International Journal of Control, Automation, and Systems

  • 제6권2호
  • /
  • Pages.171-179
  • /
  • 2008
  • /
  • 1598-6446(pISSN)
  • /
  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

LMI-Based Synthesis of Robust Iterative Learning Controller with Current Feedback for Linear Uncertain Systems

  • Xu, Jianming (College of Information Engineering, Zhejiang University of Technology) ;
  • Sun, Mingxuan (College of Information Engineering, Zhejiang University of Technology) ;
  • Yu, Li (College of Information Engineering, Zhejiang University of Technology)
  • 발행 : 2008.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.

키워드

참고문헌

  1. S. Arimoto, S. Kawamura, and F. Miyazaki, "Bettering operation of robots by learning," Journal Robotic Systems, vol. 1, no. 1, pp. 123-140, 1984 https://doi.org/10.1002/rob.4620010203
  2. R. W. Longman, "Iterative learning control and repetitive control for engineering practice," International Journal of Control, vol. 73, no. 10, pp. 930-954, 2000 https://doi.org/10.1080/002071700405905
  3. K. S. Lee, S. H. Bang, and K. S. Chang, "Feedback-assisted iterative learning control based on an inverse process model," Journal of Process Control, vol. 4, no. 2, pp. 77-89, 1994 https://doi.org/10.1016/0959-1524(94)80026-X
  4. N. Amann, D. H. Owens, E. Rogers, and A. Wahl, "An $H^[\infty}$ approach to linear iterative learning control design," International Journal of Adaptive Control and Signal Processing, vol. 10, no. 6, pp. 767-781, 1996 https://doi.org/10.1002/(SICI)1099-1115(199611)10:6<767::AID-ACS420>3.0.CO;2-L
  5. D. D. Roover, "Synthesis of a robust iterative learning controller using an $H^[\infty}$ approach," Proc. of the 35th Conf. on Decision and Control, pp. 3044-3049, 1996
  6. J. H. Moon, T. Y. Doh, and M. J. Chung, "A robust approach to iterative learning control design for uncertain systems," Automatica, vol. 34, no. 8, pp. 1001-1004, 1998 https://doi.org/10.1016/S0005-1098(98)00028-4
  7. T. Y. Doh, J. H. Moon, K. B, Jin, and M. J. Chung, "Robust ILC with current feedback for uncertain linear systems," International Journal of Systems Science, vol. 30, no. 1, pp. 39-47, 1999 https://doi.org/10.1080/002077299292650
  8. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, Englewood Cliffs, NJ, 1996
  9. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, SIAM, 1994
  10. L. Yu and J. Chu, "An LMI approach to guaranteed cost control of linear uncertain timedelay systems," Automatica, vol. 35, no. 6, pp. 1155-1159, 1999 https://doi.org/10.1016/S0005-1098(99)00007-2
  11. P. Gahinet and P. Apkarian, "A linear matrix inequality approach to $H^[\infty}$ control," International Journal of Robust and Nonlinear Control, vol. 4, no. 4, pp. 421-448, 1994 https://doi.org/10.1002/rnc.4590040403
  12. A. Packard, K. Zhou, P. Pandey, and G. Becker, "A collection of robust control problems leading to LMI's," Proc. of the 30th Conf. on Decision and Control, pp. 1245-1250, 1991
  13. D. Gorinevsky, "Loop shaping for iterative control of batch processes," IEEE Control Systems Magazine, vol. 22, no. 6, pp. 55-65, 2002 https://doi.org/10.1109/MCS.2002.1077785