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Dynamics and control of an orbiting space platform based tethered satellite system Lakshmanan, Prem Kumar


A relatively general mathematical model is proposed for studying the coupled attitude dynamics of space platform supported tethered subsatellite systems accounting for offset of the tether attachment point. The offset is treated as a function of time subject to constraints. General energy expressions allowing for flexibility of the tether as well as the platform are derived. The governing equations account for: (i) three-dimensional librational motion of the platform; (ii) inplane and out-of-plane libration of the tether of finite mass and connected to the platform with an offset; (iii) time dependent variations on the attachment point of the tether; (iv) generalized force contributions due to various active controllers; (v) orbits of arbitrary eccentricities; (vi) deployment and retrieval of the tether from the space platform. The second order coupled, nonlinear, nonautonomous, differential equations are linearized about a quasi-static equilibrium position. After nondimensionalizing with respect to the orbital rate and characteristic dimensions of the structure, they are collated into matrix form and integrated numerically. An extensive response analysis is carried out over a range of system parameters, operational maneuvers and orbit eccentricity to assess complex interactions involved and help evolve suitable control strategies. Two control schemes, tether tension modulation and thruster control, are extended to the case of an offset of the tether attachment point. It is shown that a linear control strategy is sufficient to control the tether inplane as well as out-of-plane librations in the presence of an out-of-plane offset. A new approach to control of platform based tethered satellite systems is proposed that utilizes motion of the offset to control the coupled system dynamics. The scheme involves specification of offset accelerations based on feedback of system states and feedforward of offset states. Controllability of the linearized equation is established numerically and relative merits of the three control strategies assessed. Results indicate that the controllers are effective even in the presence of severe disturbances during all three mission phases of deployment, stationkeeping and retrieval. During stationkeeping, the tension control procedure demands larger energy for shorter tethers. Damping characteristics of the thruster control are indeed superior but at the expense of the energy. The offset control has a tendency to dynamically isolate the tethered subsatellite from the space platform. From energy consideration, it proved to be the best, particularly at shorter tether lengths. However, due to offset constraint in a practical situation, its effectiveness diminishes with an increase in the tether length and becomes virtually ineffective for a tether length over 1 km. During retrieval, hybrid control strategies utilizing tension or thruster control at the onset of retrieval, with offset control at shorter tether lengths proved to be quite energy efficient. For space application, the thruster-offset hybrid control strategy appears to be quite promising both in terms of system dynamics and energy demand.

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