Modeling and control of perturbation torques and mass distribution impact on a tethered system for a 12U CubeSat in sun-synchronous orbit

Tethered CubeSat systems are characterized by momentum exchange and gravity gradient stabilization, and encounter stability challenges, especially with shorter tethers in highly inclined and eccentric orbits. This study investigates the libration dynamics of a 12U CubeSat in its stowed configuration, which separates into two satellites connected via tether, throughout its deployment, station-keeping, and retrieval phases. Two deployed configurations, symmetrical 6U-6U, and asymmetrical 8U-4U connected by a non-conductive tether with a maximum length of 100 m are analyzed. The study accounts for perturbations including Earth's oblateness, atmospheric drag, solar radiation pressure, and lunisolar gravitation, modeling the tether as a rigid, extendable rod and the satellites as lumped masses. The translational and rotational dynamics are decoupled, assuming the system's center of mass follows an unperturbed Keplerian Sun-synchronous orbit at altitudes between 400 and 600 km. A tension control strategy based on Lyapunov's direct method and supplemented by external actuation torques is explored. Results show high orbit eccentricity significantly affects the maximum in-plane libration angle. The 6U-6U system experiences smaller disturbance torques but greater tether tension variations than the 8U-4U system. Both configurations exhibit larger in-plane oscillations compared to near-zero out-of- plane oscillations, nonetheless, eclipse passages exacerbate the out-of-plane libration of the 8U-4U system. Relative stability is maintained during deployment, however, retrieval is chaotic, with notable oscillations in libration angles and tether tension. The tension control strategy effectively dampens oscillations during retrieval but loses effectiveness as tether tension approaches zero at retrieval's conclusion. External actuation torques, ranging from 1-2 mN m for deployment to 15 mN m for retrieval, complement tension control.