Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation
Ahmad, A., Abdelaziz, A., Abd El Naby, A., Abdel-Aziz, Y. (2025). Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation. EKB Journal Management System, 15(2), 192-201. doi: 10.21608/sjdfs.2025.402163.1243
Ahmad Yousof Ahmad; Ahmed magdy Abdelaziz; Abd El Hakeem Abd El Naby; Yehia Ahmed Abdel-Aziz. "Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation". EKB Journal Management System, 15, 2, 2025, 192-201. doi: 10.21608/sjdfs.2025.402163.1243
Ahmad, A., Abdelaziz, A., Abd El Naby, A., Abdel-Aziz, Y. (2025). 'Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation', EKB Journal Management System, 15(2), pp. 192-201. doi: 10.21608/sjdfs.2025.402163.1243
Ahmad, A., Abdelaziz, A., Abd El Naby, A., Abdel-Aziz, Y. Chaos Suppression in an Electrodynamic Tethered Satellite System via Sliding Mode Control Under J2 Perturbation. EKB Journal Management System, 2025; 15(2): 192-201. doi: 10.21608/sjdfs.2025.402163.1243

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

Scientific Journal for Damietta Faculty of Science
Volume 15, Issue 2, August 2025, Page 192-201  XML PDF (1.06 MB)
Document Type: Original articles
DOI: 10.21608/sjdfs.2025.402163.1243
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Authors
Ahmad Yousof Ahmad email 1; Ahmed magdy Abdelazizorcid 2; Abd El Hakeem Abd El Nabyorcid 3; Yehia Ahmed Abdel-Azizorcid 4
1Mathematics department, faculty of science, Damietta university, new Damietta, Egypt.
2National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt
3Department of mathematics, Faculty of science, Damietta University
4National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt.
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
Chaos; Earth' s oblateness; Electromagnetic Force; Sliding Mode Control; Tethered Satellite System
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