Analysis and control of the equilibrium position in bare electrodynamic tether systems

This study focuses on the calculation of the equilibrium position of the bare electrodynamic tether (BEDT) and the implementation of stable control during the de-orbiting process. A novel method for calculating the equilibrium position of the BEDT system is proposed, utilizing integral variable substitution. This approach provides an analytical expression for the equilibrium position, thereby addressing the limitations of numerical curve-fitting methods and facilitating further dynamic analysis and controller design. To address the influence of variations in geomagnetic field strength and electron density on the tether attitude during deorbiting, a sliding mode controller based on prescribed performance is designed to stabilize the BEDT around its equilibrium position by adjusting the tether length. This adjustment simultaneously regulates angular momentum and current on the tether. In contrast to conventional current switching methods, the proposed strategy effectively mitigates undesired transient responses and additional system disturbances, and accurately stabilizing the BEDT system around the equilibrium position. Numerical simulations show that the analytical equilibrium calculations closely match the nonlinear model, with an error margin of less than 5%. Additionally, the tether length adjustment strategy successfully stabilizes the system around the equilibrium position, achieving an angular deviation of less than 0.2 degrees and enhanced deorbit efficiency compared to the current switching control method.