Control while an Electrodynamic Tether System with Current-Conducting Non-Insulated Tether Deploying

Аuthors

Zabolotnov Y. M.^*, Bystranova T. A.^**

Samara National Research University, Moskovskoe shosse, 34, Samara, Russia

*e-mail: yumz@yandex.ru
**e-mail: tsskd@mail.ru

Abstract

The article regards the deployment process control of the electrodynamic space tether system (EDSTS), comprising a small satellite, a conductive non-insulated tether and a load. Non-insulated conductive tether interaction with the Earth magnetic field leads to the decelerating force occurrence, which can be employed for the worked-out nano-satellites and small spacecraft quick deorbiting. Having in mind the non-insulated tethers employing for the low mass spacecraft, the authors analyze the possibility of applying the most simple program being realized without a feedback, which significantly simplifies control system, for the system deployment. In this regard, the article considers the disturbances impact on the accuracy of putting the system into the specified state. In this regard, the article considers the disturbances impact on the accuracy of putting the system into the specified state, and demonstrates that the errors inevasibly occurring while the system deployment can be compensated by the current force in the tether control on the system forming completion. A model, in which the tether is rectilinear and inextensible (a beam model) is used for preliminary analysis. A model with distributed parameters, in which the tether is being represented by the set of material points with unilateral mechanical elastic connections, is used for the more thorough check. This allows accounting for the tether tensibility, its bending vibrations as the result of distributed load from the electromagnetic forces, impact phenomena (“rebounds”) after reaching the tether final length.
The following inferences can be drawn by the results of the conducted study:
1. The article demonstrates that the suggested program for the tether outthrow can be implemented while deploying the electrodynamic space tether system with non-insulated conductivity tether without a feedback, which according to the authors’ will simplify significantly the system motion control. Thus, this approach may be applied for quick deorbiting of the small-sized spacecraft and nano-satellites.
2. Estimation of the disturbances impact (initial conditions of the spacecraft and cargo separation, tether extensibility) on the EDSTS deployment process was performed, and it was demonstrated that the inevasible errors of the system deployment in vertical position occurring herewith could be compensated with rather simple algorithm for the relay control of the tether current strength.
3. It was found that permissible range of the spacecraft and cargo separation conditions was being limited by the limiting or critical case, when during the deployment process the tether entered horizontal position, which led to its weakening and entanglement.
Compared to the known works the article, according to the authors opinion, proposes and substantiates the new approach to the deployment of the EDSTS with conducting tether , which may be employed for quick deorbiting of the small spacecraft and nano-satellites of small weight and size. Finally, we would like to note that the program being suggested can be considered as a backup option of control in the emergencies, when it is impossible to apply standard control methods with feedback.

Keywords:

electrodynamic space tether system, conductive non-insulated tether, cable system deploying control, stabilizing cable system movement after deployment

