Libration control of bare electrodynamic tether for three-dimensional deployment


Various promising applications of electrodynamic tether have been proposed for space missions over the past decades. A crucial issue of these missions is to deploy an electrodynamic tether under a rapid and stable state. This paper aims to stabilize the libration motions of a bare electrodynamic tether during its three-dimensional deployment. The tethered system under consideration consists of a main-satellite and a sub-satellite connected to each other through a bare electrodynamic tether. A widely used dumbbell assumption considering the tether as rigid and inflexible is adopted to facilitate the dynamic modeling and analysis of the tethered system. A pair of active control laws is synthesized by simultaneously regulating the electric current and tether tension to achieve an efficient stabilization of the three-dimensional libration of the bare electrodynamic tether in the deployment process. Moreover, comparisons of three groups of numerical simulations are performed to evaluate the in uences of orbital inclinations and geomagnetic field models and the performance of the active control laws.

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  1. [1]

    Wen, H., Jin, D.P., Hu, H.Y. Advances in dynamics and control of tethered satellite systems. Acta Mechanica Sinica, 2008, 24(3): 229–241.

    Article  MATH  Google Scholar 

  2. [2]

    Carroll, J.A. Tether applications in space transportation. Acta Astronautica, 1986, 13(4): 165–174.

    Article  MATH  Google Scholar 

  3. [3]

    Colombo, G. Orbital transfer and release of tethered payloads. NASA Report, NASA–CR–170779, 1983.

    Google Scholar 

  4. [4]

    Cartmell, M., Ziegler, S. Experimental scale model testing of a motorised momentum exchange propulsion tether. In: Proceedings of the 37th Joint Propulsion Conference and Exhibit, 2001, AIAA: 3914.

    Google Scholar 

  5. [5]

    Kawamoto, S., Makida, T., Sasaki, F., Okawa, Y., Nishida, S. Precise numerical simulations of electrodynamic tethers for an active debris removal system. Acta Astronautica, 2006, 59(1–5): 139–148.

    Article  Google Scholar 

  6. [6]

    Sanmartin, J., Charro, M., Lorenzini, E., Garrett, H., Bombardelli, C., Bramanti, C. Electrodynamic tether at Jupiter-I: capture operation and constraints. IEEE Transactions on Plasma Science, 2008, 36(5): 2450–2458.

    Article  Google Scholar 

  7. [7]

    Puig-Suari, J., Longuski J.M., Tragesser, S.G., A tether sling for lunar and interplanetary exploration. Acta Astronautica, 1995, 36(6): 291–295.

    Article  MATH  Google Scholar 

  8. [8]

    Mantri P. Deployment dynamics of space tether systems. Ph.D. Dissertation. North Carolina State University, 2007.

    Google Scholar 

  9. [9]

    Samantha Roy, R.I., Hastings, D.E., Ahedo, E. Systems analysis of electrodynamic tethers. Journal of Spacecraft and Rockets, 1992, 29(3): 415–424.

    Article  Google Scholar 

  10. [10]

    Estes, R.D., Lorenzini, E.C., Sanmartin, J., Pelaez, J., Martinez-Sanchez, M., Johnson, C.L., Vas, I.E. Bare tethers for electrodynamic spacecraft propulsion. Journal of Spacecraft and Rockets, 2000, 37(2): 205–211.

    Article  Google Scholar 

  11. [11]

    Wen, H., Zhu, Z., Jin, D., Hu, H. Constrained tension control of a tethered space-tug system with only length measurement. Acta Astronautica, 2016, 119: 110–117.

    Article  Google Scholar 

  12. [12]

    Sanmartin, J.R., Martinez-Sanchez, M., Ahedo, E., Bare wire anodes for electrodynamic tethers. Journal of Propulsion and Power, 1993, 9(3): 353–360.

    Article  Google Scholar 

  13. [13]

    Sanmartin, J., Lorenzini E., Martinez-Sanchez, M., Electrodynamic tether applications and constraints. Journal of Spacecraft and Rockets, 2010, 47(3): 442–456.

    Article  Google Scholar 

  14. [14]

    Hoyt, R., Slostad, J., Barnes, I., Voronka, N., Lewis, M. Cost-effective end-of-mission disposal of LEO microsatellites: The Terminator Tape. In: Proceedings of the 24th Annual AIAA/USU Conference on Small Satellites, Technical Session X: Mission Enabling Technologies 1, 2010.

    Google Scholar 

  15. [15]

    Peláez, J., Lara, M. Periodic solutions in electrodynamic tethers on inclined orbits. Journal of Guidance, Control, and Dynamics, 2003, 26(3): 395–406.

    Article  Google Scholar 

  16. [16]

    Zhong, R., Zhu, Z.H. Libration dynamics and stability of electrodynamic tethers in satellite deorbit. Celestial Mechanics and Dynamical Astronomy, 2013, 116(3): 279–298.

    MathSciNet  Article  Google Scholar 

  17. [17]

    Steindl, A., Troger, H. Optimal control of deployment of a tethered subsatellite. Nonlinear Dynamics, 2003, 31(3): 257–274.

    MathSciNet  Article  MATH  Google Scholar 

  18. [18]

    Sun, G., Zhu, Z.H. Fractional-order tension control law for deployment of space tether system. Journal of Guidance, Control, and Dynamics, 2014, 37(6): 2057–2062.

    Article  Google Scholar 

  19. [19]

    Pradeep, S. A new tension control law for deployment of tethered satellites. Mechanics Research Communications, 1997, 24(3): 247–254.

