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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
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.
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.
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.
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.
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
T. Söderström, P. Stoica. System Identification, Prentice Hall International, Series in Systems and Control Engineering, New York, USA: Prentice Hall, 1989.
J. P. Richard. Time-delay systems: An overview of some recent advances and open problems. Automatica, vol. 39, no. 10, pp. 1667–1694, 2003.
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.
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.
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.
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.
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.
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.
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.
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.
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
H. Kurz, W. Goedecke. Digital parameter-adaptive control of process with unknown dead time. Automatica, vol. 17, no. 1, pp. 245–252, 1981.
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.
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.
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.
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.
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.
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.
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.
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.
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.
G. Ferretti, C. Maffezzoni, R. Scattolini. Recursive estimation of time delay in sampled systems. Automatica, vol. 27, no. 4, pp. 653–661, 1991.
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.
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.
V. J. Mathews, G. L. Sicuranza. Polynominal Signal Processing, New York, USA: Wiley, 2000.
T. Ogunfunmi. Adaptive Nonlinear System Identification: The Volterra and Wiener Model Approaches, New York, USA: Springer, 2007.
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.
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.
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.
O. Nelles. Nonlinear System Identification: From Classical Approach to Neural Networks and Fuzzy Models, New York, USA: Springer, 2001.
Author information
Authors and Affiliations
Corresponding author
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
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11633-012-0681-x