Advertisement

Repetitive Control

  • Germán A. RamosEmail author
  • Ramon Costa-Castelló
  • Josep M. Olm
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 446)

Summary

This Chapter describes the concepts and basics of RC. The standard IM and the plug-in scheme structure are used to introduce the design, as well as stability and robustness approaches that are traditionally employed in this technique. The performance of the RC interface of frequency variations or uncertainty is analyzed using the magnitude response of the IM and the closed loop phase behavior of the system. These response characteristics evidence the dramatic loss of performance that occurs when the period of the reference/disturbance signal is time varying or uncertain. Section 2.1 introduces the IM, the controller structure, stability conditions and design criteria in RC, while in Section 2.2 the performance degradation under varying frequency conditions is analysed.

Keywords

Magnitude Response Repetitive Control Repetitive Controller Stability Robustness Internal Model Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chang, W.S., Suh, I.H., Kim, T.W.: Analysis and design of two types of digital repetitive control systems. Automatica 31(5), 741–746 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chew, K.K., Tomizuka, M.: Steady-state and stochastic performance of a modified discrete-time prototype repetitive controller. Journal of Dynamic Systems, Measurement, and Control 112, 35–41 (1990)zbMATHCrossRefGoogle Scholar
  3. 3.
    Costa-Castelló, R., Nebot, J., Griñó, R.: Demonstration of the internal model principle by digital repetitive control of an educational laboratory plant. IEEE Transactions on Education 48(1), 73–80 (2005)CrossRefGoogle Scholar
  4. 4.
    Escobar, G., Hernandez-Briones, P., Torres-Olguin, R., Valdez, A.: A repetitive-based controller for the compensation of 6l±1 harmonic components. In: Proceedings of the IEEE International Symposium on Industrial Electronics, pp. 3397–3402 (2007)Google Scholar
  5. 5.
    Escobar, G., Torres-Olguin, R., Valdez, A., Martinez-Montejano, M., Hernandez-Briones, P.: Practical modifications of a repetitive-based controller aimed to compensate 6l+1 harmonics. In: Proceedings of the 11th IEEE International Power Electronics Congress, CIEP 2008, pp. 90–95 (August 2008)Google Scholar
  6. 6.
    Francis, B., Wonham, W.: Internal model principle in control theory. Automatica 12, 457–465 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Griñó, R., Costa-Castelló, R.: Digital repetitive plug-in controller for odd-harmonic periodic references and disturbances. Automatica 19(4), 1060–1068 (2004)Google Scholar
  8. 8.
    Hillerström, G., Lee, R.C.: Trade-offs in repetitive control. Technical Report CUED/F-INFENG/TR 294, University of Cambridge (June 1997)Google Scholar
  9. 9.
    Inoue, T.: Practical repetitive control system design. In: Proceedings of the 29th IEEE Conference on Decision and Control, pp. 1673–1678 (1990)Google Scholar
  10. 10.
    Inoue, T., Nakano, M., Kubo, T., Matsumoto, S., Baba, H.: High accuracy control of a proton synchroton magnet power supply. In: Proceedings of the 8th IFAC World Congress, pp. 216–220 (1981)Google Scholar
  11. 11.
    Leyva-Ramos, J., Escobar, G., Martinez, P., Mattavelli, P.: Analog circuits to implement repetitive controllers for tracking and disturbance rejection of periodic signals. IEEE Transactions on Circuits and Systems II: Express Briefs 52(8), 466–470 (2005)CrossRefGoogle Scholar
  12. 12.
    Tomizuka, M., Tsao, T.-C., Chew, K.-K.: Analysis and synthesis of discrete-time repetitive controllers. Journal of Dynamic Systems, Measurement, and Control 111, 353–358 (1989)zbMATHCrossRefGoogle Scholar
  13. 13.
    Tsao, T.-C., Tomisuka, M.: Adaptive and repetitive digital control algorithms for non circular machining. In: Proceedings of the 1988 American Control Conference (1988)Google Scholar
  14. 14.
    Tsao, T.-C., Tomizuka, M.: Robust adaptive and repetitive digital tracking control and application to a hydraulic servo for noncircular machining. Journal of Dynamic Systems, Measurement, and Control 116(1), 24–32 (1994)zbMATHCrossRefGoogle Scholar
  15. 15.
    Weiss, G., Häfele, M.: Repetitive control of MIMO systems using H  ∞  design. Automatica 35(7), 1185–1199 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Yamamoto, Y.: Learning control and related problems in infinite-dimensional systems. In: Proceedings of the European Control Conference, pp. 191–222 (1993)Google Scholar
  17. 17.
    Yeol, J.W., Longman, R.W., Ryu, Y.S.: On the settling time in repetitive control systems. In: Proceedings of 17th International Federation of Automatic Control (IFAC) World Congress (July 2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Germán A. Ramos
    • 1
    Email author
  • Ramon Costa-Castelló
    • 2
  • Josep M. Olm
    • 3
  1. 1.Department of Electrical and Electronic EngineeringUniversidad Nacional de Colombia BogotáColombia
  2. 2.Escola Tècnica Superior d’Enginyeria Industrial de Barcelona (ETSEIB)Universitat Politècnica de Catalunya (UPC) BarcelonaSpain
  3. 3.Department of Applied Mathematics IV Universitat Politècnica de CatalunyaCastelldefelsSpain

Personalised recommendations