Skip to main content
SpringerLink
Log in

Reference model iterative learning control for nonlinear systems with repeatable and non-repeatable uncertainties

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper deals with iterative learning control (ILC) design for nonlinear systems with repeatable and non-repeatable uncertainties and performing repetitive tasks to follow a reference model (also called desired system). This desired system does not necessarily have the same structure, nor the same parameters as the real systems (there is no dependence between the reference model system and the real system). For this purpose, two ILC schemes are considered and analysed. The first controller assures the asymptotic stability with a simple condition to verify, whereas the second assures this stability without condition to verify. The λ-norm is adopted as the topological measure in our proof of the asymptotic stability of the closed loop system over the whole finite time interval when the iteration number tends to infinity. Finally, two simulation results on nonlinear system are provided to illustrate the effectiveness of the proposed controllers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arimoto S, Miyazaki F (1984) Stability and robustness of PID feedback control for robots manipulators of sensory capability. The 1st International Symposium of Robotics Research. MIT Press, Cambridge

    Google Scholar 

  2. Lozano R, Taoutaou D (2001) Commande adaptative et application. Hermes Science Publications, Paris

    Google Scholar 

  3. Slotine JJE, Sastry SS (1983) Tracking control of nonlinear systems using sliding surface with application to robot manipulator. Int J Control 38:465–492

    Article  MATH  MathSciNet  Google Scholar 

  4. Chang YC, Chen BS (2000) Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems: adaptive fuzzy approach. IEEE Trans Fuzzy Syst 8:46–66

    Article  Google Scholar 

  5. Bouakrif F, Boukhetala D, Boudjema F (2010) Passivity based controller–observer for robot manipulators. Int J Robot Autom 25(1)

  6. Arimoto S, Kawamura S, Miyazaki F (1984) Bettering operation of robots by learning. J Robot Syst 1(2):123–140

    Article  Google Scholar 

  7. Xu JX, Tan Y (2003) Linear and nonlinear iterative learning control. Lecture notes in control and information sciences. Springer, Berlin

    Google Scholar 

  8. Xu JX, Yan R (2005) On initial conditions in iterative learning control. IEEE Trans Automat Contr 50(9):1349–1354

    Article  MathSciNet  Google Scholar 

  9. Bouakrif F, Boukhetala D, Boudjema F (2007) Iterative learning control schemes for robot manipulators. The Mediterranean Journal of Measurement and Control 3(3):104–112

    Google Scholar 

  10. Tayebi A (2004) Adaptive iterative learning control for robot manipulators. Automatica 40:1195–1203

    Article  MATH  MathSciNet  Google Scholar 

  11. Sun M, Ge SS, Mareels IMY (2006) Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Trans on Robotics 22(3):563–568

    Article  Google Scholar 

  12. Bouakrif F, Boukhetala D and Boudjema F (2007) Iterative learning control for robot manipulators. Archives of Control Sciences Vol. 17, No. 1

  13. Tayebi A (2007) Analysis of two particular iterative learning control schemes in frequency and time domains. Automatica 43:1565–1572

    Article  MATH  MathSciNet  Google Scholar 

  14. Cai Z, Freeman CT, Lewin PL, Rogers R (2008) Iterative learning control for a non-minimum phase plant based on a reference shift algorithm. Control Eng Pract 16:633–643

    Article  Google Scholar 

  15. Bien Z, Huh KM (1989) Higher-order iterative learning control algorithm control theory and applications. EE Proc, Control Theory Appl 136(3):105–112

    Article  MATH  Google Scholar 

  16. Chen YQ, Xu JX, Lee T (1996) An iterative learning controller using current iteration tracking error information and initial state learning. Proceedings of the 35th IEEE Decision and Control, pp 3064–3069

  17. Chen W, Chowdhury FN (2006) Model reference iterative learning control. Proceedings of the 2006 American Control Conference, Minnesota, pp 1654–1658

  18. Wang D (1998) Model reference learning approach and its applications to robot impedance control. Proceedings of the 37th IEEE Decision and Control, Tampa, FL, pp 684–689

Download references

Author information

Authors and Affiliations

  1. LAMEL Laboratory, University of Jijel, BP. 98, Ouled Aissa, Jijel, 18000, Algeria

    Farah Bouakrif

Authors
  1. Farah Bouakrif
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farah Bouakrif.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bouakrif, F. Reference model iterative learning control for nonlinear systems with repeatable and non-repeatable uncertainties. Int J Adv Manuf Technol 51, 1159–1169 (2010). https://doi.org/10.1007/s00170-010-2669-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-010-2669-4

Keywords

Search

Navigation