Continuous-time model identification of fractional-order models with time delays

Author(s): A. Narang ; S.L. Shah ; T. Chen
DOI: 10.1049/iet-cta.2010.0718

For access to this article, please select a purchase option:

Buy article PDF

Buy Knowledge Pack

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership

Recommend Title Publication to library

IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Author(s): A. Narang ¹ ; S.L. Shah ¹ ; T. Chen ²
- Affiliations: 1: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada
  2: Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada
Source: Volume 5, Issue 7, 5 May 2011, p. 900 – 912
DOI: 10.1049/iet-cta.2010.0718 , Print ISSN 1751-8644, Online ISSN 1751-8652

Modelling of real physical systems having long memory transients and infinite dimensional structures using fractional-order dynamic models has significantly attracted interest over the last few years. For this reason, many identification techniques both in the frequency domain and time domain have been developed to model these fractional-order systems. However, in many processes time delays are also present and estimation of time delays along with continuous-time fractional-order model parameters have not been addressed anywhere. This study deals with the continuous-time model identification of fractional-order system models with time delays. In this study, a new linear filter is introduced for simultaneous estimation of all model parameters for commensurate fractional-order system models with time delays. The proposed method simultaneously estimates time delays along with other model parameters in an iterative manner by solving simple linear regression equations. For the case when the fractional order is unknown, we also propose a nested loop optimisation method where the time delay along with other model parameters are estimated iteratively in the inner loop and the fractional order is estimated in the non-linear outer loop. The applicability of the developed procedure is demonstrated by simulations on a fractional-order system model by doing Monte Carlo simulation analysis in the presence of white noise. The proposed algorithm has also been applied to identify a process of thermal diffusion in a wall in simulation, which are characterised by fractional-order behaviour.

References

1. 1)
  - Narang, A., Shah, S.L., Chen, T.: `Continuous time model identification of fractional order models with time delays', 15thIFAC Symp. on System Identification, 2009, Saint-Malo, France, p. 916–921.
2. 2)
  - Matignon, D.: `Stability properties for generalized fractional differential systems', ESAIM Proc., 1998, p. 145–158.
3. 3)
  - Q.G. Wang , Y. Zhang . Robust identification of continuous systems with dead-time from step responses. Automatica , 377 - 390
4. 4)
  - Gabano, J.D., Poinot, T.: `Fractional identification algorithms applied to thermal parameter estimation', 15thIFAC Symp. on System Identification, 2009, Saint-Malo, France, p. 1316–1321.
5. 5)
  - J. Sabatier , M. Aoun , A. Oustaloup , G. Grégoire , F. Ragot , P. Roy . Fractional system identification for lead acid battery state of charge estimation. Signal Process. , 2645 - 2657
6. 6)
  - M. Aoun , R. Malti , F. Levron , A. Oustaloup . Synthesis of fractional Laguerre basis for system approximation. Automatica , 1640 - 1648
7. 7)
  - M. Ortigueira , J. Tenreiro . Signal processing special issue: fractional calculus applications in signals and systems. Signal Process. , 2285 - 2480
8. 8)
  - Q. Bi , W.J. Cai , E.L. Lee , Q.G. Wang , C.C. Hang , Y. Zhang . Robust identification of first-order plus dead-time model from step response. Control Eng. Pract. , 71 - 77
9. 9)
  - Victor, S., Malti, R., Oustaloup, A.: `Instrumental variable method with optimal fractional differentiation order for continuous-time system identification', 15thIFAC Symp. on System Identification, 2009, Saint-Malo, France, p. 904–909.
10. 10)
  - Lin, J.: `Modélisation et identification de systémes d'ordre non entier', 2001, PhD, Université de Poitiers, Poitiers, France.
11. 11)
  - B.M. Vinagre , I. Podlubny , A. Hernandez , V. Feliu . Some approximations of fractional order operators used in control theory and applications. Fractional Calculus & Applied Analysis , 3 , 231 - 248
12. 12)
  - Malti, R., Sabatier, J., Akçay, H.: `Thermal modeling and identification of an aluminum rod using fractional calculus', 15thIFAC Symp. on System Identification, 2009, Saint-Malo, France, p. 958–963.
13. 13)
  - Cois, O.: `Systèmes linéaires non entiers et identification par modèle non entier: application en thermique', 2002, PhD, Université Bordeaux, Talence, France.
14. 14)
  - A. Benchellal , T. Poinot , J.-C. Trigeassou . Approximation and identification of diffusive interfaces by fractional models. Signal Process. , 2712 - 2727
15. 15)
  - M. Muddu , A. Narang , S.C. Patwardhan . Reparametrized ARX models for predictive control of staged and packed bed distillation columns. Control Eng. Pract. , 2 , 114 - 130
16. 16)
  - Y. Chen , K.L. Moore . Discretization schemes for fractional differentiators and integrators. IEEE Trans. Circuits Syst.1: Fundam. Theory Appl. , 3 , 363 - 367
17. 17)
  - I. Podlubny . (1999) Fractional differential equations.
18. 18)
  - Cois, O., Oustaloup, A., Poinot, T., Battaglia, J.L.: `Fractional state variable filter for system identification by fractional model', IEEE Sixth European Control Conf. (ECC'2001), 2001, Portugal.
19. 19)
  - P.C. Young . An instrumental variable method for real time identification of noisy process. Automatica , 271 - 287
20. 20)
  - K.B. Oldham , J. Spanier . (1974) The fractional calculus.
21. 21)
  - R. Malti , S. Victor , A. Oustaloup . Advances in system identification using fractional models. J. Comput. Nonlinear Dyn. , 021401 (1 - 7)
22. 22)
  - V.G. Jenson , G.V. Jeffreys . (1977) Mathematical methods in chemical engineering.
23. 23)
  - R.L. Bagley , P. Torvik . On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. , 1 , 294 - 298
24. 24)
  - S. Ahmed , B. Huang , S.L. Shah . Novel identification method from step response. Control Eng. Pract. , 545 - 556
25. 25)
  - D.E. Seborg , T.F. Edgar , D.A. Mellichamp . (1989) Process dynamics and control.
26. 26)
  - M. Muddu , A. Narang , S.C. Patwardhan . Development of ARX models for predictive control using fractional order and orthonormal basis filter parametrization. Ind. Eng. Chem. Res. , 19 , 8966 - 8979
27. 27)
  - A. Oustaloup . (1995) La Dérivation non entiére.
28. 28)
  - Malti, R., Victor, S., Oustaloup, A., Garnier, H.: `An optimal instrumental variable method for continuous-time fractional model identification', Proc. 17th IFAC World Congress, 2008, Korea, p. 14379–14384.
29. 29)
  - Manabe, S.: `Early development of fractional order control', Proc. ASME 2003 Design Engineering and Technology Conf., 2003, Chicago, p. 609–616.
30. 30)
  - Benchellal, A., Bachir, S., Poinot, T., Trigeassou, J.C.: `Identification of a non-integer model of induction machines', IFAC Workshop on Fractional Differentiation and its Applications (FDA'04), 2004, Bordeaux, France, p. 400–407.
31. 31)
  - Le Lay, L.: `Identification fréquentielle et temporelle par modèle non entier', 1998, PhD, Université Bordeaux, Talence, France.

Continuous-time model identification of fractional-order models with time delays

Continuous-time model identification of fractional-order models with time delays

Buy article PDF

Buy Knowledge Pack

Thank you

References

Related content