Repetitive Control for Systems with Time-Delays and Application to Robotic Servo Motor

  • Jing Na
  • Xuemei Ren
  • Ramon Costa-Castelló
  • Robert Griñó
  • Yu Guo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7429)


In many industrial robotic applications there is a need to track periodic reference signals and/or reject periodic disturbances. This paper presents a novel repetitive control design for systems with constant time-delays in both forward and feedback control channels. An additional delay is introduced together with plant delays to construct an internal model for periodic signals, and a simple proportional control is utilized to stabilize the closed-loop system. Sufficient stability conditions of the closed-loop system and the robustness analysis under modeling uncertainties are studied. Experimental results are included to evaluate the validity and effectiveness of the proposed method.


Time-delay systems repetitive control periodic signals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hokayem, P.F., Spong, M.W.: Bilateral teleoperation: An historical survey. Automatica 42(12), 2035–2057 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Huang, J.Q., Lewis, F.L.: Neural-network predictive control for nonlinear dynamic systems with time delay. IEEE Trans. on Neural Networks 14(2), 377–389 (2003)CrossRefGoogle Scholar
  3. 3.
    Liu, G.P., Xia, Y.Q., Chen, J., Rees, D., Hu, W.S.: Networked predictive control of systems with random network delays in both forward and feedback channels. IEEE Trans. on Industrial Electronics 54(3), 1282–1297 (2007)CrossRefGoogle Scholar
  4. 4.
    Nuño, E., Basañez, L., Ortega, R.: Passivity-based control for bilateral teleoperation: A tutorial. Automatica 47(3), 485–495 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Ryu, J.-H., Artigas, J., Preusche, C.: A passive bilateral control scheme for a teleoperator with time-varying communication delay. Mechatronics 20(7), 812–823 (2010)CrossRefGoogle Scholar
  6. 6.
    Griñó, R., Cardoner, R., Costa-Castelló, R., Fossas, E.: Digital repetitive control of a three-phase four-wire shunt active filter. IEEE Trans. on Industrial Electronics 54(3), 1495–1503 (2007)CrossRefGoogle Scholar
  7. 7.
    Liuzzo, S., Tomei, P.: A global adaptive learning control for robotic manipulators. Automatica 44(5), 1379–1384 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Costa-Castelló, R., Nebot, J., Griñó, R.: Demonstration of the internal model principle by digital repetitive control of an educational laboratory plant. IEEE Trans. on Education 48(1), 73–80 (2005)CrossRefGoogle Scholar
  9. 9.
    Hara, S., Yamamoto, Y., Omata, T., Nakano, M.: Repetitive control system: a new type servo system for periodic exogenous signals. IEEE Transactions on Automatic Control 33(7), 659–668 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Chew, K.K., Tomizuka, M.: Digital control of repetitive errors in disk drive systems. IEEE Control Systems Magazine 10(1), 16–19 (1990)CrossRefGoogle Scholar
  11. 11.
    Zhou, K., Wang, D.: Digital repetitive learning controller for three phase CVCF PWM inverter. IEEE Trans. on Industrial Electronics 48(4), 820–830 (2001)CrossRefGoogle Scholar
  12. 12.
    Francis, B.A., Wonham, W.M.: Internal model principle in control theory. Automatica 12(5), 457–465 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Watanabe, K., Yamada, K.: Repetitive control of time-delay systems. In: Proc. of the 29th IEEE Conference on Decision and Control, pp. 1685–1690 (1990)Google Scholar
  14. 14.
    Tan, K.K., Chua, K.Y., Zhao, S., Yang, S., Tham, M.T.: Repetitive control approach towards automatic tuning of smith predictor controllers. ISA Transactions 48(1), 16–23 (2009)CrossRefGoogle Scholar
  15. 15.
    Tan, K.K., Zhao, S., Huang, S., Lee, T.H., Tay, A.: A new repetitive control for LTI systems with input delay. Journal of Process Control 19(4), 711–716 (2009)CrossRefGoogle Scholar
  16. 16.
    Na, J., Griñó, R., Costa-Castelló, R., Ren, X., Chen, Q.: Repetitive controller for time-delay systems based on disturbance observer. IET Control Theory & Applications 4(11), 2391–2404 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Na, J., Costa-Castelló, R., Griñó, R., Ren, X.: Discrete-time repetitive controller for time-delay systems with disturbance observer. Asian Journal of Control (2011) (pages Accepted for publication),
  18. 18.
    Normey-Rico, J.E., Camacho, E.F.: Dead-time compensators: a survey. Control Engineering Practice 16(4), 407–428 (2008)CrossRefGoogle Scholar
  19. 19.
    Yamamoto, Y.: Learning control and related problems in infinite-dimensional systems. In: Proc. of the 2nd European Control Conference, pp. 191–222 (1993)Google Scholar
  20. 20.
    Khalil, H.: Nonlinear systems, 3rd edn. Prentice Hall (2001)Google Scholar
  21. 21.
    Weiss, G., Hafele, M.: Repetitive control of MIMO systems using H_inf design. Automatica 35(7), 1185–1199 (1999)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jing Na
    • 1
  • Xuemei Ren
    • 2
  • Ramon Costa-Castelló
    • 3
  • Robert Griñó
    • 3
  • Yu Guo
    • 1
  1. 1.Faculty of Mechanical & Electrical EngineeringKunming University of Science and TechnologyKunmingChina
  2. 2.School of AutomationBeijing Institute of TechnologyBeijingP.R. China
  3. 3.Institute of Industrial and Control EngineeringUniversitat Politècnica de Catalunya (UPC)BarcelonaSpain

Personalised recommendations