Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Design of a Low-Order H∞ Controller Using an Iterative LMI Method

반복 선형행렬부등식을 이용한 저차원 H∞ 제어기 설계

  • 김춘경 (한국전기연구원 계측제어그룹) ;
  • 김국헌 (원전계측제어개발사업단) ;
  • 문영현 (연세대학교 전기전자공학부) ;
  • 김석주 (한국전기연구원 계측제어그룹)
  • Published : 2005.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.

Keywords

References

  1. K. C. Goh, M. G. Safonov and G. P. Papavassilopoulos, 'A global optimization approach for the BMI problem', In Proc. IEEE Conf. on Decision and Control, pp. 2009-2114, 1994 https://doi.org/10.1109/CDC.1994.411445
  2. J. C. Geromel, C. C. de Souza and R. E. Skelton, 'LMI numerical solution for output feedback stabilization', In Proc. of the American Control Conference, pp. 40-44, 1994 https://doi.org/10.1109/ACC.1994.751689
  3. T. Iwasaki and R. E. Skelton, 'The XY-centering algorithm for the dual LMI problem : a new approach to fixed order control design', International Journal of Control, vol. 62, no. 6, pp. 1257-1272, 1995 https://doi.org/10.1080/00207179508921598
  4. K. M. Grigoriadis and R. E. Skelton, 'Low order control design for LMI problems using alternating projection methods', Automatica, vol. 32, no. 8, pp. 1117-1125, 1996 https://doi.org/10.1016/0005-1098(96)00057-X
  5. T. Iwasaki, 'The dual iteration for fixed order control', IEEE Trans. on Automatic Control, Vol. 44, No.4, pp.783-788, 1999 https://doi.org/10.1109/9.754818
  6. L. El Ghaoui, F. Oustry and M. Rami, 'A cone complementarity linearization algorithm for static output feedback and related problems', IEEE Trans. on Automatic Control, Vol. 42, No.8, 1171-1176, 1997 https://doi.org/10.1109/9.618250
  7. M. C. de Oliveira and J. C. Geromel, 'Numerical comparison of output feedback design methods', In Proc. of the American Control Conference, pp. 72-76, 1997 https://doi.org/10.1109/ACC.1997.611757
  8. M. Fazel H. Hindi and S. Boyd, 'Log-det heuristic for matrix rank minimization with application to Hankel and euclidean distance matrices', In Proc. of the American Control Conference, pp. 2156-2162, 2003 https://doi.org/10.1109/ACC.2003.1243393
  9. P. Apkarian, D. Noll and H. D. Tuan, 'Fixed-order $H{\infty}$ control design via a partially augmented lagrangian method', International Journal of Robust and Nonlinear Control, vol. 13, pp. 1137-1148, 2003 https://doi.org/10.1002/rnc.807
  10. D. Noll, M. Torki and P. Apkarian, 'Partially augmented lagrangian method for matrix inequalities constraints', Preprint, Available from http://www-ext.cert.fr/dcsd/cdin/apkarian https://doi.org/10.1137/S1052623402413963
  11. 김석주, 이종무, 권순만, 문영현, '고정 구조를 가지는 $H_{\infty}$ 전력계통 안정화 장치 설계', 전기학회논문지, 53권 12호, pp. 655-660, 2004
  12. P. Gahinet and P. Apkarian, 'A linear matrix inequality approach to $H_{\infty}$ control', International Journal of Robust and Nonlinear Control, vol. 4, pp. 421-448, 1994 https://doi.org/10.1002/rnc.4590040403
  13. R. A. Horn and C. R. Johnson, 'Matrix analysis', Cambridge University Press, 1986
  14. A. Fujimori, 'Optimization of static output feedback using substitutive LMI formulation', IEEE Trans. on Automatic Control, vol. 49, no. 6, pp. 995-999, 2004 https://doi.org/10.1109/TAC.2004.829633
  15. G. Calafiore. F. Dabbene and R. Tempo, 'Randomized algorithms for reduced order $H_{\infty}$ controller design', In Proc. of the American Control Conference, pp. 3837-3839, 2000 https://doi.org/10.1109/ACC.2000.876940