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

Abdelbaki Djouambi; Abdelfatah Charef; Alina Voda besancon

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 4, page 455-462
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Djouambi, Abdelbaki, Charef, Abdelfatah, and Voda besancon, Alina. "Optimal approximation simulation and analog realization of the fundamental fractional order transfer function." International Journal of Applied Mathematics and Computer Science 17.4 (2007): 455-462. <http://eudml.org/doc/207850>.

@article{Djouambi2007,
abstract = {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.},
author = {Djouambi, Abdelbaki, Charef, Abdelfatah, Voda besancon, Alina},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {simulation and distribution of the relaxation times function; approximation; fractional systems},
language = {eng},
number = {4},
pages = {455-462},
title = {Optimal approximation simulation and analog realization of the fundamental fractional order transfer function},
url = {http://eudml.org/doc/207850},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Djouambi, Abdelbaki
AU - Charef, Abdelfatah
AU - Voda besancon, Alina
TI - Optimal approximation simulation and analog realization of the fundamental fractional order transfer function
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 4
SP - 455
EP - 462
AB - 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.
LA - eng
KW - simulation and distribution of the relaxation times function; approximation; fractional systems
UR - http://eudml.org/doc/207850
ER -

References

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