DOI QR코드

DOI QR Code

Structured Controller Synthesis Using a Penalized LMI Method

페널티화된 LMI를 이용한 구조적 제약이 있는 제어기 설계

  • 김석주 (한국전기연구원 계측제어그룹) ;
  • 권순만 (한국전기연구원 계측제어그룹) ;
  • 천종민 (한국전기연구원 계측제어그룹) ;
  • 문영현 (연세대학교 전기전자공학)
  • Published : 2005.08.01

Abstract

This paper is concerned with an iterative linear matrix inequality (LMI) approach to the design of a structurally constrained output feedback controller such as decentralized control. The structured synthesis is formulated as a novel rank-constrained LMI optimization problem, where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices. An iterative penalty method is applied to solve the rank-constrained LMI problem. Numerical experiments are performed to illustrate the effectiveness of the proposed method.

Keywords

References

  1. M. G. Safonov, K. C. Goh, and J. H. Ly, 'Control system synthesis via bilinear matrix inequality,' In Proc. Amer. Control Conf., pp.45-49, 1994 https://doi.org/10.1109/ACC.1994.751690
  2. R. E. Skelton, T. Iwasaki, and K. Grigoriadis, A Unified Approach to Linear Control Design. Taylor & Francis, 1997
  3. 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
  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. P. Apkarian, D. Noll and H. D. Tuan, 'Fixed-order $H_{\infty}$ control design via a partially augmented Lagrangian method,' Int. J. Robust Nonlinear Control, vol. 13, pp.1137-1148, 2003 https://doi.org/10.1002/rnc.807
  6. Y. Ebihara and T. Hagiwara, 'Structured controller synthesis using LMI and alteranating projection algorithm method,' In Proc. Conf. on Decision and Control, pp.5632-5637, 2003 https://doi.org/10.1109/CDC.2003.1271901
  7. M. C. de Oliveira, J. F. Camino, and R. E. Skelton, 'A convexifying algorithm for the design of structured linear controllers,' In Proc. Conf. on Decision and Control, pp.2781-2786, 2000 https://doi.org/10.1109/CDC.2000.914229
  8. J. Han and R. E. Skelton, 'An LMI optimization approach for structured linear controllers,' In Proc. Conf. on Decision and Control, pp.5143-5148, 2003 https://doi.org/10.1109/CDC.2003.1272453
  9. K. Tan and K. M. Grigoriadis, 'Robust decentralized control using alternating projection approach,' In Proc. Amer. Control Conf, pp.801-805, 2000 https://doi.org/10.1109/ACC.2000.876610
  10. S. J. Kim, Y. H. Moon, S. Kwon and K. H. Kim, 'Rank-constrained LMI approach to mixed $H_2/H_{\infty}$ static ouptut feedback controllers', IFAC World Congress, 2005
  11. 김석주, 이종무, 권순만, 문영현, '고정 구조를 가지는 $H_{\infty}$ 전력계통 안정화 장치 설계,' 전기학회논문지, 제53권, 제12호, pp.655-660, 2004
  12. 김석주, 김춘경, 김국헌, 문영현, '반복 선형행렬부등식을 이용한 저차원 $H_{\infty}$ 제어기 설계,' 제어·자동화·시스템공학 논문지, 제11권, 제4호, pp.279-283, 2005 https://doi.org/10.5302/J.ICROS.2005.11.4.279
  13. C. Scherer, P. Gahinet, and M. Chilali, 'Multiobjective output-feedback control via LMI optimization,' IEEE Trans. Automat. Control., vol. 42, no. 7, pp. 896-911, 1993 https://doi.org/10.1109/9.599969
  14. Chilali, M. and Gahinet, P., 1996, 'Desgin with Pole Placement Constraints : An LMI Approach,' IEEE Trans on Automatic Control, Vol. 41 (3), pp. 358-369 https://doi.org/10.1109/9.486637
  15. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1986
  16. P. Apkarian, D. Noll, and J. B. Thevenet, 'A spectral quadratic-SDP method with applications to fixed-order $H_2$ and $H_{\infty}$ synthesis,' available:http://www-ext.cert.fr/dcsd/cdin/apkarian https://doi.org/10.3166/ejc.10.527-538
  17. M. C. de Oliveira, J. C. Geromel, and J. Bernussou, 'Extended $H_2$ and $H_{\infty}$ norm characterization and controller parameterizations for discrete-time systems,' Int. J. Control, vol. 75, no. 9, pp.666-679, 2002 https://doi.org/10.1080/00207170210140212
  18. M. T. Ho, A. Datta, and S. P. Bhattacharyya, 'Control system design using low order controllers: constant gain, PI and PID,' In Proc. Amer. Control Conf, pp.571-578, 1997 https://doi.org/10.1109/ACC.1997.611864