DOI QR코드

DOI QR Code

Design of Repetitive Control System for Linear Systems with Time-Varying Uncertainties

시변 불확실성을 가지는 선형 시스템을 위한 반복 제어 시스템의 설계

  • 정명진 (한국과학기술원 전자전산학과) ;
  • 도태용 (한밭대학교 전기전자제어공학부)
  • Published : 2005.01.01

Abstract

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.

References

  1. S. Hara, Y. Yamamoto, T. Omata, and M. Nakano, 'Repetitive control system: a new type servo system for periodic exogenous signals', IEEE Trans. Automatic Control, vol. 37, no. 7, pp. 659-668, 1988 https://doi.org/10.1109/9.1274
  2. L. Guvenc, 'Stability and performance robustness analysis of repetitive control systems using structured singular values', ASME Journal of Dynamic Systems, Measurement, and Control, vol. 118, no. 3, pp.593-597, 1996 https://doi.org/10.1115/1.2801185
  3. J.-H. Moon, M.-N. Lee, and M. J. Chung, 'Repetitive control for the track-following servo system of an optical disk drive', IEEE Trans. Control Systems Technology, vol. 6, no. 5, pp. 663-670, 1998 https://doi.org/10.1109/87.709501
  4. G. Weiss and M. Hafele, 'Repetitive control of MIMO systems using $H_{\infty}$ design', Automatica, vol. 35, no. 7, pp. 1185-1199, 1999 https://doi.org/10.1016/S0005-1098(99)00036-9
  5. J. Li and T.-C. Tsao, 'Robust performance repetitive control systems', ASME Journal of Dynamic Systems, Measurement, and Control, vol. 123, no. 3, pp. 330-337, 2001 https://doi.org/10.1115/1.1387015
  6. Y. Onuki and H. Ishioka, 'Compensation for repeatable tracking errors in hard drives using discrete-time repetitive controllers', IEEE Trans. Mechatronics, vol. 6, no. 2, pp. 132-136, 2001 https://doi.org/10.1109/3516.928726
  7. J. Abedor, J., K. Nagpal, P. P. Khargoneckar, and K. Poolla, 'Robust regulation in the presence of norm- bounded uncertainty', IEEE Trans. Automatic Control, vol. 40, no. 1, pp. 147-152, 1995 https://doi.org/10.1109/9.362881
  8. M.-N. Lee, J.-H. Moon, K. B. Jin, and M. J. Chung, 'Robust $H_{\infty}$ control with multiple constraints for the track-following system of an optical disk drive', IEEE Trans. Industrial Electronics, vol. 45, no. 4, pp. 638-645, 1998 https://doi.org/10.1109/41.704893
  9. M. S. Mahmoud, Robust Control and Filtering for Time-Delay Systems, Marcel Dekker, Inc., 2000
  10. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, 'Linear matrix inequalities in system and control theory', SIAM Studies in Applied Mathematics 15, SIAM Philadelphia, 1994
  11. H. Kokame, H. Kobayashi, and T. Mori, 'Robust $H_{\infty}$ performance for linear delay-differential systems with time-varying uncertainties', IEEE Trans. Automatic Control, vol. 43, no. 2, pp. 223-226, 1998 https://doi.org/10.1109/9.661069
  12. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, 'LMI control toolbox user's guide', The Math Works, Inc., 1995