On the fundamental linear fractional order differential equation |
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Authors: | Abdelfatah Charef Hassene Nezzari |
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Institution: | 1.Département d’Electronique,Université Mentouri-Constantine,Constantine,Algeria |
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Abstract: | This paper deals with the rational function approximation of the irrational transfer function
G(s) = \fracX(s)E(s) = \frac1(t0s)2m + 2z(t0s)m + 1]G(s) = \frac{X(s)}{E(s)} = \frac{1}{(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]} of the fundamental linear fractional order differential equation
(t0)2m\fracd2mx(t)dt2m + 2z(t0)m\fracdmx(t)dtm + x(t) = e(t)(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t), for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and
the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude
and the usefulness of the approximation method. |
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Keywords: | |
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