Skip to main content
SpringerLink
Log in

On-line identification algorithm and convergence analysis for sandwich systems with backlash

  • Technical Notes and Correspondence
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, an on-line algorithm for identification of sandwich systems with backlash is proposed. In this method, the sandwich systems with backlash can be transformed into a special model where all the model parameters are separated based on the so-called key term separation principle. In this case, a piecewise model with linear coefficients combining with nonlinear variables is obtained. Thus, an extended recursive identification algorithm is used to estimate the parameters of the proposed model. Finally, the modeling results on an X-Y positioning stage are presented.

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

Similar content being viewed by others

References

  1. R. K. Pearson, “Nonlinear input/output modeling,” J. Process Control, vol. 5, no. 4, pp. 197–211, 1995.

    Article  Google Scholar 

  2. G. Tao, X. Ma, and Y. Ling, “Optimal and nonlinear decoupling control of systems with sandwiched backlash,” Automatica, vol. 37, pp. 165–176, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Vörös, “Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones,” IEEE Trans. on Automatic Control, vol. 48, no. 12, pp. 2203–2206, 2003.

    Article  Google Scholar 

  4. J. Vörös, “Identification of nonlinear dynamic system using extended Hammerstein and Wiener models,” Control-Theory and Advanced Technology, vol. 10, pp. 1203–1212, 1995.

    MathSciNet  Google Scholar 

  5. C. Z. Fang, System Identification, Qinghua University Press, Beijing, 2004.

    Google Scholar 

  6. L. Ljung, “Analysis of recursive stochastic algorithms,” IEEE Trans. on Automatic Control, vol. 22, no. 4, pp. 271–287, 1977.

    Google Scholar 

  7. V. Cerone and D. Regruto, “Bounding the parameters of linear systems with input backlash,” Proc. of American Control Conference, pp. 4476–4481, 2005

  8. M. Nordin and P. O. Gutman, “Controlling mechanical systems with backlash—a survey,” Automatica, vol. 38, pp. 1633–1649, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  9. X. Hong, R. J. Mitchell, S. Chen, C. J. Harris, K. Li, and G. W. Irwin, “Model selection approaches for non-linear system identification: a review,” International Journal of Systems Science, vol. 39, no. 10, pp. 925–946, 2008.

    Article  MathSciNet  Google Scholar 

  10. M. Boutayeb and M. Darouach, “Recursive identification method for MISO Wiener-Hammerstein model,” IEEE Trans. on Automatic Control, vol. 40, no. 2, pp. 287–291, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. H. Tan and K. Godfrey, “Identification of Wiener-Hammerstein models using linear interpolation in frequency domain,” IEEE Trans. on Instrumentation and Measurement, vol. 51, no. 3, pp. 509–521, 2002.

    Article  Google Scholar 

  12. P. Crama and J. Schoukens, “Computing an initial estimate of a Wiener-Hammerstein system with a random phase multisine excitation,” IEEE Trans. on Instrumentation and Measurement, vol. 54, no. 1, pp. 117–122, 2005.

    Article  Google Scholar 

  13. S. A. Billings and S. Y. Fakhouri, “Identification of a class of nonlinear systems using correlation analysis,” Proc. IEE. vol. 125, pp. 691–697, 1978.

    MathSciNet  Google Scholar 

  14. A. Kibangou and G. Favier, “Wiener-Hammerstein systems modeling using diagonal Volterra kernels coefficients,” IEEE Signal Proc. Letters, vol. 13, no. 6, pp. 381–384, 2006.

    Article  Google Scholar 

  15. S. Billings and S. Fakhouri, “Identification of systems containing linear dynamics and static nonlinear elements,” Automatica, vol. 18, pp. 15–26, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  16. N. Bershad, P. Celka, and S. Mc Laughlin, “Analysis of stochastic gradient identification of Wiener-Hammerstein systems for nonlinearities with Hermite polynomial expansions,” IEEE Trans. Signal Proc., vol. 49, no. 5, pp. 1060–1072, 2001.

    Article  Google Scholar 

  17. S. Billings and S. Fakhouri, “Identification of nonlinear systems using correlation analysis and pseudorandom inputs,” Int. J. Systems Science, vol. 11, no. 3, pp. 261–279, 1980.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, Shanghai Normal University, Shanghai, 200234, China

    Ruili Dong & Yonghong Tan

Authors
  1. Ruili Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonghong Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonghong Tan.

Additional information

Recommended by Editorial Board member Won-Jong Kim under the direction of Editor Young Il lee. This work was supported by the projects of Shanghai Normal University (DZL811, DRL904 and DYL201005); the projects of Shanghai Education Commission (09ZZ141 and 11YZ92); the project of NSFC (Grant No. 60971004), and the projects of Science and Techn. Commission of Shanghai (09220503000, 10JC1412200 and 09ZR1423400).

Ruili Dong received her Ph.D. degree in Control Engineering from Shanghai Jiaotong University in 2009. Presently, she is a lecturer at the College of Mechanical and Electronic Engineering, Shanghai Normal University, China. Her research interests include identification of nonlinear systems, and mechatronics.

Yonghong Tan obtained his Ph.D. degree in Electrical Engineering from University of Ghent, Belgium in 1996. Now, he is a full professor at College of Mechanical and Electronic Engineering, Shanghai Normal University, China. His research interests include identification and control of nonlinear systems, mechatronics, and biomedical signal processing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dong, R., Tan, Y. On-line identification algorithm and convergence analysis for sandwich systems with backlash. Int. J. Control Autom. Syst. 9, 588–594 (2011). https://doi.org/10.1007/s12555-011-0320-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-011-0320-2

Keywords

Search

Navigation