Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function 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 sys...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science 2007-12, Vol.17 (4), p.455-462
Main Authors: Djouambi, Abdelbaki, Charef, Abdelfatah, Besançon, Alina
Format: Article
Language:English
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Engineering Sciences
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Summary:Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function 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 for a 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.
ISSN:1641-876X
2083-8492
DOI:10.2478/v10006-007-0037-9