Skip to main content
SpringerLink
Log in

On the Closed-Loop System Identification with Fractional Models

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, the fractional closed-loop system identification problem is addressed. Using the indirect approach, which supposes the knowledge of the controller, both coefficients and fractional orders of the process are estimated. The optimal instrumental variable method combined with a nonlinear optimization algorithm is handled to identify the fractional closed-loop transfer function. Also, two techniques are used for model selection the Akaike’s information criterion and the \(R_T^2\) criterion. The performances of the proposed scheme are illustrated by a numerical example via Monte Carlo simulation and by real electronic system identification.

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
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Amairi, Recursive set-membership parameter estimation using fractional model. Circuits Syst. Signal Process. (2015). doi:10.1007/s00034-015-0036-2

  3. M. Amairi, S. Najar, M. Aoun, Z. Lassoued, M.N. Abdelkrim, OBE-based set-membership parameter estimation of fractional models. Trans. Syst. Signals Devices 17(1), 32–42 (2014)

    Google Scholar 

  4. M. Aoun, M. Amairi, S. Najar, M.N. Abdelkrim, Simulation method of fractional systems based on the discrete-time approximation of the caputo fractional derivatives. in 8th International Multi-Conference on Systems, Signals and Devices (SSD), (IEEE, 2011) pp. 1–6

  5. M. Amairi, M. Aoun, S. Najar, M.N. Abdelkrim, Set membership parameter estimation of linear fractional systems using parallelotopes. in 9th International Multi-Conference on Systems, Signals and Devices (SSD), (IEEE, 2012) pp. 1–6

  6. M. Aoun, R. Malti, F. Levron, A. Oustaloup, Synthesis of fractional laguerre basis for system approximation. Automatica 43(9), 1640–1648 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. J.L. Battaglia, J.C. Batsale, Estimation of heat flux and temperature in a tool during turning. Inverse probl. Eng. 8(5), 435–456 (2000)

    Article  Google Scholar 

  8. M. Chetoui, M. Thomassin, R. Malti, M. Aoun, S. Najar, M.N. Abdelkrim, A. Oustaloup, New consistent methods for order and coefficient estimation of continuous-time errors-in-variables fractional models. Comput. Math. Appl. 66(5), 860–872 (2013)

    Article  MathSciNet  Google Scholar 

  9. O. Cois, A. Oustaloup, T. Poinot, J.L. Battaglia, Fractional state variable filter for system identification by fractional model. in European Control Conference, (ECC, 2001) pp. 2481–2486

  10. M. Dalir, M. Bashour, Applications of fractional calculus. Appl. Math. Sci. 4(21), 1021–1032 (2010)

    MATH  MathSciNet  Google Scholar 

  11. U. Forssell, L. Ljung, Closed-loop identification revisited. Automatica 35(7), 1215–1241 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. H. Garnier, L. Wang, P.C. Young, Direct Identification of Continuous-Time Models from Sampled Data: Issues, Basic Solutions and Relevance (Springer, NY, 2008)

    Book  Google Scholar 

  13. M. Gilson, P.V. den Hof, Instrumental variable methods for closed-loop system identification. Automatica 41(2), 241–249 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. I.D. Landau, Y.D. Landau, G. Zito, Digital Control Systems: Design, Identification and Implementation (Springer, NY, 2006)

    Google Scholar 

  15. L. Lennart, System Identification: Theory for the User (Preniice Hall Inf and System Sciencess Series, New Jersey, 1999)

    Google Scholar 

  16. H.S. Li, Y. Luo, Y.Q. Chen, A fractional order proportional and derivative (fopd) motion controller: tuning rule and experiments. IEEE Trans. Control Syst. Technol. 18(2), 516–520 (2010)

    Article  Google Scholar 

  17. D. Matignon, Stability properties for generalized fractional differential systems. in ESAIM: proceedings, 5, (EDP Sciences, 1998) pp. 145–158

  18. K. Oldham, J. Spanier, The fractional calculus: theory and applications of differentiation and integration to arbitrary order. (1974)

  19. A. Oustaloup, La dérivation non entière. Hermès, (1995)

  20. J. Schorsch, H. Garnier, M. Gilson, Instrumental variable methods for identifying partial differential equation models of distributed parameter systems. in 16th IFAC Symposium on System Identification, SYSID’2012, 16, pp. 840–845 (2012)

  21. M.J. Paul, D.H. Van, R.J. Schrama, Identification and control closed-loop issues. Automatica 31(12), 1751–1770 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  22. M.T.K. Tavazoei, M. Saleh, Proportional stabilization and closed-loop identification of an unstable fractional order process. J. Process Control 24(5), 542–549 (2014)

    Article  Google Scholar 

  23. S. Victor, R. Malti, Model order identification for fractional models. in European Control Conference (ECC), (IEEE, 2013) pp. 3470–3475

  24. S. Victor, R. Malti, H. Garnier, A. Oustaloup, Parameter and differentiation order estimation in fractional models. Automatica 49(4), 926–935 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. Z. Yakoub, M. Chetoui, M. Amairi, M. Aoun, Indirect approach for closed-loop system identification with fractional models. in International Conference on Fractional Differentiation and its Applications (ICFDA), (IEEE, 2014) pp. 1–6

  26. X.J. Yang, D. Baleanu, J.A.T. Machado, Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. Bound. Value Probl. 1, 1–16 (2013)

    Google Scholar 

  27. X.J. Yang, D. Baleanu, J.A.T. Machado, Application of the Local Fractional Fourier Series to Fractal Signals. Discontin. Complex. Nonlinear Phys. Syst. Springer, 63–89, (2014)

  28. W.X. Zheng, C.B. Feng, A bias-correction method for indirect identification of closed-loop systems. Automatica 31(7), 1019–1024 (1995)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Unit Modeling, Analysis and Control of Systems (MACS)06/UR/11-12, National Engineering School of Gabes (ENIG), University of Gabes, Omar Ibn el Khattab street, 6029, Gabes, Tunisia

    Z. Yakoub, M. Amairi, M. Chetoui & M. Aoun

Authors
  1. Z. Yakoub
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Amairi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Chetoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Aoun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Amairi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yakoub, Z., Amairi, M., Chetoui, M. et al. On the Closed-Loop System Identification with Fractional Models. Circuits Syst Signal Process 34, 3833–3860 (2015). https://doi.org/10.1007/s00034-015-0046-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-015-0046-0

Keywords

Search

Navigation