Tether Deformation of Spinning Electrodynamic Tether System and Its Suppression with Optimal Controller
Publication: Journal of Aerospace Engineering
Volume 34, Issue 2
Abstract
Spinning electrodynamic tether systems are considered ideal platforms for payload transportation, removal of space debris, artificial gravity, and so on, for they provide a propellantless solution to orbital maneuver and good centrifugal stability. However, all spinning electrodynamic tether systems have to transition into a spinning state from the equilibrium state, during which tethers are likely to become deformed because of Lorentz forces. This paper studies tether deformation during such a transition process. Two open-loop programs are proposed in the Lagrangian model as the reference trajectories of acceleration under different mission backgrounds. The dynamic characteristic of tether is studied in a more accurate model with distributed parameters (bead model). Considering the significant tether deformation in the case of high electrical current, an optimal controller is proposed based on Bellman dynamic programming. Numerical results indicate that the proposed control laws can ensure a safe transition of the proposed tether system into a spin and limit tether deformation to a reasonable level.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors gratefully acknowledge the support of the Shaanxi Science and Technology Program, China (2017KW-ZD-04), the National Natural Science Foundation of China (51808447), and the Natural Science Basic Research Plan in Shaanxi Province of China (2020JQ-209). The research of H. Lu is also funded by the Chinese Scholarship Council.
References
Aslanov, V. S., and A. S. Ledkov. 2012. Dynamics of tethered satellite systems. Oxford, UK: Woodhead.
Beletsky, V. V., and E. M. Levin. 1993. Dynamic of space tether systems. San Diego: American Astronautical Society.
Bellman, R. E., and S. E. Dreyfus. 2015. Vol. 2050 of Applied dynamic programming. Princeton, NJ: Princeton University Press.
China National Standardization Management Committee. 2017. Round wire concentric lay overhead electrical stranded conductors. GB/T 1179-2017. Beijing: China National Standardization Management Committee.
Cosmo, M. L., and E. C. Lorenzini. 1997. Tethers in space handbook. 3rd ed. Washington, DC: National Aeronautics and Space Administration.
French, D. B., and A. P. Mazzoleni. 2009. “Near-Earth object threat mitigation using a tethered ballast mass.” J. Aerosp. Eng. 22 (4): 460–465. https://doi.org/10.1061/(ASCE)0893-1321(2009)22:4(460).
Gou, X. W., A. J. Li, H. C. Tian, C. Q. Wang, and H. S. Lu. 2018. “Overload control of artificial gravity facility using spinning tether system for high eccentricity transfer orbits.” Acta Astronaut. 147 (Jun): 383–392. https://doi.org/10.1016/j.actaastro.2018.03.005.
Hoyt, R. P. 2001. Moon & mars orbiting spinning tether transport. Washington, DC: National Aeronautics and Space Administration.
Huang, P., F. Zhang, J. Cai, D. Wang, Z. Meng, and J. Guo. 2017. “Dexterous tethered space robot: Design, measurement, control, and experiment.” IEEE Trans. Aerosp. Electron. Syst. 53 (3): 1452–1468. https://doi.org/10.1109/TAES.2017.2671558.
Ismail, N. A., and M. P. Cartmell. 2016. “Three dimensional dynamics of a flexible motorised momentum exchange tether.” Acta Astronaut. 120 (Mar–Apr): 87–102. https://doi.org/10.1016/j.actaastro.2015.12.001.
Kang, J., and Z. H. Zhu. 2019. “A unified energy-based control framework for tethered spacecraft deployment.” Nonlinear Dyn. 95 (2): 1117–1131. https://doi.org/10.1007/s11071-018-4619-x.
Lanoix, E. L., A. K. Misra, V. J. Modi, and G. Tyc. 2005. “Effect of electromagnetic forces on the orbital dynamics of tethered satellites.” J. Guidance Control Dyn. 28 (6): 1309–1315. https://doi.org/10.2514/1.1759.
Levin, E. M. 2007. Vol. 126 of Dynamic analysis of space tether missions. San Diego: Univelt.
