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IEVref:351-45-51ID:
Language:enStatus: Standard
Term: rational transfer element
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Definition: 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=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadEeadaqadaqaaiaadohaaiaawIcacaGLPaaacqGH9aqpdaWcaaqaaiaadAfadaqadaqaaiaadohaaiaawIcacaGLPaaaaeaacaWGvbWaaeWaaeaacaWGZbaacaGLOaGaayzkaaaaaiabg2da9maalaaabaGaamOyamaaBaaaleaacaaIWaaabeaakiabgUcaRiaadkgadaWgaaWcbaGaaGymaaqabaGccqGHflY1caWGZbGaey4kaSIaeSOjGSKaey4kaSIaamOyamaaBaaaleaacaWGTbaabeaakiabgwSixlaadohadaahaaWcbeqaaiaad2gaaaaakeaacaWGHbWaaSbaaSqaaiaaicdaaeqaaOGaey4kaSIaamyyamaaBaaaleaacaaIXaaabeaakiabgwSixlaadohacqGHRaWkcqWIMaYscqGHRaWkcaWGHbWaaSbaaSqaaiaad6gaaeqaaOGaeyyXICTaam4CamaaCaaaleqabaGaamOBaaaaaaaaaa@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.


Publication date:2013-11
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