Abstract
The iterative learning control (ILC) is attractive for its simple structure, easy implementation. So the ILC is applied to various fields. But the unexpected huge overshoot can be observed as iteration repeat when we use the ILC to the real world applications. Such bad transient becomes an obstacle for using the ILC in the real field. Designers use a projection method to avoid the bad transient usually. However, the projection method does not show a good error performance enough. Therefore we propose a new learning rule to reduce such a bad transient effectively. The simple normalized learning rules for P-type and PD-type are presented and we prove their convergence. Numerical examples are given to show the effectiveness of the proposed learning control algorithms.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
M. K. Kang, J. S. Lee, and K. L. Han, “Kinematic pathtracking of mobile robot using iterative learning control,” Journal of Robotic Systems, vol. 22, no. 2, pp. 111–121, 2005. [click]
B. You, M. Kim, D. Lee, J. Lee, and J. S. Lee, “Iterative learning control of molten steel level in a continuous casting process,” Control Engineering Practice, vol. 19, no. 3, pp. 234–242, 2011.
B. You, T. Shim, M. Kim, D. Lee, J. Lee, and J. S. Lee, “Molten steel level control based on an adaptive fuzzy estimator in a continuous caster,” ISIJ International, vol. 49, no. 8, pp. 1174–1183, 2009. [click]
A. Tayebi and S. Islam, “Adaptive iterative learning control for robot manipulators: experimental results,” Control Engineering Practice, vol. 14, no. 7, pp. 843–851, 2006. [click]
H. S. Lee and Z. Bien, “A note on convergence property of iterative learning controller with respect to sup norm,” Automatica, vol. 33, no. 8, pp. 1591–1593, 1997. [click]
H. Elci, R. W. Longman, M. Q. Phan, J. N. Juang, and R. Ugoletti, “Simple learning control made practical by zerophase filtering: applications to robotics,” IEEE Trans. on Circuits and Ststems, vol. 49, no. 6, pp. 753–767, 2002. [click]
R. W. Longman, “Iterative learning control and repetitive control for engineering practice,” International Journal of Control, vol. 73, no. 10, pp. 930–954, 2000. [click]
H. S. Lee and Z. Bien,“Design issues on robustness and convergence of iterative learning controller,” Intelligent Automation and Soft Computing, vol. 8, no. 2, pp. 95–106, 2002. [click]
J. X. Xu, R. Yan, and Y. Q. Chen, “On initial conditions in iterative learning control,” Proceedings of the American Control Conference, pp. 1349–1354, 2006.
S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of robots by learning,” Journal of Robotic Systems, vol. 1, no. 2, pp. 123–140, 1984. [click]
S. S. Saab, “A discrete-time learning control algorithm for a class of linear time-invariant systems,” IEEE Trans. Automatic Control, vol. 40, no. 6, pp. 1138–1142, 1995. [click]
T. Sugie and T. Ono, “An iterative learning control law for dynamic systems,” Automatica, vol. 27, no. 4, pp. 729–732, 1991. [click]
D. Wang, “Convergence and robustness of discrete time nonlinear systems with iterative learning control,” Automatica, vol. 34, no. 10, pp. 1445–1448, 1998.
D. Y. Pi and K. Panaliappan, “Robustness of discrete nonlinear systems with open-closed loop iterative learning control,” Proc. of the 1st Int Conf on Machine Learning and Cybernetics, pp. 1263–1266, 2002.
H. S. Lee and Z. Bien, “Study on robustness of iterative learning control with non-zero initial error,” International Journal of Control, vol. 64, no. 3, pp. 345–359, 1996. [click]
Z. Yang and C. W. Chan, “Perfect tracking of repetitive signals for a class of nonlinear systems,” Proceedings of the 17th World Congress IFAC, pp. 1490–1495, 2008. [click]
H. S. Lee and Z. Bien, “Design issues on robustness and convergence of iterative learning controller,” Intelligent Automation and Soft Conputing, vol. 8, no. 2, pp. 95–106, 2002. [click]
T. Y. Kuc, J. S. Lee, and K. H. Nam, “An iterative learning control theory for a class of nonlinear dynamic systems,” Automatica, vol. 28, no. 6, pp. 1215–1251, 1992.
J. X. Xu, “Analysis of iterative learning control for a class of nonlinear discrete-time systems,” Automatica, vol. 33, no. 10, pp. 1905–1907, 1997.
G. Heinzinger, D. Fenwick, B. Paden, and F. Miyazaki, “Robust learning control,” Proc. of 28th IEEE Conf. on Decision and Control, pp. 436–440, 1989. [click]
C. J. Chien and J. S. Liu, “A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems,” International Journal of Control, vol. 64, no. 2, pp. 319–334, 1996. [click]
T. J. Jang, C. H. Choi, and H. S. Ahn, “Iterative learning control in feedback systems,” Automatica, vol. 31, no. 2, pp. 243–248, 1995.
M. Sun and D. Wang, “Closed-loop iterative learning control for non-linear systems with initial shifts,” International Journal of Adaptive Control and Signal Processing, vol. 16, no. 7, pp. 515–538, 2002.
M. Kim, T. Y. Kuc, H. S. Kim, and J. S. Lee, “Adaptive iterative learning controller with input learning technique for a class of uncertain MIMO nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp. 315–328, 2017. [click]
A. Madady, “PID type iterative learning control with optimal gains,” International Journal of Control, Automation, and Systems, vol. 6, no. 2, pp. 194–203, 2008.
A. Madady, “An extended PID type iterative learning control,” International Journal of Control, Automation, and Systems, vol. 11, no. 3, pp. 470–481, 2013. [click]
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Jessie (Ju H.) Park.
Byungyong You received his B.S. degree in Electronic Electrical Engineering from Hanyang University in 2004, and his M.S. and Ph.D. degrees in Electronic Electrical Engineering from POSTECH, in 2006 and 2010, respectively. He is an assistant professor the School of Mechanical and Automotive Engineering, Kyungil University. His research interests include iterative learning control, autonomous vehicle system and functional safety.
Rights and permissions
About this article
Cite this article
You, B. Normalized Learning Rule for Iterative Learning Control. Int. J. Control Autom. Syst. 16, 1379–1389 (2018). https://doi.org/10.1007/s12555-017-0194-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-017-0194-z