Fractional Order System Identification

  • Saptarshi DasEmail author
  • Indranil Pan
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


This chapter discusses various time domain and frequency domain system identification methods for fractional order systems from practical test data. System identification is important in cases where it is difficult to obtain the model from basic governing equations and first principles, or where there is only input–output data available and the underlying phenomena are largely unknown. As is evident, fractional order models are better capable of modeling system dynamics than their integer order counterparts. Hence, identification using fractional order models is of practical interest from the system designer’s point of view.


Time domain FO system identification Frequency domain FO system identification Levy’s identification method Vinagre’s identification method 


  1. Aoun, M., Malti, R., Levron, F., Oustaloup, A.: Synthesis of fractional Laguerre basis for system approximation. Autom. 43(9), 1640–1648 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  2. Djamah, T., Mansouri, R., Djennoune, S., Bettayeb, M.: Optimal low order model identification of fractional dynamic systems. Appl. Math. Comput. 206(2), 543–554 (2008). doi: 10.1016/j.amc.2008.05.109 MathSciNetzbMATHCrossRefGoogle Scholar
  3. Gabano, J.D., Poinot, T.: Estimation of thermal parameters using fractional modelling. Signal Process. 91(4), 938–948 (2011). doi: 10.1016/j.sigpro.2010.09.013 zbMATHCrossRefGoogle Scholar
  4. Gabano, J.D., Poinot, T.: Fractional modelling and identification of thermal systems. Signal Process. 91(3), 531–541 (2011). doi: 10.1016/j.sigpro.2010.02.005 zbMATHCrossRefGoogle Scholar
  5. Gabano, J.D., Poinot, T., Kanoun, H.: Identification of a thermal system using continuous linear parameter-varying fractional modelling. Control Theory & Applications, IET 5(7), 889–899 (2011)CrossRefGoogle Scholar
  6. Ghanbari, M., Haeri, M.: Order and pole locator estimation in fractional order systems using bode diagram. Signal Process. 91(2), 191–202 (2011). doi: 10.1016/j.sigpro.2010.06.021 zbMATHCrossRefGoogle Scholar
  7. Hartley, T.T., Lorenzo, C.F.: Fractional-order system identification based on continuous order-distributions. Signal Process. 83(11), 2287–2300 (2003). doi: 10.1016/s0165-1684(03)00182-8 zbMATHCrossRefGoogle Scholar
  8. Malti, R., Victor, S., Nicolas, O., Oustaloup, A.: System identification using fractional models: state of the art. ASME Conf. Proc. 2007(4806X), 295–304 (2007). doi: 10.1115/detc2007-35332 Google Scholar
  9. Nazarian, P., Haeri, M.: Generalization of order distribution concept use in the fractional order system identification. Signal Process. 90(7), 2243–2252 (2010). doi: 10.1016/j.sigpro.2010.02.008 zbMATHCrossRefGoogle Scholar
  10. Sabatier, J., Aoun, M., Oustaloup, A., Grégoire, G., Ragot, F., Roy, P.: Fractional system identification for lead acid battery state of charge estimation. Signal Process. 86(10), 2654–2657 (2006). doi: 10.1016/j.sigpro.2006.02.030 CrossRefGoogle Scholar
  11. Sanathanan, C., Koerner, J.: Transfer function synthesis as a ratio of two complex polynomials. Autom. Control IEEE Trans. 8(1), 56–58 (1963)CrossRefGoogle Scholar
  12. Valério, D., Costa, J.: Identification of fractional models from frequency data. In: Sabatier et al. (eds.) Advances in fractional calculus, part 4, pp. 229–242. Springer (2007). doi: 10.1007/978-1-4020-6042-7_16
  13. Valerio, D., Ortigueira, M.D., da Costa, J.S.: Identifying a transfer function from a frequency response. J. Comput. Nonlinear Dyn. 3(2), 021207–021207 (2008). doi: 10.1115/1.2833906 CrossRefGoogle Scholar
  14. Valério, D., Sá da Costa, J.: Levy’s identification method extended to commensurate fractional order transfer functions. In: Fifth EUROMECH Nonlinear Dynamics Conference 2005, pp. 1357–1366. EUROMECHGoogle Scholar
  15. Valério, D., Sá da Costa, J.: Finding a fractional model from frequency and time responses. Commun. Nonlinear Sci. Numer. Simul. 15(4), 911–921 (2010). doi: 10.1016/j.cnsns.2009.05.014 MathSciNetCrossRefGoogle Scholar
  16. Valério, D., Sá da Costa, J.: Identifying digital and fractional transfer functions from a frequency response. Int. J. Control 84(3), 445–457 (2011). doi: 10.1080/00207179.2011.560397 zbMATHCrossRefGoogle Scholar
  17. Wang, L., Cheng, P., Wang, Y.: Frequency domain subspace identification of commensurate fractional order input time delay systems. Int. J. Control Autom. Syst. 9(2), 310–316 (2011)CrossRefGoogle Scholar

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© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Power Engineering, School of Nuclear Studies and ApplicationsJadavpur UniversityKolkataIndia
  2. 2.Department of Power EngineeringJadavpur UniversityKolkataIndia

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