Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Adaptive Optimal Control of a Rotary Inverted Pendulum Using Lagrange Interpolation and a Pole's Moving-Range

라그랑지 보간과 근의 이동범위를 이용한 회전형 도립진자의 적응 최적 제어

  • Park, Minho (Electrical & Electronics Engineering, Chungnam Provincial Chengyang College) ;
  • Han, Sang-Wan (Electrical & Electronics Engineering, Chungnam Provincial Chengyang College)
  • 박민호 (충남도립청양대학 전기전자과) ;
  • 한상완 (충남도립청양대학 전기전자과)
  • Received : 2014.01.16
  • Accepted : 2014.02.05
  • Published : 2014.02.28
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Abstract

This paper presents a new design method of optimal control of system which are changed the system parameters. The method used for this purpose are the Lagrange interpolation method and Pole's Moving range method. We selects a system within the scope of the changing the system parameters. Using pole's moving range we calculated the state weighting matrix of optimal control. The optimal controller is designed by Lagrange interpolation method of the state weighting matrix. We are compared with a traditional optimal controller and proposed method by simulation. The simulation showed that the proposed method is better control performance than traditional method of optimal controller.

이 논문은 변수가 변화하는 시스템의 새로운 최적제어 설계 방법에 관한 것이다. 이 문제를 다루는데 사용된 방법은 라그랑지 보간법과 근의 이동범위이다. 변수가 변화하는 범위 내에서 선택된 시스템의 최적제어기의 설계 변수를 근의 이동범위를 이용하여 상태가중행렬을 계산하고 상태가중행렬을 라그랑지 보간법으로 보간하여 최적제어기를 설계하였다. 모의실험을 통해 기존의 방식과 제안한 방법을 비교하고, 기존의 최적제어 설계법보다 제안한 방식이 더 좋은 결과가 얻어지는 것을 확인하였다.

Keywords

References

  1. O. A. Solheim, "Design of optimal control systems with prescribed eigenvalues," Int. J. Control, vol. 15, no. 1, pp. 143-160, 1972. DOI: http://dx.doi.org/10.1080/00207177208932136
  2. T. Fujinaka and S. Omatu, "Pole placement using optimal regulators," T.IEE japan, vol. 121-C, no. 1, pp. 240-245, 2001.
  3. M. Park, S.K. Hong, S.H. Lee, "Design of an LQR Controller Considering Pole's Moving-Range", Journal of Control, Automation and System Engineering Vol 11, No. 10, pp. 854-869, 2005. DOI: http://dx.doi.org/10.5302/J.ICROS.2005.11.10.864
  4. M. Park, M.S. Park, D. Park, S.K. Hong, S.H. Lee, "LQR Controller Design with Pole-Placement," Journal of Control, Automation and System Engineering Vol 13, No 6, pp. 574-580, 2007. DOI: http://dx.doi.org/10.5302/J.ICROS.2007.13.6.574
  5. Minho Park, "Pole Placement by an LQ Controller," Journal of Control, Automation and System Engineering Vol 15, No 3, pp. 249-254, 2009 DOI: http://dx.doi.org/10.5302/J.ICROS.2009.15.3.249
  6. Y.H. Lee, J.K. Ahn, G.G. Jin, M.O. So, "Interpolation -Based Adaptive LQ Control for Nonliner System." Vol. 32. No. 4, pp. 618-623, 2008 https://doi.org/10.5916/jkosme.2008.32.4.618
  7. G. Strang, Linear Algebra and its applications, 3rd Ed., Harcourt Brace & Company, 1988.
  8. B. D. O. Anderson, J. B. Moore, Optimal Control, Prentice-Hall, 1989.
  9. J. B. Burl, Linear Optimal Control: $H_2$ and $H_{\infty}$ Methods, Addison Wesley Longman, 1999.s