Liu, L. 1995. “To outer space on a tether.” J. Aerosp. Eng. 8 (2): 126–128. https://doi.org/10.1061/(ASCE)0893-1321(1995)8:2(126).
Lorenzini, E. C., M. L. Cosmo, M. Kaiser, M. E. Bangham, D. J. Vonderwell, and L. Johnson. 2000. “Mission analysis of spinning systems for transfers from low orbits to geostationary.” J. Spacecraft Rockets 37 (2): 165–172. https://doi.org/10.2514/2.3562.
Lu, H., A. Li, C. Wang, and Y. M. Zabolotnov. 2018. “Impact analysis and adaptive sliding mode control for cislunar payload transportation using spinning tether system.” Aircr. Eng. Aerosp. Technol. 90 (8): 1168–1179. https://doi.org/10.1108/AEAT-02-2017-0067.
Lu, H., A. Li, C. Wang, and Y. M. Zabolotnov. 2019. “Stability analysis and motion control of spinning electrodynamic tether system during transition into spin.” Acta Astronaut. 177 (Dec): 871–881. https://doi.org/10.1016/j.actaastro.2019.11.032.
Sánchez-Arriaga, G., C. Bombardelli, and X. Chen. 2015. “Impact of nonideal effects on bare electrodynamic tether performance.” J. Propul. Power 31 (3): 951–955. https://doi.org/10.2514/1.B35393.
Van Pelt, M. 2009. Space tethers and space elevators. New York: Springer.
Voevodin, P. S., and Y. M. Zabolotnov. 2017. “Modeling and analysis of oscillations of electrodynamic tether system on orbit of Earth satellite.” [In Russian.] Matematicheskoe modelirovanie 29 (6): 21–34.
Voevodin, P. S., and Y. M. Zabolotnov. 2019. “Stabilizing the motion of a low-orbit electrodynamic tether system.” J. Comput. Syst. Sci. Int. 58 (2): 270–285. https://doi.org/10.1134/S1064230719020175.
Wang, C., G. Li, Z. H. Zhu, and A. Li. 2016. “Mass ratio of electrodynamic tether to spacecraft on deorbit stability and efficiency.” J. Guidance Control Dyn. 39 (9): 2192–2198. https://doi.org/10.2514/1.G000429.
Wen, H., D. Jin, and H. Hu. 2016. “Three-dimensional deployment of electro-dynamic tether via tension and current control with constraints.” Acta Astronaut. 129 (Dec): 253–259. https://doi.org/10.1016/j.actaastro.2016.09.019.
Williams, P. 2006. “Dynamics and control of spinning tethers for rendezvous in elliptic orbits.” J. Vib. Control 12 (7): 737–771. https://doi.org/10.1177/1077546306065710.
Williams, P. 2012. “Optimal control of electrodynamic tether orbit transfers using timescale separation.” J. Guidance Control Dyn. 33 (1): 88–98. https://doi.org/10.2514/1.45250.
Zabolotnov, Y. M. 2017. “Dynamics of the formation of a rotating orbital tether system with the help of electro-thruster.” Procedia Eng. 185: 261–266. https://doi.org/10.1016/j.proeng.2017.03.339.
Zhong, R., and Z. H. Zhu. 2011. “Dynamic analysis of deployment and retrieval of tethered satellites using a hybrid hinged-rod tether model.” Int. J. Aerosp. Lightweight Struct. 1 (2): 239–259. https://doi.org/10.3850/S2010428611000146.
Zhong, R., and Z. H. Zhu. 2012. “Long-term libration dynamics and stability analysis of electrodynamic tethers in spacecraft deorbit.” J. Aerosp. Eng. 27 (5): 04014020. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000310.
Zhong, R., and Z. H. Zhu. 2014. “Optimal control of nanosatellite fast deorbit using electrodynamic tether.” J. Guidance Control Dyn. 37 (4): 1182–1194. https://doi.org/10.2514/1.62154.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 34 • Issue 2 • March 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 15, 2020
Accepted: Sep 8, 2020
Published online: Jan 13, 2021
Published in print: Mar 1, 2021
Discussion open until: Jun 13, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.