Queries, comments, suggestions? Please contact us.



Area Control technology / Characteristics of functional units in control systems

IEV ref351-50-03

en
second-order lag element
linear time-invariant transfer element the transfer function of which has exactly two poles with negative real parts which may be real or complex conjugate and no zeros

Note 1 to entry: The transfer function of a second-order lag element is given as

V( s ) U( s ) = K Ρ ( 1+ T 1 s )( 1+ T 2 s ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaSqaaiaabg6aaeqaaaGcbaWaaeWaaeaacaaIXaGaey4kaSIaamivamaaBaaaleaacaaIXaaabeaakiabgwSixlaadohaaiaawIcacaGLPaaacqGHflY1daqadaqaaiaaigdacqGHRaWkcaWGubWaaSbaaSqaaiaaikdaaeqaaOGaeyyXICTaam4CaaGaayjkaiaawMcaaaaaaaa@5209@ for two real poles

and as

V( s ) U( s ) = K Ρ s 2 ω 0 2 +2ϑ s ω 0 +1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvam aabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaa dohaaiaawIcacaGLPaaaaaGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaS qaaiaabg6aaeqaaaGcbaWaaSaaaeaacaWGZbWaaWbaaSqabeaacaaI YaaaaaGcbaGaeqyYdC3aa0baaSqaaiaaicdaaeaacaaIYaaaaaaaki abgUcaRiaaikdacqGHflY1cqaHrpGscqGHflY1daWcaaqaaiaadoha aeaacqaHjpWDdaWgaaWcbaGaaGimaaqabaaaaOGaey4kaSIaaGymaa aaaaa@520D@ for a complex conjugate pair of poles

where
KPis the proportional action coefficient;
T1, T2are the time constants;
ϑ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbbjxAHXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaeqabiGaciGacaqadmaadaqaaqaaaOqaaiabeg9akbaa@36F5@ is the damping ratio;
ω0is the characteristic angular frequency;
sis the complex variable of the Laplace transform;
U(s)is the input transform;
V(s)is the output transform.

Note 2 to entry: This entry was numbered 351-28-14 in IEC 60050-351:2006.


fr
élément de retard du second ordre, m
élément de transfert linéaire invariant dans le temps dont la fonction de transfert a exactement deux pôles avec des parties réelles négatives, qui peuvent être réels ou imaginaires conjugués, et pas de zéro

Note 1 à l’article: La fonction de transfert d'un élément de retard de second ordre est donnée par

V( s ) U( s ) = K Ρ ( 1+ T 1 s )( 1+ T 2 s ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaSqaaiaabg6aaeqaaaGcbaWaaeWaaeaacaaIXaGaey4kaSIaamivamaaBaaaleaacaaIXaaabeaakiabgwSixlaadohaaiaawIcacaGLPaaacqGHflY1daqadaqaaiaaigdacqGHRaWkcaWGubWaaSbaaSqaaiaaikdaaeqaaOGaeyyXICTaam4CaaGaayjkaiaawMcaaaaaaaa@5209@ pour deux pôles réels

et par

V( s ) U( s ) = K Ρ s 2 ω 0 2 +2ϑ s ω 0 +1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvam aabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaa dohaaiaawIcacaGLPaaaaaGaeyypa0ZaaSaaaeaacaWGlbWaaSbaaS qaaiaabg6aaeqaaaGcbaWaaSaaaeaacaWGZbWaaWbaaSqabeaacaaI YaaaaaGcbaGaeqyYdC3aa0baaSqaaiaaicdaaeaacaaIYaaaaaaaki abgUcaRiaaikdacqGHflY1cqaHrpGscqGHflY1daWcaaqaaiaadoha aeaacqaHjpWDdaWgaaWcbaGaaGimaaqabaaaaOGaey4kaSIaaGymaa aaaaa@520D@ pour une paire de pôles imaginaires conjugués

KPest le coefficient d’action proportionnelle;
T1, T2sont les constantes de temps;
ϑ MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiabeg9akbaa@36F8@ est le taux d’amortissement;
ω0est la pulsation caractéristique;
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 2 à l'article: Cet article était numéroté 351-28-14 dans la CEI 60050-351:2006.


ar
عنصر تأخير من الدرجة الثانية

de
Verzögerungsglied zweiter Ordnung, n
P-T2-Glied, n

es
elemento de retraso de segundo orden, m

fi
toisen asteen vaiheenjättöelementti

it
elemento di ritardo del secondo ordine

ko
이차 지연 요소

ja
二次遅れ要素

pl
człon inercyjny drugiego rzędu
element inercyjny drugiego rzędu

pt
elemento de atraso de segunda ordem

zh
二阶滞后元件

Publication date: 2013-11
Copyright © IEC 2020. All Rights Reserved.