Skip to main content
SpringerLink
Log in

Robust PD-type iterative learning control for discrete systems with multiple time-delays subjected to polytopic uncertainty and restricted frequency-domain

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper proposes the PD-type iterative learning control (ILC) for multiple time-delays systems with polytopic parameter uncertainty. Based on repetitive process framework, the system under study is equivalently converted into a class of uncertain repetitive processes with multiple time-delays. This approach accounts for effective inclusion of both time and trial domain objectives and hence some requirements on transient dynamics and trial-to-trial error convergence are incorporated for robust design procedures. Additionally, this approach can easily avoid the need for computation with very large dimensioned matrices as it is required for the lifting approach. Also, the proposed controller is designed with the generalized Kalman-Yakubovich-Popov lemma to ensure the monotonic trial-to-trial error convergence in finite frequency domain. This allows us to reduce the conservatism inherent to entire frequency range approaches since the reference signal spectrum reside in a known frequency range. Moreover, the sufficient conditions for the convergence of the resulting scheme are expressed by linear matrix inequalities and hence they are amenable to effective algorithmic solution. Finally, numerical simulations of different scenarios are presented to illustrate the effectiveness of the proposed method. In particular, to highlight the potential interest in PD-type ILC the robust tracking performance is compared with the results for P and D types of ILC.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Arimoto, S., Kawamura, S., & Miyazaki, F. (1984). Bettering operation of robots by learning. Journal of Robotic Systems, 1(2), 123–140.

    Article  Google Scholar 

  • Bristow, D. A., Tharayil, M., & Alleyne, A. (2006). A survey of iterative learning control. IEEE Control Systems Magazine, 26(3), 96–114.

    Article  Google Scholar 

  • Dai, X. S., Tu, X. M., & Zhao, Y. (2018). Iterative learning control for MIMO parabolic partial difference systems with time delay. Advances in Difference Equations, 32(8), 1434–1438.

    MathSciNet  Google Scholar 

  • Ding, J., & Lin, J. (2014). Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits, systems and signal processing, 33(5), 1439–1449.

    Article  Google Scholar 

  • Gahinet, P., & Apkarian, P. (1994). A linear matrix inequality approach to \({H}_{\infty }\) control. International Journal of Robust and Nonlinear Control, 4(4), 421–448.

    Article  MathSciNet  Google Scholar 

  • Hladowski, L., Galkowski, K., & Cai, Z. (2010). Experimentally supported 2D systems based iterative learning control law design for error convergence and performance. Control Engineering Practice, 18(4), 339–348.

    Article  Google Scholar 

  • Iwasaki, T., & Hara, S. (2005). Generalized KYP lemma: Unified frequency domain inequalities with design applications. IEEE Transactions on Automatic Control, 50(1), 41–59.

    Article  MathSciNet  Google Scholar 

  • Jia, Y., Du, J., Meng, D., & Yu, F. (2010). Robust iterative learning control design for uncertain time-delay systems based on a performance index. Control Theory and Applications, IET, 4(5), 759–772.

    Article  MathSciNet  Google Scholar 

  • Jian, J., Hong, Yan, & Xiao, F. (2010). Robust D stabilization of singular systems with polytopic uncertainties. Control Theory and Applications, 8(4), 540–544.

    Article  MathSciNet  Google Scholar 

  • Kurek, J., & Zaremba, M. (1993). Iterative learning control synthesis based on 2-D system theory. IEEE Transactions on Automatic Control, 38(1), 121–125.

    Article  MathSciNet  Google Scholar 

  • Li, J. M. (2011). Adaptive iterative learning control for nonlinearly parameterized systems with time-varying delays. Acta Mathematica Scientia, 31(3), 682–690.

    Article  MathSciNet  Google Scholar 

  • Li, N. N., & Jiang, W. (2017). Convergence analysis of fractional iterative learning control for nonlinear systems with multiple time delays. Pure and Applied Mathematics, 33(1), 69–81.

    MathSciNet  MATH  Google Scholar 

  • Li, D., & Li, J. M. (2012). Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delay and unknown control direction. International Journal of Automation and Computing, 9(6), 578–586.

    Article  Google Scholar 

  • Li, J., Wang, Y. L., & Li, X. M. (2011). Adaptive iterative learning control for nonlinear parametric systems with unknown time-varying delays. Journal of Control Theory and Applications, 16(6), 861–868.

    Google Scholar 

  • Li, X. J., & Yang, G. H. (2017). Finite frequency \(L_2\)-\({L}_{\infty }\) filtering of T-S fuzzy systems with unknown membership functions. IEEE Transactions on Systems Man and Cybernetics Systems, 47(8), 1884–1897.

    Article  Google Scholar 

  • Longman, R. (2000). Iterative learning control and repetitive control for engineering practice. International Journal of Control, 73(10), 930–954.

