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UBC Theses and Dissertations

Dynamics and control of a flexible tethered system with offset Pidgeon, Robert W.

Abstract

A mathematical model of a platform based flexible tethered satellite system in an arbitrary orbit, undergoing planar motion, is obtained using the Lagrangian procedure. The governing equations of motion account for the platform and tether pitch, longtitu-dinal tether oscillations, offset of the tether attachment point as well as deployment and retrieval of the tether. A numerical parametric study of the highly nonlinear, nonautonomous and coupled equations of motion gives considerable insight into the system dynamics useful in its design. Of particular interest are the interactions involving orbital eccentricity, system librations, tether flexibility and offset, retrieval maneuvers and initial disturbances. Results show that the offset strongly couples tether and platform dynamics, and the resulting responses show high frequency modulations corresponding to the longtitudinal tether oscillations. The system was found to be unstable during retrieval. The Linear Quadratic Regulator based offset control strategy, in conjunction with the platform mounted momentum gyros, is proposed to alleviate the situation. Results show that a strategy involving independent parallel control of low and high frequency responses can damp rather severe disturbances in a fraction of an orbit.

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