Back-stepping sliding mode control for libration control of large swing angles of electrodynamic tether system

Due to its widespread use in the field of space exploration, the electrodynamic tether system has undergone intensive research and is expected to pave the way for future developments in space technology. It has been demonstrated that, if not carefully regulated, the electrodynamic tether system easily deviates from equilibrium positions during a mission. The system works well in this instance because the equilibrium points of the cable near the vertical can be considered the “working equilibrium positions.” It implies that the in-plane and out-of-plane libration motion will mirror the cable's swing dynamics. The primary goal of this article is to alter the tether current and out-of-plant thrust in order to get the tether close to the vertical. A nonlinear control law using back-stepping control law in conjunction with sliding mode control can reduce the tether's attitude angles and increase robustness taking into account the extremely nonlinear and coupled properties of the system. The in-plane angle control subsystem, the out-of-plane angle control subsystem, and the auxiliary stabilization subsystem make up the control scheme. To confirm the efficacy of the suggested control methods and the stability of the control system, numerical simulations were run.