References

1.  Kruijff M, van der Heide EJ, Ockels WJ. Data analysis of a tethered SpaceMail experiment. Journal of Spacecraft and Rockets. 2009;46(6):1272-1287. DOI: 10.2514/1.41878
2.  Ekimovskaya AA, Ermakov VYu, Tufan A. Study of a rotating tethered space system depending on the tether tension force. Engineering Journal: Science and Innovation. 2025;(10):3. (In Russ.).  EDN TDCCMG
3.  Zhong R, Zhu ZH. Dynamics of Nanosatellite Deorbit by Bare Electrodynamic Tether in Low Earth Orbit. Journal of Spacecraft and Rockets. 2013;50(3):691–700. DOI: 10.2514/1.A32336
4.  Ohkawa Y, Kawamoto S, Okumura T, et al. Review of KITE – Electrodynamic tether experiment on the H-II Transfer Vehicle. Acta Astronautica. 2020;177(2):750–758. DOI: 10.1016/j.actaastro.2020.03.014
5. Beletskii VV, Levin EM. Dynamics of space cable systems. Moscow: Nauka; 1990. 329 p. (In Russ.).  
6. Chernov KS, Ivanov DS. Investigation of the motion of a group of four coupled spacecraft under the control of Lorentz forces. Cosmic Research. 2023;61(4):339–352. (In Russ.). DOI: 10.31857/S0023420623600022 EDN UMATAE
7. Zabolotnov YuM, Nazarova AA. Method of forming a triangular rotating tethered constellation of spacecraft using electromagnetic forces. Journal of Computer and Systems Sciences International. 2022;61(4):677-692. (In Russ.). DOI: 10.1134/s1064230722040141 EDN TBAFED
8. Kul'kov VM. Electrodynamics Tether System Design Parameter Analyze and Orbit Motion Control Modes Investigation. Aerospace MAI Journal. 2011;18(2):41–46. (In Russ.).  
9. Kulkov VM, Yegorov YuG, Tuzikov SA. Peculiarities of design for small-size space electrodynamic tether systems. Izvestiya RAN. Energetika. 2019(3):52–67. (In Russ.). DOI: 10.1134/S0002331019030117
10. Aslanov VS, Yudintsev VV. Parameters selection of space debris removal system with elastic elements by cable towing. Aerospace MAI Journal. 2018;25(1):7-17. (In Russ.).  
11. Yudintsev VV. Rotating space debris objects net capture dynamics. Aerospace MAI Journal. 2018;25(4):37-48. (In Russ.).  
12. Chen X, Sanmartin JR. Bare-tether cathodic contact through thermionic emission by low–work–function materials. 39th European Physical Society Conference on Plasma Physics & 16th International Congress on Plasma Physics (July 2–6, 2012; Stockholm, Sweden). Vol. 19:073508. DOI: 10.1063/1.4736987
13. Sánchez-Arriaga G, Bombardelli C, Chen X. Impact of Nonideal Effects on Bare Electrodynamic Tether Performance. Journal of Propulsion and Power. 2015;31(3):951–955. DOI: 10.2514/1.B35393
14. Sanmartin JR, Martinez-Sánchez M, Ahedo E. Bare wire anodes for electrodynamic tethers. Journal of Propulsion and Power. 1993;9(3):353–360. DOI: 10.2514/3.23629
15. Xie K, Liang F, Xia Q, et al. Power Generation on a Bare Electrodynamic Tether during Debris Mitigation in Space. International Journal of Aerospace Engineering. 2021. DOI: 10.1155/2021/8834196
16. Sanmartin JR, Chen X, Sánchez-Arriaga G. Analysis of Thermionic Bare Tether Operation Regimes in Passive Mode. Physics of Plasma. 2017;24(1):013515. DOI: 10.1063/1.4974764
17. Bystranova TA, Zabolotnov YM. On the possibility of determining the parameters of the ionosphere when removing a nanosatellite from orbit using an uninsulated conductive tether. Vestnik of Samara University. Aerospace and Mechanical Engineering. 2025;24(1):19-30. (In Russ.). DOI: 10.18287/2541-7533-2025-24-1-19-30
18. Menon C, Kruijff M, Vavonliotis A. Design and Testing of a Space Mechanism for Tether Deployment. Journal of Spacecraft and Rockets. 2007;44(4):927–939. DOI: 10.2514/1.23454
19. Voevodin PS, Zabolotnov YuM. Modeling and analysis of oscillations of electrodynamic tether system on orbit of earth satellite. Mathematical Models and Computer Simulations. 2017;29(6):21–34. (In Russ.).  
20. Voevodin PS, Zabolotnov YuM. Modeling the braking process of a nanosatellite using an electrodynamic cable system. Materialy XXI Mezhdunarodnoi konferentsii “Problemy upravleniya i modelirovaniya v slozhnykh sistemakh” (September 03–06, 2019; Samara). Samara: Ofort, 2019. Vol. 1. p. 232–237. (In Russ.).  
21. Zabolotnov YuM. Control of the deployment of an orbital tether system that consists of two small spacecraft. Cosmic Research. 2017;55(3):224-233. (In Russ.).  
22. Dong Z. Analysis of dynamics and motion control of low-orbital space tether system. Aerospace MAI Journal. 2018;25(1):84-91. (In Russ.).  
23. Okhotsimskii DE, Sikharulidze YuG. Fundamentals of space flight mechanics. Moscow: Nauka; 1990. 445 p. (In Russ.).