Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation

Ahmad, Ahmad Yousof; Abdelaziz, Ahmed Magdy; Abd El Naby, Abd El Hakeem; Abdel-Aziz, Yehia Ahmed

doi:10.21608/sjdfs.2025.402163.1243

Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation

Document Type : Original articles

Authors

¹ Mathematics department, faculty of science, Damietta university, new Damietta, Egypt.

² National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt

³ Department of mathematics, Faculty of science, Damietta University

⁴ National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt.

10.21608/sjdfs.2025.402163.1243

Abstract

This paper investigates the chaotic dynamics of an in-plane electrodynamic tethered satellite system (EDTSS) influenced by Earth's oblateness. The system is modelled using the dumbbell model, and the equations of motion are derived via the Lagrangian approach, accounting for the Lorentz force and the perturbation caused by the J2 zonal harmonic. The onset of chaos is analytically examined using Melnikov’s method, which provides a necessary condition for the emergence of chaotic behavior in the system. To address this instability, a novel control strategy based on sliding mode control (SMC) is proposed, with the tether length serving as the control input. The controller is designed to suppress chaotic motion and guide the system toward either a desired oscillatory behavior or a predefined equilibrium point. Numerical simulations are carried out to verify the analytical condition for chaos and to evaluate the effectiveness of the proposed SMC-based tether length control. The results confirm the controller’s capability to stabilize the system and eliminate undesired chaotic responses.

Keywords