    Article  MATH  Google Scholar 

  20. [20]

    Steindl, A. Optimal deployment of a tethered satellite using tension control. IFAC-PapersOnLine, 2015, 48(1): 53–54.

    Article  Google Scholar 

  21. [21]

    Wen H, Zhu, Z., Jin, D., Hu, H. Tension control of space tether via online quasi-linearization iterations. Advances in Space Research, 2016, 57(3): 754–763.

    Article  Google Scholar 

  22. [22]

    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.

    Article  Google Scholar 

  23. [23]

    Li, G., Zhu, Z.H., Cain, J., Newland, F., Czekanski, A. Libration control of bare electrodynamic tethers considering elastic-thermal-electrical coupling. Journal of Guidance, Control, and Dynamics, 2016, 36(3): 642–654.

    Article  Google Scholar 

  24. [24]

    Takeichi, N. Practical operation strategy for deorbit of an electrodynamic tethered system. Journal of Spacecraft and Rockets, 2006, 43(6): 1283–1288.

    Article  Google Scholar 

  25. [25]

    Wen, H., Jin, D., Hu, H. Three-dimensional deployment of electro-dynamic tether via tension and current control with constraints. Acta Astronautica, 2016, 129: 253–259.

    Article  Google Scholar 

  26. [26]

    Zhang, J., Zhu, Z.H., Sun, Z.W. Reduction of libration angle in electrodynamic tether deployment by Lorentz force. Journal of Guidance, Control, and Dynamics, 2017, 40(1):164–169.

    Article  Google Scholar 

  27. [27]

    Tahara, H., Nishio, H., Onishi, T. Basic study of electron collection by a bare-tether satellite. Vacuum, 2004, 73(3–4): 455–460.

    Article  Google Scholar 

  28. [28]

    Peláez, J., Sanjurjo, M. Generator regime of self- balanced electrodynamic bare tethers. Journal of Spacecraft and Rockets, 2006, 43(6): 1359–1369.

    Article  Google Scholar 

  29. [29]

    Li, G., Zhu Z., Ruel, S., Meguid, S.A. Multiphysics elastodynamic finite element analysis of space debris deorbit stability and efficiency by electrodynamic tethers. Acta Astronautica, 2017, 137: 320–333.

    Article  Google Scholar 

  30. [30]

    Anguero V.M, Adamo R.C. Space applications of spindt cathode field emission arrays. In: Proceedings of the 6th Spacecraft Charging Conference, 1998: 347–352.

    Google Scholar 

  31. [31]

    Williams, P., Blanksby, C., Trivailo, P. The use of electromagnetic Lorentz forces as a tether control actuator. In: Proceedings of the 34th COSPAR Scientific Assembly, 2002.

    Google Scholar 

  32. [32]

    Pelaez, J., Lorenzini, E.C., Lopez-Rebollal, O., Ruiz, M. A new kind of dynamic instability in electrodynamic tethers. Advances in the Astronautical Sciences, 2000, 105: 1367–1386.

    Google Scholar 

  33. [33]

    Barton, C.E. International geomagnetic reference field: the seventh generation. Journal of Geomagnetism and Geoelectricity, 1997, 49(2–3): 123–148.

    Article  Google Scholar 

  34. [34]

    Li, G.Q., Zhu, Z. Dynamic modeling of space electrodynamic tether system using the nodal position finite element and symplectic integration. In: Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, 2014.

    Google Scholar 

  35. [35]

    Davis, J. Mathematical modeling of Earth’s magnetic field. Technical Note, 2004: 1157–1163.

    Google Scholar 

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This work was supported by the National Natural Science Foundation of China (Grant No. 11772150), by the Civil Aerospace Pre-research Project of China, and by the Natural Science Foundation of Hunan Province (Grant No. 2016JJ3141).

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Correspondence to Hao Wen.

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Caoqun Luo received his bachelor degree from Nanjing University of Aeronautics and Astronautics, in 2015. Currently, he is a Ph.D. candidate from Nanjing University of Aeronautics and Astronautics majoring in dynamics and control. His current research interests are deployment, retrieval of space tether, and deorbit of space debris.

Hao Wen is a professor in dynamics and control at the Department of Aerospace Engineering, from Nanjing University of Aeronautics and Astronautics. He earned his bachelor and Ph.D. degrees from Nanjing University of Aeronautics and Astronautics. in 2002 and in 2009, respectively. His doctoral research has won the National Excellent Doctoral Dissertation Award (Top 100) from China, in 2011. He stayed at the York University in Canada as a visiting scholar from November,in 2014 to November, in 2015. Currently, he is an IEEE member and a senior AIAA member. His area of expertise is in the dynamic modeling, motion/vibration control, and ground-based experiments of space structures and spacecraft. His current research interests are space tether, in-orbit autonomous assembly, and deployable space structure.

Dongping Jin is a professor in applied mechanics at the Department of Aerospace Engineering, from Nanjing University of Aeronautics and Astronautics. He received his Ph.D. and B.S. degrees from Tianjin University. His research area ranges over the topics of space tether, structural dynamics, and nonlinear dynamics.

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Luo, C., Wen, H. & Jin, D. Libration control of bare electrodynamic tether for three-dimensional deployment. Astrodyn 2, 187–199 (2018).

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  • bare electrodynamic
  • tether
  • deployment
  • three-dimensional
  • libration
  • control