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Area Control technology / Characteristics of functional units in control systems

IEV ref351-50-18

en
derivative action gain
for a proportional plus derivative element with an additional first-order lag the ratio of the maximum gain resulting from the proportional plus derivative action with first-order lag to the gain resulting from proportional action only

SEE: Figure 18.

Note 1 to entry: The transfer function of a PD element with first-order lag is

V( s ) U( s ) = K Ρ 1+ T d s 1+ T 1 s MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0Jaam4samaaBaaaleaacaqGHoaabeaakiabgwSixpaalaaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaeizaaqabaGccqGHflY1caWGZbaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaGymaaqabaGccqGHflY1caWGZbaaaaaa@4F22@

and using the derivative action gain a = Td/T1 the transfer function may be written

V( s ) U( s ) = K Ρ 1+ T d s 1+ T d s a MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0Jaam4samaaBaaaleaacaqGHoaabeaakiabgwSixpaalaaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaeizaaqabaGccqGHflY1caqGZbaabaGaaGymaiabgUcaRmaalaaabaGaamivamaaBaaaleaacaqGKbaabeaakiabgwSixlaadohaaeaacaWGHbaaaaaaaaa@5042@

where
KPis the proportional action coefficient;
Tdis the rate time;
T1is the time constant;
ais the derivative action gain, 1 < a < ∞;
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 351-28-29 in IEC 60050-351:2006.


fr
gain d'action par dérivation, m
pour un élément à action proportionnelle et par dérivation avec retard additionnel du premier ordre, rapport du gain maximal résultant d'une action proportionnelle et par dérivation, avec un retard du premier ordre, au gain dû à la seule action proportionnelle

VOIR: Figure 18.

Note 1 à l’article: La fonction de transfert d’un élément PD avec un retard du premier ordre est

V( s ) U( s ) = K Ρ 1+ T d s 1+ T 1 s MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0Jaam4samaaBaaaleaacaqGHoaabeaakiabgwSixpaalaaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaeizaaqabaGccqGHflY1caWGZbaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaGymaaqabaGccqGHflY1caWGZbaaaaaa@4F22@

et utilisant le gain d'action par dérivation a = Td/T1, la fonction de transfert peut être écrite

V( s ) U( s ) = K Ρ 1+ T d s 1+ T d s a MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaamOvamaabmaabaGaam4CaaGaayjkaiaawMcaaaqaaiaadwfadaqadaqaaiaadohaaiaawIcacaGLPaaaaaGaeyypa0Jaam4samaaBaaaleaacaqGHoaabeaakiabgwSixpaalaaabaGaaGymaiabgUcaRiaadsfadaWgaaWcbaGaaeizaaqabaGccqGHflY1caqGZbaabaGaaGymaiabgUcaRmaalaaabaGaamivamaaBaaaleaacaqGKbaabeaakiabgwSixlaadohaaeaacaWGHbaaaaaaaaa@5042@

KPest le coefficient d’action proportionnelle;
Tdest le temps de dosage de dérivation;
T1est la constante de temps;
aest le gain d’action par dérivation, 1 < a < ∞;
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 351-28-29 dans la CEI 60050-351:2006.

Figure 18 – Step response of a proportional plus derivative element with additional first order delay

Figure 18 – Réponse à un échelon d'un élément à action proportionnelle et par dérivation avec retard additionnel du premier ordre


ar
كسب فعل اشتقاقي

de
Vorhaltverstärkung, f

es
ganancia de acción PD, f

fi
derivoinnin maksimivahvistus

it
guadagno d’azione per derivazione

ko
미분 동작 이득

ja
微分動作利得
微分動作ゲイン

pl
wzmocnienie różniczkowania

pt
ganho de ação derivada

zh
微分作用增益

Publication date: 2013-11
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