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

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Radial Type Satellite Attitude Controller Design using LMI Method and Robustness Analysis

LMI 방법을 이용한 방사형 인공위성 제어로직 설계 및 강건성 분석

  • Received : 2015.04.04
  • Accepted : 2015.10.23
  • Published : 2015.11.01
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Abstract

The $H_{\infty}$ control theory using LMI method is applied to design an attitude controller of radial type satellite that has strongly coupled channels due to the large product of inertia. It is observed that the cross-over frequency of open-loop with $H_{\infty}$ controller is lower than that of open-loop without controller, which is not typical phenomenon in an optimal control design result: it is interpreted that due to a large product of inertia, there is certain limit in increasing agility of satellite by just tuning weighting function. ${\mu}$-analysis is performed to verify the stability and performance robustness with the assumption of +/-5% MOI variation. ${\mu}$-analysis result shows that the variation of principal MOI degrades the stability and performance robustness more than the variation of POI does.

방사형 인공위성 경우, 관성곱이 커서 단일 입 출력 가정이 불가능하기 때문에 고전적 제어기 설계방법을 사용하기 어렵다. 본 논문에서 현대 제어 이론인 $H_{\infty}$ 제어기 설계이론을 사용하여 방사형 인공위성의 자세 제어기 설계를 수행하였다. 설계 알고리즘으로 보다 안정적인 LMI 방법이 사용되었고, 설계 결과에 대한 안정성과 성능에 대한 강건성 해석을 위해 ${\mu}$-해석 방법이 적용되었다. 설계 결과, 일반적인 경우와 다르게 제어기가 포함되지 않은 개루프보다 제어기가 포함된 개루프의 cross-over frequency가 더 낮게 설계되는 것이 관측되었다. 즉 상대적으로 큰 관성곱 영향 때문에 단지 weighting 함수 조정으로 위성 기동성을 증가시키는데 한계가 있는 것으로 해석된다. ${\mu}$-해석을 위해 +/-5%의 관성모멘트 변화를 가정하였다. 안정성 및 성능에 대한 강건성 해석결과, +/-7% 관성모멘트 변화까지 시스템 안정성 및 성능이 보장됨이 확인되었고, 관성곱 변화보다 주관성모멘트 변화가 안정성 및 성능 저하에 더 영향을 주는 것으로 확인되었다.

