Nonlinear Dynamics

, Volume 74, Issue 4, pp 1113–1131 | Cite as

Stability and control of tethered satellite with chemical propulsion in orbital plane

  • Liang Sun
  • Guowei Zhao
  • Hai Huang
Original Paper


The tethered satellite with chemical propulsion has broad application prospects in the disposal of abandoned satellites, the orbital rescue of spacecrafts, and the transportation of space supplies, which is completely different from the traditional applications of tethered satellites. Therefore, new research on its dynamics, stability, and control becomes useful and interesting. In this article, based on a dumbbell model of tethered satellite, the dynamics equations of tethered system in orbital maneuvering are established. Furthermore, according to the definitions of transversal and radial propulsive coefficients, analytical solutions of the equilibrium position for librational angle are derived during maneuvering in orbital plane; meanwhile, the effects of propulsive coefficients on librational stability are analyzed, which provides a basis for a selection of expected attitude trajectory. Then, a method of hierarchical sliding-mode tension control is presented to track the expected in-plane angle. This method can address the underactuated problem of tethered systems without either complex coordinate transformation for the system state model or constraint equation restrictions. During orbital flight, in-plane and out-of-plane angles are decoupled, so the tether tension control cannot be conducted to inhibit the out-of-plane angle. To solve this problem, the binormal component of thrust acceleration normal to the orbital plane is adopted as a control variable, and a feedback linearization-based thrust controller is designed to damp out the out-of-plane angle. Afterwards, orbital transfer cases between two circular orbits are studied to demonstrate the effectiveness of the tethered satellite with chemical propulsion. Numerical simulation results indicate that the stability of librational angles has a close relation to propulsive coefficients, and distributions of stable centers and unstable saddle points are totally different on both sides of bifurcation point. In addition, tracking control requirements for tethered satellite are guaranteed by designed controllers, which ensure flight safety in orbital maneuvering.


Tethered satellite Stability Sliding mode control Maneuvering 



This work was supported by the Fundamental Research Funds for the Central Universities.


  1. 1.
    Manakala, K.K., Agrawal, S.K.: Dynamic modeling and simulation of impact in Tether/Gripper systems. Multibody Syst. Dyn. 11(3), 235–250 (2004) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Johnson, N.L.: Developments in space debris mitigation policy and practices. Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 221(6), 907–909 (2007) CrossRefGoogle Scholar
  3. 3.
    Williams, P.: Optimal orbital maneuvers using electrodynamic tethers. Adv. Astronaut. Sci. 120(2), 1671–1690 (2005) Google Scholar
  4. 4.
    Corsi, J., Iess, L.: Stability and control of electrodynamic tethers for deorbiting applications. Acta Astronaut. 48(5–18), 491–501 (2001) CrossRefGoogle Scholar
  5. 5.
    Peláez, J., Lorenzini, E.C., López-Rebollal, O., et al.: A new kind of dynamic instability in electro-dynamic tethers. J. Astronaut. Sci. 48(4), 449–476 (2000) Google Scholar
  6. 6.
    Pearson, J., Carroll, J., Levin, E., et al.: Overview of the electrodynamic delivery express. In: 39th AIAA/ASME/SAE ASEE Joint Propulsion Conference and Exhibition, Huntsville, AL, 20–23 July 2003 Google Scholar
  7. 7.
    Krupa, M., Poth, W., Schagerl, M.: Modelling dynamics and control of tethered satellite systems. Nonlinear Dyn. 43(1–2), 73–96 (2006) MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Williams, P.: Deployment/retrieval optimization for flexible tethered satellite systems. Nonlinear Dyn. 52(1–2), 159–179 (2008) CrossRefMATHGoogle Scholar
  9. 9.
    Jin, D.P., Wen, H.: Nonlinear resonance of a subsatellite on a short constant tether. Nonlinear Dyn. 71(3), 479–488 (2013) MathSciNetCrossRefGoogle Scholar
  10. 10.
    Misra, A.K., Modi, V.J.: Dynamic and control of tethered satellite system. Acta Astronaut. 63(11–12), 1169–1177 (2008) CrossRefGoogle Scholar
  11. 11.
    Cho, S., McClamroch, N.H.: Optimal orbit transfer of a spacecraft with fixed length tether. J. Astronaut. Sci. 51(2), 195–204 (2003) MathSciNetGoogle Scholar
  12. 12.
    Sun, L., Zhao, G.W., Huang, H.: Tether-dragging maneuver strategy and tether control method. In: Proceedings of 2010 Asia-Pacific International Symposium on Aerospace Technology (CSAA), Xi’an, pp. 719–723 (2010) Google Scholar
  13. 13.
    Zhao, G.W., Sun, L., Tan, S.P., Huang, H.: Librational characteristics of a dumbbell modeled tethered satellite under small, continuous, constant thrust. Proc. Inst. Mech. Eng., Part G: J Aerospace Eng. (2012) Google Scholar
  14. 14.
    Sun, L., Zhao, G.W., Huang, H., et al.: Analysis of librational and vibrational characteristics for tethered systems during orbital transfer in plane. Acta Aeronaut. Astronaut. Sin. 33(7), 1245–1254 (2012) Google Scholar
  15. 15.
    Wen, H., Jin, D.P., Hu, H.Y.: Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations. Nonlinear Dyn. 51(4), 501–514 (2008) MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Qian, D.W., Liu, X.J., Yi, J.Q.: Adaptive control based on hierarchical sliding mode of under-actuated systems. In: Proceedings of 2012 IEEE International Conference on Mechatronics and Automation, Chengdu, 5–8 August, pp. 1050–1055 (2012) CrossRefGoogle Scholar
  17. 17.
    Wang, W., Liu, X.D., Yi, J.Q.: Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems. IET Control Theory Appl. 1(1), 163–172 (2007) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Beihang University BeijingBeijingChina

Personalised recommendations