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2007 | 17 | 4 | 455-462

Tytuł artykułu

Optimal approximation simulation and analog realization of the fundamental fractional order transfer function

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This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit, which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.








Opis fizyczny




  • Department of Electronics, University of Oum El-Bouaghi, Oum El-Bouaghi, Algeria
  • Department of Electronics, University Mentouri of Constantine, Route Ain El-Bey, Constantine, Algeria
  • Laboratory of Automatic Control of Grenoble, LAG-ENSIEG, BP 46 Rue de la Houille Blanche, St Martin d'Heres, France


  • Aoun M., Malti R., Levron F and Oustaloup A. (2003): Numerical simulation of fractional systems. Proceedings of DETC'03 ASME 2003 Design Engineering Technical Conference and Computers and Information in Engineering Conference, Chicago, USA.
  • Barbosa R.S., Machado T.J.A. and Silva M.F. (2006): Descritization of complex-order differintegrals. Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, pp.340-345.
  • Cole K.S. and Cole R.H. (1941): Dispersion and absorption in dielectrics, alternation current characterization. Journal of Chemical Physics Vol.9, pp.341-351.
  • Charef A., Sun H.H., Tsao Y.Y. and Onaral B. (1992): Fractal system as represented by singulary function. IEEE Transactions on Automatic Control, Vol.37, No.9, pp.1465-1470.
  • Chen Y.Q. and Moore K.L. (2002): Discretization schemes for fractional-order differentiators and integrators. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol.49, No.3, pp.363-367.
  • Davidson D. and Cole R. (1950), Dielectric relaxation in glycerine. Journal of Chemical Physics, Vol.18, pp.1417-1418.
  • Fuross R.M. and Kirkwood J.K. (1941): Electrical properties of solids VIII-Dipole moments in polyvinyl chloride biphenyl systems. Journal of the American Chemical Society, Vol.63,pp.385-394.
  • Hartley T.T. and Lorenzo C.F. (1998): A solution of the fundamental linear fractional order differential equation. Technical Report No.TP-1998-208693, NASA, Ohio.
  • Goldberger A.L., Bhargava V., West B.J. and Mandell A.J. (1985): On the mechanism of cardiac electrical stability. Biophysics Journal, Vol.48, pp.525-528.
  • Ichise M., Nagayanagi Y and Kojima T. (1971): An analog simulation of non-integer order transfer functions for analysis of electrode processes. Journal of Electro-Analytical Chemistry, Vol.33, pp.253-265.
  • Kuo, Benjamin C. (1995): Automatic Control Systems. Englewood Cliffs: Prentice-Hall.
  • Manabe S. (1961): The non-integer integral and its application to control systems. ETJ of Japan, Vol.6, Nos.3-4, pp.83-87.
  • Miller K.S. and Ross B. (1993): An Introduction to the Fractional Calculus and Fractional Differential Equations. New-York: Wiley.
  • Oustaloup A. (1983) : Systemes Asservis Lineaires d'Ordre Fractionnaire: Theorie et Pratique. Paris: Masson.
  • Oustaloup A. (1995) : La Derivation Non Entiere, Theorie, Synthese et Application. Paris: Hermes.
  • Poinot T. and Trigeassou J. C. (2004): Modelling and simulation of fractional systems. Proceedings of the 1st IFAC Workshop on Fractional Differentiation and its Application, Bordeaux, France, pp.656-663.
  • Podlubny I. (1994): Fractional-order systems and fractional-order controllers. Technical Report No.UEF-03-94, Slovak Academy of Sciences, Kosice, Slovakia.
  • Podlubny I. (1999): Fractional Differential Equations. San Diego: Academic Press.
  • Petras I., Podlubny I., Vinagre M., Dorcak L. and O'Learya P.(2002): Analogue Realization of Fractional Order Controllers. Fakulta Berg, Technical University of Kosice, Slovakia.
  • Sun H.H. and Onaral B. (1983): A unified approach to represent metal electrode polarization. IEEE Transactions on Biomedical Engineering, Vol.30, pp.399-406.
  • Sun H.H., Charef A., Tsao Y.Y. and Onaral B. (1992): Analysis of polarization dynamics by singularity decomposition method. Annals of Biomedical Engineering, Vol.20, pp.321-335.
  • Torvik P.J. and Bagley R.L. (1984): On the appearance of the fractional derivative in the behavior of real materials. Transactions of the ASME, Vol.51, pp.294-298.
  • Vinagere B.M., Podlubny I., Hernandez A. and Feliu V. (2000): Some approximations of fractional order operators used in control theory and applications. Journal of Fractional Calculus and Applied Analysis, Vol.3, No.3, pp.231-248

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