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

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

Frequency Weighted Controller Reduction of Closed-Loop System Using Lyapunov Inequalities

Lyapunov 부등식을 이용한 페루프시스템의 주파수하중 제어기 차수축소

  • 오도창 (건양대학교 정보전자통신공학부) ;
  • 정은태 (창원대학교 제어계측공학과) ;
  • 이갑래 (두원공과대학교 컴퓨터응용제어과) ;
  • 김종해 (경북대학교 센서기술연구센터) ;
  • 이상경 (두원공과대학교 공장자동화학과)
  • Published : 2001.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers a new weighed model reduction method using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of the reduced order system is guaranteed and an a priori error bound is proposed. to achieve this after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical examples.

Keywords

References

  1. B. D. O. Anderson and Y. Liu, 'Controller reduction: Concepts and approach,' IEEE Trans. Automat. Contr., vol. 34, pp. 802-812, Aug., 1989 https://doi.org/10.1109/9.29422
  2. L. Pemebo and L. M. Silverman, 'Model reduction via balancedstate space representations,' IEEE Trans. Automatic Control, vol. 27, no. 2, pp. 382-387, April, 1982 https://doi.org/10.1109/TAC.1982.1102945
  3. K. Glover, 'All optimal Hankel-norm approximation of linear multi variable systems and their $L^{infty}$ error bounds,' Int. J. of Control vol. 39, no. 6, pp. 1115-1193, June, 1984 https://doi.org/10.1080/00207178408933239
  4. Y. Liu and B. D. O. Anderson, 'Singular perturbation approximation of balanced systems,' Int. J. of Control, vol. 50, no. 4, pp. 1379-1405, April, 1989 https://doi.org/10.1080/00207178908953437
  5. A. Helmersson, 'Model reduction from an TEX>$L^{infty}$ / LMI perspective,' Europ. Cant. Conf., pp. 232-238, Oct., 1995
  6. D. Enns, 'Model reduction for control systems design,' Ph. D. dissertation, Stanford Univ., 1984
  7. S. W. Kim and B. D. O. Anderson, and A. G. Madievski, 'Error bound for trnsfer function order reduction using frequency weighted balanced truncation,' Syst. Contr. Lett., vol. 24, pp. 183-192, 1995 https://doi.org/10.1016/0167-6911(94)00033-R
  8. V. Sreeram, B. D. O. Anderson, and A. G. Madievski, 'New results on frequency weighted balanced reduction technique,' Proc. of Amer. Contr. Conf., Washington, pp. 4004-4009, 1995
  9. G. Wang, V. Sreeram, and W. Q. Liu, 'A new frequency-weighted balanced truncation and error bound,' IEEE Trans. Automatic Control, vol. 44, no. 9, pp. 1734-1737, Sept., 1999 https://doi.org/10.1109/9.788542
  10. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994
  11. K. Zhou, C. D'Souza, and J. R. Cloutier, 'Structurally balanced controller order reduction with guaranteed closed loop performance,' Systs. Contr. Lett., vol. 24, pp. 235-242, 1995 https://doi.org/10.1016/0167-6911(94)00028-T
  12. D. C. Oh, K. H. Bang, and H. B. Park, 'Controller order reduction using singular perturbation approximation,' Automatica, vol 33, no. 6, pp. 1203-1207, 1997 https://doi.org/10.1016/S0005-1098(97)00041-1