Skip to main content
SpringerLink
Log in

Electrodynamic attitude stabilization of a satellite in the Konig frame

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper deals with a satellite in a circular near-Earth orbit. The satellite is equipped with an electrodynamic attitude control system based on Lorentz and magnetic torque properties. The gravitational disturbing torque acting on the satellite attitude dynamics is taken into account since it is the largest disturbing torque. The possibility of using electrodynamic attitude control system for satellite three-axis stabilization in the Konig frame is analyzed. By the use of the Lyapunov direct method, conditions under which electrodynamic control solves the problem for a dynamically symmetric satellite are obtained. The procedure for the successive constructing of Lyapunov functions is suggested. On the basis of the analysis of nonlinear differential equations system, the domain of the control parameter values is found for which one can guarantee the asymptotic stability of the programmed satellite motion. The results of a numerical simulation are presented to demonstrate the effectiveness of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Wertz, J.R.: Spacecraft Attitude Determination and Control. D. Reidel Publishing Co., Dordrecht (1985)

  2. Hughes, P.C.: Spacecraft Attitude Dynamics. Wiley, New York (1986)

    Google Scholar 

  3. Smirnov, G.V., Ovchinnikov, M., Miranda, F.: On the magnetic attitude control for spacecraft via the e-strategies method. Acta Astronaut. 63, 690–694 (2008)

    Article  Google Scholar 

  4. Battagliere, M.L., Santoni, F., Piergentili, F., Ovchinnikov, M., Graziani, F.: Passive magnetic attitude stabilization system of the EduSAT microsatellite. Proc. Inst. Mech. Eng. G J. Aerosp. Eng. 224, 1097 (2010)

    Article  Google Scholar 

  5. Wisniewski, R.: Linear time-varying approach to satellite attitude control using only electromagnetic actuation. J. Guid. Control Dyn. 23, 640–647 (2000)

    Article  Google Scholar 

  6. Guelman, M., Waller, R., Shiryaev, A., Psiaki, M.: Design and testing of magnetic controllers for Satellite stabilization. Acta Astronaut. 56, 231–239 (2005)

    Article  Google Scholar 

  7. Ovchinnikov, M., Roldugin, D., Penkov, V.: Three-axis active magnetic attitude control asymptotical study. Acta Astronaut. 110, 279–286 (2015)

    Article  Google Scholar 

  8. Psiaki, M.L.: Nanosatellite attitude stabilization using passive aerodynamics and active magnetic torquing. J. Guid. Control Dyn. 27, 347–355 (2004)

    Article  Google Scholar 

  9. Kumar, K.D., Tahk, M.J., Bang, H.C.: Satellite attitude stabilization using solar radiation pressure and magnetotorquer. Control Eng. Pract. 17, 267–279 (2009)

    Article  Google Scholar 

  10. Sussingham, J.C., Watkins, S.A., Cocks, F.H.: Forty years of development of active systems for radiation protection of spacecraft. J. Astronaut. Sci. 47, 165–175 (1999)

    Google Scholar 

  11. Trukhanov, K.A., Ryabova, T.Ya., Morozov, D.Kh: Active Shielding of Spacecraft (in Russian). Atomizdat, Moscow (1970)

    Google Scholar 

  12. Joshi, R.P., Qiu, H., Tripathi, R.K.: Configuration studies for active electrostatic space radiation shielding. Acta Astronaut. 88, 138–145 (2013)

    Article  Google Scholar 

  13. Tikhonov, A.A.: Effect of charge asymmetry on the rotary motion of a shielded body in the geomagnetic field. Leningr. Univ. Mech. Bull. 4, 37–43 (1987)

    Google Scholar 

  14. Tikhonov, A.A.: On the nonlinear resonance oscillation of a charged body under conditions of time-varying magnetic field. Part 1. Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya 3, 58–65 (1992)

  15. Tikhonov, A.A.: On nonlinear resonance oscillation of charged solid body under conditions of time-varying magnetic field. Part 2. Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya 4, 86–91 (1992)

