Graphical Abstract
![](https://wqketang.oss-cn-beijing.aliyuncs.com/zip-unzip/zip-77f801d3-9b72-435e-a20b-451f55a1b62c/astrodynamics-8-2-237/files/astrodynamics-8-2-237-FE1.jpg?Expires=1725755668&OSSAccessKeyId=STS.NT5eViCkqzTYdbfdqxMkjpyyq&Signature=wB6fC6oM2ouUowPoLB8iji9QPJw%3D&security-token=CAISywJ1q6Ft5B2yfSjIr5eALuzdrrRQzZayZkTXgHEtQeRGn7zSkzz2IHtKenhsBOsbtfk1mG5W5%2FgZlqJ9SptIAEfJa9d99MzUP%2FpFltCT1fau5Jko1beHewHKeTOZsebWZ%2BLmNqC%2FHt6md1HDkAJq3LL%2Bbk%2FMdle5MJqP%2B%2FUFB5ZtKWveVzddA8pMLQZPsdITMWCrVcygKRn3mGHdfiEK00he8TouufTinpHMskGA1Aell7Mvyt6vcsT%2BXa5FJ4xiVtq55utye5fa3TRYgxowr%2Fwo0v0YpGya5YzHXwcPskvdKZbo78UqLQlla6w%2BGqFJqvPxr%2Fp8t%2Fx5fWJKAezhVgs8cVM8JOjIqKOscIsiJsO71SmqFV55c8Fdm%2BgUooJVgIMhTnduUfAPJAGOxzJitP%2BUVGGphr60TEnBL4rB5MUctfzRp75SXVPUTzDnGoABjuNLcf76FQN6p3t%2BSlCg%2FxR5C72RIk78k%2BUi44L9ZBmFT6F8GV7aXA52D1Ps56knKF6PAnhRivwyTxgsolycBfvccb3t5jGJ24SgY0aYosAECutxAo7sJhSwlwZvGwGDZJsop1vGiZ8eN1MbtZeRRuMeaZ2I%2BQo%2BnVP6Cf%2F0pDsgAA%3D%3D)
Discover the SciOpen Platform and Achieve Your Research Goals with Ease.
This study focuses on stabilizing the libration dynamics of an electrodynamic tether system (EDTS) using generalized torques induced by the Lorentz force. In contrast to existing numerical optimization methods, a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only. The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS. To enhance the robustness of the proposed controller, multiple perturbations of the orbital dynamics, modeling uncertainties, and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously, such that these perturbations are well compensated for during the control design of the EDTS. Furthermore, a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law. The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.
Jablonski, A. M., Scott, R. L. Deorbiting of low Earth orbit (LEO) microsatellites. Canadian Aeronautics and Space Journal, 2009, 55(2): 55–67.
Forward, R. L., Hoyt, R. P., Uphoff, C. W. Terminator tether: A spacecraft deorbit device. Journal of Spacecraft and Rockets, 2000, 37(2): 187–196.
Zhong, R., Zhu, Z. H. Optimal control of nanosatellite fast deorbit using electrodynamic tether. Journal of Guidance, Control, and Dynamics, 2014, 37(4): 1182–1194.
Zhong, R., Zhu, Z. H. Optimal current switching control of electrodynamic tethers for fast deorbit. Journal of Guidance, Control, and Dynamics, 2014, 37(5): 1501–1511.
Ma, X., Wen, H. Deep learning for deorbiting control of an electrodynamic tether system. Acta Astronautica, 2023, 202: 26–33.
Cosmo, M. L., Lorenzini, E. C. Tethers in Space Handbook, 3rd edn. Cambridge, Massachusetts, USA: Smithsonian Astrophysical Observatory, 1997.
Wen, H., Jin, D., Hu, H. Advances in dynamics and control of tethered satellite systems. Acta Mechanica Sinica, 2008, 24(4): 473.
Huang, P., Zhang, F., Chen, L., Meng, Z., Zhang, Y., Liu, Z., Hu, Y. A review of space tether in new applications. Nonlinear Dynamics, 2018, 94: 1–19.
Peláez, J., Andrés, Y. N. Dynamic stability of electrodynamic tethers in inclined elliptical orbits. Journal of Guidance, Control, and Dynamics, 2005, 28(4): 611–622.
Williams, P. Libration control of electrodynamic tethers using predictive control with time-delayed feedback. Journal of Guidance, Control, and Dynamics, 2009, 32(4): 1254–1268.
Williams, P. Optimal control of electrodynamic tether orbit transfers using timescale separation. Journal of Guidance, Control, and Dynamics, 2010, 33(1): 88–98.
Kojima, H., Sugimoto, T. Switching delayed feedback control for an electrodynamic tether system in an inclined elliptic orbit. Acta Astronautica, 2010, 66(7–8): 1072–1080.
Li, G., Zhu, Z. H., Meguid, S. A. Libration and transverse dynamic stability control of flexible bare electrodynamic tether systems in satellite deorbit. Aerospace Science and Technology, 2016, 49: 112–129.
Liu, J., Zhu, Z. H., Li, G., Zhan, X. Fuzzy-based continuous current control of electrodynamic tethers for stable and efficient orbital boost. Aerospace Science and Technology, 2021, 118: 106999.
Ma, Z., Sun, G. Adaptive sliding mode control of tethered satellite deployment with input limitation. Acta Astronautica, 2016, 127: 67–75.
Xu, S., Sun, G., Ma, Z., Li, X. Fractional-order fuzzy sliding mode control for the deployment of tethered satellite system under input saturation. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(2): 747–756.
Ma, Z., Huang, P. Discrete-time sliding mode control for deployment of tethered space robot with only length and angle measurement. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(1): 585–596.
Chen, S., Li, A., Wang, C. Liu, C. Adaptive sliding mode control for deployment of electro-dynamic tether via limited tension and current. Acta Astronautica, 2020, 177: 842–852.
Li, X., Sun, G., Han, S., Shao, X. Fractional-order nonsingular terminal sliding mode tension control for the deployment of space tethered satellite. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(5): 2759–2770.
Li, Y., Li, A., Wang, C. Back-stepping sliding mode control for libration control of large swing angles of electrodynamic tether system. Advances in Space Research, 2023, 72(2): 231–242.
Wen, H., Zhu, Z. H., Jin, D., Hu, H. Model predictive control with output feedback for a deorbiting electrodynamic tether system. Journal of Guidance, Control, and Dynamics, 2016, 39(10): 2455–2460.
Wen, H., Zhu, Z. H., Jin, D., Hu, H. Constrained tension control of a tethered space-tug system with only length measurement. Acta Astronautica, 2016, 119: 110–117.
Sanner, R. M., Slotine, J. E. Gaussian networks for direct adaptive control. IEEE Transactions on Neural Networks, 1992, 3(6): 837–863.
Bajodah, A. H. Asymptotic perturbed feedback linearisation of underactuated Euler's dynamics. International Journal of Control, 2009, 82(10): 1856–1869.