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

The paper presents an approximation method for elementary fractional order transfer func-tion containing both pole and zero. This class of transfer functions can be applied for exampleto build model - based special control algorithms. The proposed method bases on Charef ap-proximation. 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 depictedby examples.Key words: fractional order systems, fractional order transfer function, Charef approxi-mation

[1]  Alina Voda,et al.  Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function , 2007, Int. J. Appl. Math. Comput. Sci..

[2]  Tadeusz Kaczorek,et al.  Selected Problems of Fractional Systems Theory , 2011 .

[3]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[4]  Krzysztof Oprzedkiewicz,et al.  An Estimation of Accuracy of Charef Approximation , 2015, RRNR.

[5]  Jerzy Baranowski,et al.  Advances in the Theory and Applications of Non-integer Order Systems - 5th Conference on Non-integer Order Calculus and Its Applications, RRNR 2013, Cracow, Poland, July 4-5, 2013 , 2013, RRNR.

[6]  Qianqian Yang,et al.  Novel analytical and numerical methods for solving fractional dynamical systems , 2010 .

[7]  P. Skruch,et al.  Fractional-order models of the supercapacitors in the form of RC ladder networks , 2013 .

[8]  Wojciech Mitkowski,et al.  Simple Identification of Fractional Differential Equation , 2011 .

[9]  Tadeusz Kaczorek Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems , 2013 .

[10]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[11]  Saptarshi Das,et al.  Intelligent Fractional Order Systems and Control - An Introduction , 2012, Studies in Computational Intelligence.

[12]  Marc Weilbeer,et al.  Efficient Numerical Methods for Fractional Differential Equations and their Analytical Background , 2005 .

[13]  Krzysztof Oprzędkiewicz A Strejc model-based, semi-fractional (SSF) transfer function model , 2012 .

[14]  B. Onaral,et al.  Fractal system as represented by singularity function , 1992 .

[15]  I. Podlubny Matrix Approach to Discrete Fractional Calculus , 2000 .

[16]  Wojciech Mitkowski Approximation of Fractional Diffusion-Wave Equation , 2011 .

[17]  Wojciech Mitkowski,et al.  The Comparison of Parameter Identification Methods for Fractional, Partial Differential Equation , 2013 .

[18]  J. Kwaśniewski,et al.  BADANIA LABORATORYJNE WËASNO ŚCI MECHANICZNYCH PRÓBEK KOMPOZYTÓW POLIMEROWO-METALOWYCH IPMC , 2011 .

[19]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[20]  Farshad Merrikh-Bayat,et al.  Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDμ controller , 2012 .

[21]  I. Petráš Fractional Order Systems , 2011 .