Analytical deployment control law for a flexible tethered satellite system

The deployment process of a tethered satellite system in a space environment is by nature unstable due to the negative-damping effect in the system. Hence, this paper addresses the deployment stability in controlling a space flexible tethered satellite in which the perturbations from a space environment, such as the J2 perturbation, air drag force, and solar pressure, are considered. An analytical tether length rate control law for the deployment is presented by using a simplified elastic rod model of the flexible tethered satellite. Then, the stability of the controlled time-varying system during deployment is analyzed via the Floquet theory. The parameter regions for stable deployment are obtained to maintain a tensile state of the tether during the deployment phase. The numerical simulations show that the proposed analytical control law is capable of suppressing the in-plane oscillation of the flexible tethered satellite during deployment while maintaining deployment stability.