Skip to main content
Log in

New results on discrete-time delay systems identification

  • Regular Paper
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

A new approach for simultaneous online identification of unknown time delay and dynamic parameters of discrete-time delay systems is proposed in this paper. The proposed algorithm involves constructing a new generalized regression vector and defining the time delay and the rational dynamic parameters in the same vector. The gradient algorithm is used to deal with the identification problem. The effectiveness of this method is illustrated through simulation.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. C. Tsui. Observer design for systems with time-delayed states. International Journal of Automation and Computing, vol. 9, no. 1, pp. 105–107, 2012.

    Article  MathSciNet  Google Scholar 

  2. Y. Q. Chen, K. L. Moore, J. Yu, T. Zhang. Iterative learning control and repetitive control in hard disk drive industry-a tutorial. International Journal of Adaptive Control and Signal Processing, vol. 22, no. 4, pp. 325–343, 2008.

    Article  Google Scholar 

  3. J. R. Ryoo, T. Y. Doh. Feedback-based iterative learning control for MIMO LTI systems. International Journal of Control Automation and Systems, vol. 6, no. 2, pp. 269–277, 2008.

    Google Scholar 

  4. P. Balasubramaniam, T. Senthilkumar. Delay-dependent robust stabilization and H control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays. International Journal of Automation and Computing, vol. 9, no. 3, 2012.

  5. W. S. Chen, J. M. Li. Adaptive output-feedback regulation for nonlinear delayed systems using neural network. International Journal of Automation and Computing, vol.5, no. 1, pp. 103–108, 2008

    Article  Google Scholar 

  6. T. Söderström, P. Stoica. System Identification, Prentice Hall International, Series in Systems and Control Engineering, New York, USA: Prentice Hall, 1989.

    Google Scholar 

  7. J. P. Richard. Time-delay systems: An overview of some recent advances and open problems. Automatica, vol. 39, no. 10, pp. 1667–1694, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  8. V. B. Kolmanovskii, S. I. Niculescu, K. Gu. Delay effects on stability: A survey. In Proceedings of the 38th IEEE Conference on Decision and Control, IEEE, Phoenix, AZ, USA, vol. 2, pp. 1993–1998, 1999.

    Google Scholar 

  9. X. M. Ren, A. B. Rad, P. T. Chan, W. L. Lo. Online identification of continuous-time systems with unknown time delay. IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1418–422, 2005.

    Article  MathSciNet  Google Scholar 

  10. S. V. Drakunov, W. Perruquetti, J. P. Richard, L. Belkoura. Delay identification in time-delay systems using variable structure observers. Annual Reviews in Control, vol. 30, no. 2, pp. 143–158, 2006.

    Article  Google Scholar 

  11. Y. Orlov, L. Belkoura, J. P. Richard, M. Dambrine. Adaptive identification of linear time-delay systems. International Journal on Robust and Nonlinear Control, vol. 13, no. 9, pp. 857–872, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Orlov, L. Belkoura, M. Dambrine, J. P. Richard. On identifiability of linear time-delay systems. IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1319–1324, 2002.

    Article  MathSciNet  Google Scholar 

  13. M. de la Sen. Robust adaptive control of linear time-delay systems with point time-varying delays via multiestimation. Applied Mathematical Modelling, vol. 33, no. 2, pp. 959–977, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  14. Q. G. Wang, Y, Zhang. Robust identification of continuous systems with dead time from step responses. Automatica, vol. 37, no. 3, pp. 377–390, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Zhang, Y. Q. Cui. A bilateral control of teleoperators based on time delay identification. In Proceedings of the 2008 IEEE Conference on Robotics, Automation and Mechatronics, IEEE, Chengdu, China, pp. 797–802, 2008.

    Chapter  Google Scholar 

  16. S. Bedoui, M. Ltaief, K. Abderrahim, R. Ben Abdennour. Representation and control of time delay system: Multimodel approach. In Proceedings of the 8th International Multi-conference on Systems, Signals and Devices, IEEE, Sousse, Tunisia, pp. 1–6, 2011

    Chapter  Google Scholar 

  17. H. Kurz, W. Goedecke. Digital parameter-adaptive control of process with unknown dead time. Automatica, vol. 17, no. 1, pp. 245–252, 1981.

    Article  MATH  Google Scholar 

  18. P. J. Gawthrop, M. T. Nihtilä. Identification of time delays using a polynomial identification method. Systems and Control Letters, vol. 5, no. 4, pp. 267–271, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  19. S. W. Sung, I. B. Lee. Prediction error identification method for continuous-time processes with time delay. Industrial and Engineering Chemistry Research, vol. 40, no. 24, pp. 5743–5751, 2001.

    Article  Google Scholar 

  20. O. Gomez, Y. Orlov, I. V. Kolmanovsky. On-line identification of SISO linear time-invariant delay systems from output measurements. Automatica, vol. 43, no. 12, pp. 2060–2069, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Ahmed, B. Huang, S. L. Shah. Parameter and delay estimation of continuous-time models using a linear filter. Journal of Process Control, vol. 16, no. 4, pp. 323–331, 2006.

    Article  Google Scholar 

  22. A. B. Rad, W. L. Lo, K. M. Tsang. Simultaneous online identification of rational dynamics and time delay: A correlation-based approach. IEEE Transactions on Control Systems Technology, vol. 11, no. 6, pp. 957–959, 2003.

