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Pole Placement by an LQ Controller

LQ 제어기에 의한 극배치 방법

  • Published : 2009.03.01

Abstract

This paper studies the problem of pole placement by an LQ controller for system having two distinct real poles. Using the so-called Pole's Moving Range (PMR) drawn in the s-plane and relational equations between closed-loop system poles and weighting matrices, we calculate the state weighting matrix to move two distinct real poles to a pair of complex poles. By numerical examples, we show that the proposed method is applied to improve system performance.

Keywords

References

  1. O. A. Solheim, 'Design of optimal control systems with prescribed eigenvalues,' Inl. J Control, vol. 15, no. 1, pp. 143-160, 1972 https://doi.org/10.1080/00207177208932136
  2. J. Medanic, H. S. Tharp, and W. R. Perkins, 'Pole placement by performance criterion modification,' IEEE Transcations on Automatic Control, vol. 33, no. 5, pp. 469-472, 1988 https://doi.org/10.1109/9.1229
  3. Y. Ochi and K. Kanai, 'A new way of pole placement in LQR and its application to flight control,' In Proceedings of the AIAA Guidance, Navigation, and Control Conference, Monterey, CA, pp. 1295-1301, 1993
  4. Y. Ochi and K. Kanai, 'Pole placement in optimal regulator by continuous pole-shifting,' Journal of Guidance, Control, and Dynamics, vol. 18, no. 6, pp. 1253-1258, 1995 https://doi.org/10.2514/3.21538
  5. K. Sugimoto, 'A polynOlnial matrix approach to the ILQ regulator design,' Proc. IEEE CDC, Kobe, japan, pp. 4164-4169, 1996 https://doi.org/10.1109/CDC.1996.577435
  6. K. Sugimoto, 'Partial pole placement by LQ regulators: An inverse problem approach,' IEEE Transactions on Automatic Control, vol. 43, no. 5, pp. 706-708, 1998 https://doi.org/10.1109/9.668841
  7. T. Fujinaka and H. Shibata, 'Admissible region for pole positioning with optimal regulator,' Proc. IEEE CDC, Kobe, japan, pp. 3631-3635, 1996 https://doi.org/10.1109/CDC.1996.577178
  8. T. Fujinaka and S. Omatu, 'Pole placement using optimal regulators,' T.IEE japan, vol. 121-C, no. 1, pp. 240-245, 2001
  9. T. Fujinaka, G. Ghen, H. Shibata, and S. Omatu, 'Pole shifting with modal dissipative control,' Proceedings of the IEEE International Conferences on Control Applications, pp. 932-937, 2002 https://doi.org/10.1109/CCA.2002.1038727
  10. 박민호, 홍석교 'LQR 제어기의 과도 상태 개선 방법에 관한 연구,' 대한전기학회 하계학술대회 논문집, pp. 2239-2241, 2004
  11. 박민호, 홍석교, 이상혁, '근의 이동범위를 고려한 LQR 제어기 설계,' 제어.자동화.시스템공학 논문집, 제11권, 제10호, pp.864-869, 2005
  12. 박민호, 박문수, 박덕기, 홍석교, 이상혁, '극배치 특성을 갖는 LQR 제어기 설계,' 제어.자동화.시스템공학논문집, 제13권 제6호, pp. 574-580. 2007
  13. M. Saif, 'Optimal modal controller design by entire eigenstructure assignment,' IEEE Proc., vol. 136, no. 6, pp. 341-344, 1989 https://doi.org/10.1049/ip-d.1989.0047
  14. J. B. Burl, Linear Optimal Control: $R_2$and $R_{\infty}$ Methods, Addison Wesley Longman, 1999
  15. G. Strang, Linear Algebra and its applications, 3rd Ed., Harcourt Brace & Company, 1988
  16. B. D. O. Anderson, J. B. Moore, Optimal Control, Prentice-Hall, 1989