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Approximation method for a fractional order transfer function with zero and pole

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper presents an approximation method for elementary fractional order transfer function containing both pole and zero. This class of transfer functions can be applied for example to build model - based special control algorithms. The proposed method bases on Charef approximation. The problem of cancelation pole by zero with useful conditions was considered, the accuracy discussion with the use of interval approach was done also. Results were depicted by examples.
Rocznik
Strony
447--463
Opis fizyczny
Bibliogr. 20 poz., rys., tab., wzory
Twórcy
  • AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Dept. of Automatics and Biomedical Engineering, kop@agh.edu.pl
Bibliografia
  • [1] R. Caponetto, G. Dongola, L. Fortuna and I. Petras: Fractional Order Systems. Modeling and Control Applications.World Scientific Series on Nonlinear Science, Series A, 72 World Scientific Publishing, 2010
  • [2] A. Charef, H. H. Sun, Y. Y. Tsao and B. Onaral: Fractional system as represented by singularity function. IEEE Trans. on Automatic Control, 37(9), (1992), 1465-1470.
  • [3] Y. Q. Chen: Oustaloup Recursive Approximation for Fractional Order Differentiators.MathWorks, Inc. Matlab Central File Exchange, 2003.
  • [4] S. Das: Functional Fractional Calculus for System Identification and Controls.Springer, 2008.
  • [5] S. Das and I. Pan: Intelligent Fractional Order Systems and Control. An Introduction.Springer, 2013.
  • [6] A. Djouambi, A. Charef and A. Besancon: Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function.Int. J. of Applied Mathematics and Computers Science, 17(4), (2007), 455-462.
  • [7] T. Kaczorek: Selected Problems in Fractional Systems Theory. Springer, 2011.
  • [8] T. Kaczorek: Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems. Archives of Electrical Engineering, 62(2), (2013), 345-355.
  • [9] F. Merrikh-Bayat: (2012) Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDμ controller. Communications in Nonlinear Science and Numerical Simulation, 17(4), (2012) 1852-1861.
  • [10] W. Mitkowski, J. Kacprzyk and J. Baranowski: (Ed.) Advances in the Theory and Applications of Non-Integer Order Systems. 5th Conf. on Non-Integer Order Calculus and its Applications, Cracow, Poland. Lecture Notes in Electrical Engineering 257, Springer, 2013.
  • [11] W. Mitkowski: Approximation of factional diffusion-wave equation. Acta Mechanica et Automatica, 5(2), (2011), 65-68.
  • [12] W. Mitkowski and A. Obraczka: Simple identification of fractional differential equation. Solid State Phenomena, 180 (2012), 331-338.
  • [13] W. Mitkowski and P. Skruch: Fractional-order models of the supercapacitors in the form of RC ladder networks. Bulletin of the Polish Academy of Sciences.Technical Sciences, 61(3), (2013), 581-587.
  • [14] A. Obraczka and W. Mitkowski: The comparison of parameter identification methods for fractional partial differential equation. Solid State Phenomena, 210 (2014), 265-270.
  • [15] K. Oprzędkiewicz: A Strejc model-based, semi-fractional (SSF) transfer function model. Automatics, AGH UST, 16(2), (2012), pp. 145-154, full text link: http://journals.bg.agh.edu.pl/AUTOMAT/2012.16.2/automat.2012.16.2.145.pdf
  • [16] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
  • [17] I. Podlubny: Matrix approach to discrete fractional calculus. Fractional Calculus and Applied Analysis, 3(4), (2000), 359-386.
  • [18] B. M. Vinagre, I. Podlubny, A. Hernandez and V. Feliu: Some approximations of fractional order operators used in control theory and applications. Fractional Calculus and Applied Analysis, 3(3), (2000), 231-248.
  • [19] M. Weilbeer: Efficient Numerical Methods for Fractional Differential Equations and their Analytical. Technischen Universit at Braunschweig, PhD Dissertation, 2005.
  • [20] Q. Yang: Novel Analytical and Numerical Methods for Solving Fractional Dynamical Systems. Queensland University of Technology, PhD Dissertation, 2010.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-de12ae5f-a00a-4bab-994b-9e0dcc6bc36a
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