    Article  Google Scholar 

  23. T. Zhang, Y. C. Li. A fuzzy smith control of time-varying delay systems based on time delay identification. In Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, IEEE, Xian, China, vol. 1, pp. 614–619, 2003.

    Google Scholar 

  24. W. X. Zheng, C. B. Feng. Identification of stochastic time lag systems in the presence of colored noise. Automatica, vol. 26, no. 4, pp. 769–779, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  25. W. Gao, Y. C. Li, G. J. Liu, T. Zhang. An adaptive fuzzy smith control of time-varying processes with dominant and variable delay. In Proceedings of the American Control Conference, IEEE, Denver, CO, USA, vol. 1, pp. 220–224, 2003.

    Chapter  Google Scholar 

  26. W. Gao, M. L. Zhou, Y. C. Li, T. Zhang. An adaptive generalized predictive control of time-varying delay system. In Proceedings of the 2nd International Conference on Machine Learning and Cybernetics, IEEE, Shanghai, China, pp. 878–881, 2004.

    Google Scholar 

  27. G. Ferretti, C. Maffezzoni, R. Scattolini. Recursive estimation of time delay in sampled systems. Automatica, vol. 27, no. 4, pp. 653–661, 1991.

    Article  Google Scholar 

  28. A. Elnaggar, G. A. Dumont, A. L. Elshafei. New method for delay estimation. In Proceedings of the 29th IEEE Conference on Decision and Control, IEEE, Honolulu, HI, USA, vol. 3, pp. 1929–1930, 1990.

    Google Scholar 

  29. L. Xie, Y. J. Liu, H. Z. Yang. Gradient based and least squares based iterative algorithms for matrix equations AXB + CX T D = F. Applied Mathematics and Computation, vol. 217, no. 5, pp. 2191–2199, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  30. V. J. Mathews, G. L. Sicuranza. Polynominal Signal Processing, New York, USA: Wiley, 2000.

    Google Scholar 

  31. T. Ogunfunmi. Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches, New York, USA: Springer, 2007.

    MATH  Google Scholar 

  32. B. Bao, Y. Q. Xu, J. Sheng, R. F. Ding. Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data. Mathematical and Computer Modelling, vol. 53, no. 9–10, pp. 1664–1669, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  33. D. Q. Wang, F. Ding. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Processing, vol. 91, no. 5, pp. 1182–1189, 2011.

    Article  MATH  Google Scholar 

  34. D. Q. Wang, F. Ding. Input-output data filtering based recursive least squares identification for CARARMA systems. Digital Signal Processing, vol. 20, no. 4, pp. 991–999, 2010.

    Article  Google Scholar 

  35. O. Nelles. Nonlinear System Identification: From Classical Approach to Neural Networks and Fuzzy Models, New York, USA: Springer, 2001.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saïda Bedoui.

Additional information

This work was supported by Ministry of the Higher Education and Scientific Research in Tunisia.

Saïda Bedoui received the B.Eng. degree in electrical-automatic engineering in 2008, and the M. Eng. degree in automatic and smart techniques from the National School of Engineers of Gabes (ENIG), Tunisia in 2008. Currently, she is a Ph.D. candidate at Research Unit of Numerical Control of Industrial Processes (CONPRI), University of Gabes, ENIG, Tunisia.

Her research interests include time delay system identification, multimodel approaches and adaptive control.

Majda Ltaief received her B.Eng. degree in electrical-automatic from Tunisia in 1996 and the DEA for the same specialty from the National School of Engineers of Gabes (ENIG), Tunisia in 1999. In 2005, she obtained her Ph.D. degree in electricalautomatic engineering from the National School of Engineers of Tunis, Tunisia. From 2004 to 2005, she was an assistant professor in the Electric Engineering Department in the High Institute of Applied Sciences and Technology of Gabes, Tunisia. She is currently an associate professor in the Electric Engineering Department, ENIG, Tunisia.

Her research interests include multimodel and multicontrol approaches, fuzzy supervision, and numerical control of complex systems.

Kamel Abderrahim received the B.Eng. degree in electrical engineering from the National School of Engineers of Gabes (ENIG), Tunisa in 1992, and the M. Eng. degree in automatic control from Higher School of Sciences and Techniques of Tunis, Tunisia (ESSTT) in 1995, and the Ph.D. degree in electrical engineering from National School of Engineers of Tunis, Tunisia (ENIT) in 2000, and the Habilitation in electrical engineering from the University of Gabs in 2009. He has been a member of Laboratory of Numerical Control of Industrial Processes (LACONPRI) at the ENIG since 1995. He joined the ENIG as an assistant professor in 2000, and now he works as a professor at the ENIG. From 2002 to 2005, he was the director of the Electrical Engineering Department at the ENIG. And from 2005 to 2011, he was the director of Higher Institute of Industrial Systems, Tunisia (ISSIG).

His research interests include nonlinear process modeling, identification, and control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bedoui, S., Ltaief, M. & Abderrahim, K. New results on discrete-time delay systems identification. Int. J. Autom. Comput. 9, 570–577 (2012). https://doi.org/10.1007/s11633-012-0681-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-012-0681-x

Keywords

Navigation