Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Chaos Control of the Pitch Motion of the Gravity-gradient Satellites in an Elliptical Orbit

타원궤도상의 중력구배 인공위성의 Pitch운동의 혼돈계 제어

  • 이목인 (울산대학교 기계자동차공학부)
  • Received : 2010.10.20
  • Accepted : 2011.01.18
  • Published : 2011.02.01
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Abstract

The pitch motion of a gravity-gradient satellite can be chaotic, depending on the ratio of mass moments of inertia and the eccentricity of the satellite orbit. For a precise prediction of motion, chaotic pitch motion has to be changed to non-chaotic motion. Feedback control can be used to obtain nonchaotic pitch motion. For chaos control and stabilization of the pitch motion of a gravity-gradient satellite, a feedback control system is designed, based on the linear nonautonomous system obtained by linearizing the nonlinear pitch motion. The control law obtained has two parameters and is applied to chaotic nonlinear pitch motion. The nonlinear control system satisfies the proposed control objectives in the range of the nonchaotic parameter space.

중력구배 인공위성의 pitch 운동이 관성 모멘트 비와 편심율에 따라 혼돈계가 될 수 있다. 혼돈계의 경우 운동의 정확한 예측을 위하여 비혼돈계로 전환하는 혼돈계 제어가 필요하다. 혼돈계 제어에는 feedback control system을 사용할 수 있다. 중력구배 인공위성의 pitch 운동의 혼돈계 제어를 위하여, 비선형 pitch 운동 방정식을 선형화를 하여 linear nonautonomous system을 구하고, 이를 근거로 pitch 운동의 혼돈계 제어와 안정화(stabilization)를 위한 제어법칙을 설계하고 원래의 비선형 혼돈계 pitch 운동에 적용하였다. 설계된 pitch 운동 제어계는 두 개의 parameter를 가지는데, 혼돈계 제어와 안정화에 만족할 만한 결과를 보여주었다.

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References

  1. Karasopoulos, H. and Richardson, D., " Numerical Investigation of Chaos in the Attitude Motion of a Gravity-Gradient Satellite", AAS/AIAA Astrodynamics Specialist Conference, AAS-93-581, Victoria, British Columbia, Canada, 1993.
  2. Teofilatto, P., Graziani, F., and Casternuovo, M., "Investigation on the stable and unstable regions of satellites attitude motion", 44th Congress of the International Astronautical Federation, IAF-93-018, Graz, Austria, October, 1993.
  3. Baker, G. L. and Gollub, J. P., " Chaotic Dynamics: an introduction", Cambridge University Press, 1996.
  4. 이목인, "중력구배 인공위성의 Pitch운동의 Melnikov 해석", 대한기계학회논문집 A권, 제33권, 제12호, 2009, pp. 1427-1432.
  5. Jackson, E. A., " Perspective of nonlinear dynamics", Vol. 2, Cambridge University Press, 1990, pp. 190-197.
  6. Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., "Determining Lyapunov Exponents from a time series", Physica 16D, 1985, pp. 285-317.
  7. Shinbrot, T., Grebogi, C., Ott, E., and Yorke, J. A., "Using small perturbations to control chaos", Nature, Vol. 363, 3 June, 1993, pp. 411-417. https://doi.org/10.1038/363411a0
  8. Ott, E., Grebogi, C., and Yorke, J. A., "Controlling chaos," Physical Review Letters, Vol. 64, No. 11, 12 March 1990, pp. 1196-1199. https://doi.org/10.1103/PhysRevLett.64.1196
  9. Pyragas, K., "Continuous control of chaos by self-controlling feedback", Physics Letters A, Vol. 170, 1992, pp. 421-428. https://doi.org/10.1016/0375-9601(92)90745-8
  10. Yagasaki, K., " A Simple Feedback Control System: Bifurcations of Periodic Orbits and Chaos", Nonlinear Dynamics, Vol. 9, 1996, pp. 391-417. https://doi.org/10.1007/BF01833363
  11. Hughes, P. C., "Spacecraft Attitude Dynamics" Wiley, 1986.
  12. Parker, T. S. and Chua, L. O., " Practical Numerical Algorithms for Chaotic Systems" Springer-Verlag, 1989, pp. 66-81.
  13. Sidi, M. J., "Spacecraft Dynamics and Control" Cambridge University Press, 1997, pp. 112-131.
  14. Kaplan, M. H., "Modern spacecraft Dynamics & Control" John Wiley & Son, 1976, pp. 203-204.
  15. Jordan, D. W. and Smith, P., "Nonlinear Ordinary Differential Equations: An introduction for scientists and engineers" Oxford University Press, 2007, pp. 293-298.