  16. Tikhonov, A.A.: Patent RU: No 2159201—C2 on the invention. The method of attitude control of artificial earth’s satellite. IPC 7 B64 G 1/38, 1/32, No 98120769, Date of priority 29.10.1998

  17. Petrov, K.G., Tikhonov, A.A.: Patent RU: No 2191146—C1 on the invention. The method of semipassive attitude stabilization of artificial earth’s satellite and device for it’s implementation. IPC 7 B64 G 1/32, 1/38, No 2001107811, Date of priority 16.03.2001

  18. Tikhonov, A.A.: A method of semipassive attitude stabilization of a spacecraft in the geomagnetic field. Cosmic Res. 41, 63–73 (2003)

    Article  Google Scholar 

  19. Antipov, K.A., Tikhonov, A.A.: Parametric control in the problem of spacecraft stabilization in the geomagnetic field. Autom. Remote Control 68, 1333–1345 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Tikhonov, A.A., Spasic, D.T., Antipov, K.A., Sablina, M.V.: Optimizing the electrodynamical stabilization method for a man-made Earth satellite. Autom. Remote Control 72, 1898–1905 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  21. Yamakawa, H., Hachiyama, S., Bando, M.: Attitude dynamics of a pendulum-shaped charged satellite. Acta Astronaut. 70, 77–84 (2012)

    Article  Google Scholar 

  22. Aleksandrov, A.Yu., Tikhonov, A.A.: Electrodynamic stabilization of Earth-orbiting satellites in equatorial orbits. Cosmic Res. 50, 313–318 (2012)

    Article  Google Scholar 

  23. Aleksandrov, A.Yu., Tikhonov, A.A.: Monoaxial electrodynamic stabilization of Earth satellite in the orbital coordinate system. Autom. Remote Control 74, 1249–1256 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  24. Antipov, K.A., Tikhonov, A.A.: On satellite electrodynamic attitude stabilization. Aerosp. Sci. Technol. 33, 92–99 (2014)

    Article  Google Scholar 

  25. Abdel-Aziz, Y.A., Shoaib, M.: Numerical analysis of the attitude stability of a charged spacecraft in the Pitch-Roll-Yaw directions. Int. J. Aeronaut. Space Sci. 15, 82–90 (2014)

    Google Scholar 

  26. Peck, M.A.: Prospects and challenges for Lorentz-augmented orbits. In: Proceedings of the AIAA Guidance, Navigation, and Control Conference, SanFrancisco, CA, vol 3, pp 1631–1646. (2005)

  27. Streetman, B., Peck, M.A.: New synchronous orbits using the geomagnetic Lorentz force. J. Guid. Control. Dyn. 30, 1677–1690 (2007)

    Article  Google Scholar 

  28. Atchison, J.A., Peck, M.A.: Length scaling in spacecraft dynamics. J. Guid. Control. Dyn. 34, 231–246 (2011)

    Article  Google Scholar 

  29. Gangestad, J.W., Pollock, G.E., Longuski, J.M.: Analytical expressions that characterize propellantless capture with electrostatically charged spacecraft. J. Guid. Control. Dyn. 34, 247–257 (2011)

    Article  Google Scholar 

  30. Pollock, G.E., Gangestad, J.W., Longuski, J.M.: Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations. Acta Astronaut. 68, 204–217 (2011)

  31. Chao, P., Yang, G.: Lorentz force perturbed orbits with application to J2-invariant formation. Acta Astronaut. 77, 12–28 (2012)

  32. Tsujii, S., Bando, M., Yamakawa, H.: Spacecraft formation flying dynamics and control using the geomagnetic lorentz force. J. Guid. Control. Dyn. 36, 136–148 (2013)

    Article  Google Scholar 

  33. Huang, X., Yan, Y., Zhou, Y.: Dynamics and control of spacecraft hovering using the geomagnetic Lorentz force. Adv. Space Res. 53, 518–531 (2014)

