Nonlinear deformation and attitude control for spinning electrodynamic tether systems during spin-up stage

This paper investigates the non-linear control of a spinning electrodynamic tether system during its spin-up process. The primary challenge in the spin-up process lies in the potential irregularity of the tether shape induced by the distributed electrodynamic force, posing risks such as the entanglement of the deformed tether with the end bodies (base spacecraft and sub-satellite). In addressing this issue, the paper proposes a nonlinear control strategy aimed at minimizing tether deformation and stabilizing the attitude motions of the end bodies. Firstly, the tether system is modeled under the assumption of a flexible tether, and the minimum current required for spin-up is determined as the foundation for designing the open-loop program. Secondly, considering the under-actuation challenge, a sliding mode controller with an adaptive law is proposed to track the spinning motion and stabilize tether deformation by adjusting only the electrical current. Thirdly, considering the limit of attitude control moment, a high-gain saturated controller is proposed to stabilize the attitude motions of the end bodies. The numerical results validate that under the regulation of the proposed control strategy, tether deformation is reduced to an insignificant level, and the attitude motions of the end bodies are stabilized around designated orientations.