Keywords

References

  1. Glover, Keith, Doyle, John C., "State-space formulae for all stabilizing controllers that satisfy an $H_{\infty}$-norm bound and relations to risk sensitivity," Systems & Control Letters, Vol. 11, 1988, pp.167-172. https://doi.org/10.1016/0167-6911(88)90055-2
  2. Doyle, John C., Glover, Keith, Khargonekar, Pramod P., Frabcis, Bruce A., "State-space Solution to Standard H2 and $H_{\infty}$ Control Problems," IEEE Trans. on Automatic Control, Vol. 34, no. 8, Aug. 1989, pp.831-847. https://doi.org/10.1109/9.29425
  3. Safonov, Michael G., Limebeer, D.J.N., "Simplifying The $H_{\infty}$ Theory via Loop Shifting," Proceedings of the 27th Conference on Decision and Control, Austin, Texas, December 1988, pp.1399-1404.
  4. Gahinet, Pascal, Apkarian, Pierre, "A Linear Matrix Inequality Approach to $H_{\infty}$ Control," International J. of Robust and Nonlinear Control, Vol. 4, 1994, pp.421-448. https://doi.org/10.1002/rnc.4590040403
  5. Gahinet, Pascal, "Explicit Controller Formulas for LMI-based $H_{\infty}$ Synthesis," Automatica, Vol. 32, no. 7, 1996, pp.1007-1014. https://doi.org/10.1016/0005-1098(96)00033-7
  6. Chilali, Mahmoud, Gahinet, Pascal, "$H_{\infty}$ Design with Pole Placement Constraints: An LMI Approach," IEEE Trans. on Automatic Control, Vol. 41, no. 3, March 1996, pp.358-367. https://doi.org/10.1109/9.486637
  7. Scherer, Carsten, Gahinet, Pascal, and Chilali, Mahmoud, "Multiobjective Output-Feedback Control via LMI Optimization," IEEE Trans. on Automatic Control, Vol. 42, no. 7, July 1997, pp.896-911. https://doi.org/10.1109/9.599969
  8. Shaked, U., "Improved LMI Representations for the Analysis and the Design of Continuous-Time Systems with Polytopic Type Uncertainty," IEEE Trans. on Automatic Control, Vol. 46, no. 4, April 2001, pp.652-656. https://doi.org/10.1109/9.917671
  9. Apkarian, Pierre, Tuan, Hoang Duong, and Bernussou, J., "Continuous-Time Analysis, Eigenstructure Assignment, and H2 Synthesis with Enhanced Linear Matrix Inequalities(LMI) Characterizations," IEEE Trans. on Automatic Control, Vol. 46, no. 12, Dec. 2001, pp.1941-1946. https://doi.org/10.1109/9.975496
  10. Wei, Jia-Bo, Lee, Li, "Further Improvement on LMI Representations for the Analysis and Design of Continuous-Time Systems with Polytopic Type Uncertainty," Proceedings of the 2004 5th Control Conference, 2004, pp.1130-1136.
  11. Kim, H.J., Rhee, S.W., Shon, J.W., "A Weighting Function Design for $H_{\infty}$ Controller of Satellite Attitude Control," Conference of the Korean Society for Aeronautical and Space Sciences, 2013, pp. 465-469.
  12. Ballois, S. Le, Duc, G. "$H_{\infty}$ Control of an Earth Observation Satellite," J. of Guidance, Control, and Dynamics, Vol. 19, no. 3, 1996, pp.628-635. https://doi.org/10.2514/3.21667
  13. Valentin-Charbonnel, C., Duc, G., Ballois, S. Le, "Low-order robust attitude control of an earth observation satellite," Control Eng. Practice, Vol. 7, no. 7, 1999, pp.493-506. https://doi.org/10.1016/S0967-0661(99)00006-4
  14. Bodineau, Guillaume, Beugnon, Celine, et al., "mu-Iteration Technique Applied to the Control of Satellites with Large Flexible Appendages," 6th International ESA Conference on GNC, 17-20 October 2005, Loutraki, Greece.
  15. Ohtani, Takashi, Hamada, Yoshiro, et al., "Robust Attitude Control using mu-synthesis for the Large Flexible Satellite ETS-VIII," 7th International ESA Conference on GNC, 2-5 June 2008, Tralee, Country Kerry, Irend.
  16. Cubillos, Mendez, Souza, Gadelha, "Using of H-Infinity Control Method in Attitude Control System of Rigid-Flexible Satellite," Mathematical Problems in Engineering, Vo. 2009, Article ID 173145.
  17. Castro, J.V.C., Souza, L.C.G., "Comparison of the LQG and H-infinity Techniques to Design Experimentally a Flexible Satellite Attitude Control System," J. of Aerospace Engineering, Sciences and Applications, Vol. II, no. 2, May-Aug. 2010, pp.17-25.
  18. Bennani, Samir, Ankersen, Finn and et., "Robust Attitude Control Design for the BIOMASS Satellite," Proceedings of the 18th IFAC World Congress, Milano, Italy, Aug. 28 - Sept. 2, 2011, pp.5130-5135.
  19. Rhee, S.W., Ko, H.C., Jang, W.Y., Son, J.W, "Roll/Yaw Momentum Management Method of Pitch Momentum Biased Spacecraft," J. of the Korean Society for Aeronautical and Space Sciences, Vol. 37, no7, 2009, pp.669-677. https://doi.org/10.5139/JKSAS.2009.37.7.669
  20. Rhee, S.W., Kim, H.J., Son, J.W, "Roll of B-dot Controller and Failure Analysis for Down-dusk LEO Satellite," J. of the Korean Society for Aeronautical and Space Sciences, Vol. 41, no3, 2013, pp.200-209. https://doi.org/10.5139/JKSAS.2013.41.3.200
  21. Zhou, Kemin, Doyle, John C., Essentials of Robust Control, 1998, Prentice-Hall, Inc.
  22. Gu, Da-Wei, Petkov, Petko H. and Konstantinov, M.M., Robust Control Design with Matlab, 2013, SpringerLink.
  23. Skogestad, Sigurd, Postlethwaite, Multivariable Feedback Control Analysis and Design, 2005, John Wiley & Sons.
  24. Boyd, S., Ghaoui, L. El, Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, 1994, SIAM, Philadelphia.

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