrieval, as its practical implementation for attitude control is significantly improved. Introduction of passive dampers makes the hybrid scheme effective even for vibration control during the retrieval. For the stationkeeping phase, the offset control strategy is also used to regulate both the longitudinal as well as inplane transverse vibrations of the tether. The LQG/LTR based vibration controller using the offset strategy is implemented in conjunction with the FLT type attitude regulator utilizing thrusters as before. This hybrid controller for simultaneous regulation of attitude and vibration dynamics is found to be quite promising. The performance of the vibration controller is further improved by introduction of passive dampers. The LQG based vibration controller is found to be robust against the unmodelled dynamics of the flexible system. Finally, effectiveness of the FLT and LQG based offset controllers is assessed through a simple ground based experiment. The controllers successfully regulated attitude dynamics of the tethered system during stationkeeping, deployment and retrieval phases.

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