    Article  MathSciNet  Google Scholar 

  • Meng, D., & Moore, K. L. (2017). Robust iterative learning control for nonrepetitive uncertain systems. IEEE Transactions on Automatic Control, 62(2), 907–913.

    Article  MathSciNet  Google Scholar 

  • Oliveira, R. C. L. F., & Peres, P. L. D. (2006). LMI conditions for robust stability analysis based on polynomially parameeter-dependent Lyapunov functions. System and Control Letters, 55(1), 52–61.

    Article  Google Scholar 

  • Ouyang, P. R. (2012). PD-PD type iterative learning control for time-varying uncertain nonlinear systems. Control and Intelligent Systems, 39(2), 98–107.

    MathSciNet  MATH  Google Scholar 

  • Paszke, W., Rogers, E,, & Galkowski, K. (2013). Finite frequency domain design of dynamic controllers for differential linear repetitive processes, American Control Conference, Washington, DC, USA.

  • Paszke, W., Rogers, E., Galkowski, K., & Cai, Z. L. (2013). Robust finite frequency range iterative learning control design and experimental verification. Control Engineering Practice, 21(10), 1310–1320.

    Article  Google Scholar 

  • Rogers, E., Gałkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes, vol. 349 of lecture notes in control and information sciences. Berlin: Springer.

    Google Scholar 

  • Shen, Y., Zhou, F. Z., & Dong, X. L. (1998). A learning control method based on the principle of pd regulator for robot control with two degree of freedom. Journal of Luoyang Institute of Technology, 19(3), 55–58.

    Google Scholar 

  • Shi, J., Gao, F. R., & Wu, T. J. (2005). Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system. Journal of Process Control, 15(8), 907–924.

    Article  Google Scholar 

  • Soernmo, O., Bernhardsson, B., Kroeling, O., Gunnarsson, P., & Tenghamn, R. (2016). Frequency-domain iterative learning control of a marine vibrator. Control Engineering Practice, 47, 70–80.

    Article  Google Scholar 

  • Tao, H. F., Paszke, W., Rogers, E., Yang, H. Z., & Galkowski, K. (2017). Iterative learning fault-tolerant control for differential time-delay batch processes in finite frequency domains. Journal of Process Control, 56, 112–128.

    Article  Google Scholar 

  • Uchiyama, M. (1978). Formation of high-speed motion pattern of a mechanical arm by trial. Transactions of the Society of Instrument and Control Engineers, 14(6), 706–712.

    Article  Google Scholar 

  • Wang, L., Li, B., & Yu, J. (2018). Design of fuzzy iterative learning fault-tolerant control for batch processes with time-varying delays. Optimal Control Applications and Methods, 39(6), 1887–1903.

    Article  MathSciNet  Google Scholar 

  • Wang, L. M., Mo, S., & Qu, H. (2013). \(H_{\infty }\) design of 2D controller for batch processes with uncertainties and interval time-varying delays. Control Engineering Practice, 21(10), 1321–1333.

    Article  Google Scholar 

  • Zhang, K., Jiang, B., & Shi, P. (2015). Fault estimation observer design for discrete-time systems in finite-frequency domain. International Journal of Robust and Nonlinear Control, 25(9), 1379–1398.

    Article  MathSciNet  Google Scholar 

  • Zhang, Y. X., & Xu, J. Z. (2012). PD-type iterative learning control law for uncertain time-delay systems. Journal of Beijing Jiaotong University, 36(2), 70–73.

    MathSciNet  Google Scholar 

  • Zhou, Y., & He, L. (2017). Iterative learning control of linear motors with control time delay and loss of measurement data. Control and Decision, 32(8), 1434–1438.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Hongfeng Tao, Xiaohui Li & Huizhong Yang

  2. Institute of Automation, Electronic and Electrical Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516, Zielona Góra, Poland

    Wojciech Paszke

  3. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Dositejeva 19, 36000, Kraljevo, Serbia

    Vladimir Stojanovic

Authors
  1. Hongfeng Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaohui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wojciech Paszke
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vladimir Stojanovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Huizhong Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Stojanovic.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is supported by National Natural Science Foundation of China (61773181, 61203092), 111 Project (B12018), the Fundamental Research Funds for the Central Universities (JUSRP51733B),  National Science Centre in Poland, Grant No. 2017/27/B/ST7/01874, and Serbian Ministry of Education, Science and Technological Development (451-03-68/2020-14/200108).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tao, H., Li, X., Paszke, W. et al. Robust PD-type iterative learning control for discrete systems with multiple time-delays subjected to polytopic uncertainty and restricted frequency-domain. Multidim Syst Sign Process 32, 671–692 (2021). https://doi.org/10.1007/s11045-020-00754-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-020-00754-9

Keywords

Search

Navigation