Set-point-related indirect iterative learning control for multi-input multi-output systems

Article
First Online:
Received:
Revised:

Abstract

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser’s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.

Keywords

Iterative learning control (ILC) indirect ILC multi-input multi-output (MIMO) 2-dimensional system asymptotical stability linear matrix inequality (LMI) 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. Uchiyama. Formulation of high-speed motion pattern of a mechanical arm by trial. Transactions of the Society of Instrument and Control Engineers, vol. 14, no. 6, pp. 706–712, 1978. (in Japanese)Google Scholar
  2. [2]
    S. Arimoto, S. Kawamura, F. Miyazaki. Bettering operation of dynamic systems by learning: A new control theory for servomechanism or mechatronics system. In Proceedings of the 23th Conference of Decision and Control, Las Vegas, pp. 1064–1069, 1984.Google Scholar
  3. [3]
    X. H. Bu, Z. S. Hou. Stability of iterative learning control with data dropouts via asynchronous dynamical system. International Journal of Automation and Computing, vol.8, no. 1, pp. 29–36, 2011.CrossRefGoogle Scholar
  4. [4]
    A. Tang, D. Xiao, Z. Z. Mao. Batch-to-batch iterative learning control of a batch polymerization process based on online sequential extreme learning machine. Industrial & Engineering Chemistry Research, vol. 48, no. 24, pp. 11108–11114, 2009.CrossRefGoogle Scholar
  5. [5]
    D. H. Owens, K. Feng. Parameter optimization in iterative learning control. International Journal of Control, vol. 76, no. 11, pp. 1059–1069, 2003.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    W. S. Chen, R. H. Li, J. Li. Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays. International Journal of Automation and Computing, vol. 7, no. 4, pp. 438–446, 2010.CrossRefGoogle Scholar
  7. [7]
    Y. Wang, F. Gao, F. J. Doyle. Survey on iterative learning control, repetitive control, and run-to-run control. Journal of Process Control, vol. 19, no. 10, pp. 1589–1600, 2009.CrossRefGoogle Scholar
  8. [8]
    J. H. Wu, H. Ding. Reference adjustment for a high-acceleration and high-precision platform via A-type of iterative learning control. Journal of Systems & Control Engineering, vol. 221, no. 5, pp. 781–789, 2007.Google Scholar
  9. [9]
    J. X. Xu, R. Yan. Iterative learning control design without a priori knowledge of the control direction. Automatica, vol. 40, no. 10, pp. 1803–1809, 2004.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    P. Jiang, L. C. A. Bamforth, Z. Feng, J. E. F. Baruch, Y. Q. Chen. Indirect iterative learning control for a discrete visual servo without a camera-robot model. IEEE Transactions on Systems, Man, and Cybernetics, vol. 37, no. 4, pp. 863–876, 2007.CrossRefGoogle Scholar
  11. [11]
    G. M. Bone. A novel iterative learning control formulation of generalized predictive control. Automatica, vol. 31, no. 10, pp. 1483–1487, 1995.CrossRefMATHGoogle Scholar
  12. [12]
    A. Tayebi, C. J. Chien. A unified adaptive iterative learning control framework for uncertain nonlinear systems. IEEE Transactions on Automatic Control, vol. 52, no. 10, pp. 1907–1913, 2007.MathSciNetCrossRefGoogle Scholar
  13. [13]
    K. K. Tan, S. Zhao, J. X. Xu. Online automatic tuning of a proportional integral derivative controller based on an iterative learning control approach. IET Control Theory & Applications, vol. 1, no. 1, pp. 90–96, 2007.CrossRefGoogle Scholar
  14. [14]
    Y.Wang, F. J. Doyle. Stability analysis for set-point-related indirect iterative learning control. In Proceedings of the 48th IEEE Conference on Decision and Control, IEEE, Shanghai, PRC, pp. 5702–5707, 2009.Google Scholar
  15. [15]
    Y. Q. Ye, D. W. Wang. Learning more frequency components using P-type ILC with negative learning gain. IEEE Transactions on Industrial Electronics, vol. 53, no. 2, pp. 712–716, 2006.CrossRefGoogle Scholar
  16. [16]
    T. Kaczorek. Two-dimensional Linear Systems, Berlin, Germany: Springer-Verlag, 1985.MATHGoogle Scholar
  17. [17]
    J. Shi, F. Gao, T. J. Wu. Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system. Journal of Process Control, vol. 15, no. 8, pp. 907–924, 2005.CrossRefGoogle Scholar
  18. [18]
    G. I. Bara, M. Boutayeb. Static output feedback stabilization with H ∞ performance for linear discrete-time systems. IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 250–254, 2005.MathSciNetCrossRefGoogle Scholar
  19. [19]
    S. P. Boyd, L. E. Ghaoui, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, Philadelphia, USA: Society for Industrial Mathematics, 1994.CrossRefMATHGoogle Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.School of Information Science and Electrical EngineeringHebei University of EngineeringHandanPRC
  2. 2.School of ScienceHebei University of EngineeringHandanPRC
  3. 3.Institute of Uncertainty MathematicsHebei University of EngineeringHandanPRC

Personalised recommendations