    Article  Google Scholar 

  34. Zubov, V.I.: Theorie de la Commande (in French). Mir, Moscow (1978)

    Google Scholar 

  35. Smirnov, E.Ya.: Control of rotational motion of a free solid by means of pendulums. Mech. Solids 15, 1–5 (1980)

    Google Scholar 

  36. Smirnov, E.Ya.: Problems of stabilization of nonstationary systems with incomplete feedback. Autom. Remote Control 35, 1725–1733 (1974)

    MATH  Google Scholar 

  37. Meehan, P.A., Asokanthan, S.F.: Control of chaotic motion in a spinning spacecraft with a circumferential nutational damper. Nonlinear Dyn. 17, 269–284 (1998)

    Article  MATH  Google Scholar 

  38. El-Gohary, A.: On the control of programmed motion of a rigid containing moving masses. Int. J. Non-Linear Mech. 35, 27–35 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  39. Hu, Q.L.: Sliding mode maneuvering control and active vibration damping of three-axis stabilized flexible spacecraft with actuator dynamics. Nonlinear Dyn. 52, 227–248 (2008)

    Article  MATH  Google Scholar 

  40. Hu, Q.L.: Robust adaptive sliding mode attitude maneuvering and vibration damping of three-axis-stabilized flexible spacecraft with actuator saturation limits. Nonlinear Dyn. 55, 301–321 (2009)

    Article  MATH  Google Scholar 

  41. Hu, Q.L., Xiao, B.: Fault-tolerant sliding mode attitude control for flexible spacecraft under loss of actuator effectiveness. Nonlinear Dyn. 64, 13–23 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  42. Hu, Q.L., Li, B., Zhang, A.: Robust finite-time control allocation in spacecraft attitude stabilization under actuator misalignment. Nonlinear Dyn. 73, 53–71 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  43. Zhang, R., Qiao, J., Li, T., Guo, L.: Robust fault-tolerant control for flexible spacecraft against partial actuator failures. Nonlinear Dyn. 76, 1753–1760 (2014)

    Article  MathSciNet  Google Scholar 

  44. Martynyuk, A.A., Lakshmikantham, V., Leela, S.: Stability Analysis of Nonlinear Systems. Marcel Dekker, New York (1989)

    MATH  Google Scholar 

  45. Rauschenbakh, B.V., Ovchinnikov, M.Yu., McKenna-Lawlor, S.: Essential Spaceflight Dynamics and Magnetospherics. Kluwer & Microcosm Publ, New York (2003)

    Google Scholar 

  46. Shuster, M.D.: A survey of attitude representations. J. Astronaut. Sci. 41, 439–517 (1993)

    MathSciNet  Google Scholar 

  47. Bauchau, O.A., Trainelli, L.: The vectorial parameterization of rotation. Nonlinear Dyn. 32, 71–92 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  48. Schaub, H., Junkins, J.L.: Analytical Mechanics of Space Systems. American Institute of Aeronautics & Astronautics, Reston, Virginia (2009)

    MATH  Google Scholar 

  49. Khalil, H.K.: Nonlinear Systems. Prentice-Hall, Upper Saddle River, NJ (2002)

    MATH  Google Scholar 

Download references

Acknowledgments

The reported study was supported by the St. Petersburg State University, Project No. 9.38.674.2013 and by the Russian Foundation for Basic Research, Grant Nos. 13-01-00347-a and 13-01-00376-a.

Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics and Processes of Control, Saint Petersburg State University, Universitetsky pr., 35, Stary Peterhof, 198504, Saint Petersburg, Russia

    A. Yu. Aleksandrov & A. V. Platonov

  2. Faculty of Mathematics and Mechanics, Saint Petersburg State University, Universitetsky pr., 28, Stary Peterhof, 198504, Saint Petersburg, Russia

    K. A. Antipov & A. A. Tikhonov

Authors
  1. A. Yu. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. A. Antipov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Platonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. A. Tikhonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Aleksandrov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aleksandrov, A.Y., Antipov, K.A., Platonov, A.V. et al. Electrodynamic attitude stabilization of a satellite in the Konig frame. Nonlinear Dyn 82, 1493–1505 (2015). https://doi.org/10.1007/s11071-015-2256-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2256-1

Keywords

Search

Navigation