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Area Control technology / Behaviour and characteristics of transfer elements

IEV ref351-45-51

en
rational transfer element
linear time-invariant transfer element the transfer function of which may be written as a quotient of two polynomials in s

G( s )= V( s ) U( s ) = b 0 + b 1 s++ b m s m a 0 + a 1 s++ a n s n MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=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@63DB@ with aj and bj real, an ≠ 0, bm ≠ 0

where
ai, biare the polynomial coefficients;
sis the complex variable of the Laplace transform;
U(s)is the input transform;
V(s)is the output transform.

Note 1 to entry: In real controlled systems, m < n. With respect to mathematical denomination these elements would have to be called "proper-fractional rational transfer element" which is not usage.

Note 2 to entry: An element with dead time is an example for a non-rational transfer element.

Note 3 to entry: This entry was numbered 351-24-43 in IEC 60050-351:2006.


fr
élément de transfert rationnel, m
élément linéaire de transfert invariant dans le temps, dont la fonction de transfert peut être écrite comme un quotient de deux polynômes en s

G( s )= V( s ) U( s ) = b 0 + b 1 s++ b m s m a 0 + a 1 s++ a n s n MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=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@63DB@ avec aj et bj réel, an ≠ 0, bm ≠ 0

ai, bisont les polynom coefficients;
sest la variable complexe de la transformée de Laplace;
U(s)est la transformée de la variable d’entrée;
V(s)est la transformée de la variable de sortie.

Note 1 à l’article: Dans les systèmes commandés réels, m < n. Eu égard à la dénomination mathématique, ces éléments devraient être nommés "élément de transfert rationnel à fraction propre" mais ce terme n’est pas usité.

Note 2 à l’article: Un élément avec temps mort est un exemple d'élément de transfert non-rationnel.

Note 3 à l'article: Cet article était numéroté 351-24-43 dans la CEI 60050-351:2006.


ar
عنصر تحويل نسبى

de
rationales Übertragungsglied, n

es
elemento de transferencia racional, m

fi
rationaalinen siirtoelementti

it
elemento di trasferimento razionale

ko
유리형 전달 요소

ja
有理伝達要素

pl
człon funkcjonalny wymierny
element funkcjonalny wymierny

pt
elemento de transferência racional

zh
有理传递元件

Publication date: 2013-11
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