Queries, comments, suggestions? Please contact us.



Area Control technology / Variables and signals

IEV ref351-41-08

en
state variable
element of a vector x(t) in a system with the differential equations

x ˙ ( t )=f[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadAgadaWadaqaaiaadIhadaqadaqaaiaadshaaiaawIcacaGLPaaacaGGSaGaaGPaVlaaykW7caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaacaGLBbGaayzxaaaaaa@477A@ state equation
v( t )=g[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGNbWaamWaaeaacaWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaaiilaiaaykW7caaMc8UaamyDamaabmaabaGaamiDaaGaayjkaiaawMcaaaGaay5waiaaw2faaaaa@4770@ output equation,

and for linear systems

x ˙ ( t )=Ax( t )+Bu( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadgeacqGHflY1caWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaey4kaSIaamOqaiabgwSixlaadwhadaqadaqaaiaadshaaiaawIcacaGLPaaaaaa@47DA@ state equation
v( t )=Cx( t )+Du( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGdbGaeyyXICTaamiEamaabmaabaGaamiDaaGaayjkaiaawMcaaiabgUcaRiaadseacqGHflY1caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaaaa@47D3@ output equation,

from which for known initial values of the vector elements at any given instant t0 (often with t0 = 0) and known course of the elements of the input vector u(t) the course of the elements of the output vector v(t) may be calculated starting at t0

SEE: Figure 3.

Note 1 to entry: In case of discrete-time variables the describing equations are

xi+1 = f (xi, ui)state equation
vi = g (xi, ui)output equation,

and for linear systems

xi+1 = Φ·xi + H·uistate equation
vi = C·xi + D·uioutput equation.

Note 2 to entry: This entry was numbered 351-21-08 in IEC 60050-351:2006.


fr
variable d'état, f
élément d'un vecteur x(t) dans un système d'équations différentielles

x ˙ ( t )=f[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadAgadaWadaqaaiaadIhadaqadaqaaiaadshaaiaawIcacaGLPaaacaGGSaGaaGPaVlaaykW7caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaacaGLBbGaayzxaaaaaa@477A@ équation d'état
v( t )=g[ x( t ),u( t ) ] MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGNbWaamWaaeaacaWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaaiilaiaaykW7caaMc8UaamyDamaabmaabaGaamiDaaGaayjkaiaawMcaaaGaay5waiaaw2faaaaa@4770@ équation de sortie,

et pour les systèmes linéaires

x ˙ ( t )=Ax( t )+Bu( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiqadIhagaGaamaabmaabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadgeacqGHflY1caWG4bWaaeWaaeaacaWG0baacaGLOaGaayzkaaGaey4kaSIaamOqaiabgwSixlaadwhadaqadaqaaiaadshaaiaawIcacaGLPaaaaaa@47DA@ équation d'état
v( t )=Cx( t )+Du( t ) MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWaamGadaGadeaabaGaaqaaaOqaaiaadAhadaqadaqaaiaadshaaiaawIcacaGLPaaacqGH9aqpcaWGdbGaeyyXICTaamiEamaabmaabaGaamiDaaGaayjkaiaawMcaaiabgUcaRiaadseacqGHflY1caWG1bWaaeWaaeaacaWG0baacaGLOaGaayzkaaaaaa@47D3@ équation de sortie,

à partir desquelles la course des éléments du vecteur de sortie v(t) peut être calculée, avec des valeurs initiales connues des éléments du vecteur x(t) à tout instant t0 (souvent avec t0 = 0), avec une course connue des éléments du vecteur d’entrée u(t), et en partant de t0

VOIR: Figure 3.

Note 1 à l'article: En cas de variables à temps discret, les équations sont les suivantes:

xi+1 = f (xi, ui)équation d'état
vi = g (xi, ui)équation de sortie,

et pour les systèmes linéaires

xi+1 = Φ·xi + H·uiéquation d'état
vi = C·xi + D·uiéquation de sortie.

Note 2 à l'article: Cet article était numéroté 351-21-08 dans la CEI 60050-351:2006.

Figure 3 – Linear transfer system with state variables

Figure 3 – Système de transfert linéaire avec variables d'état


ar
متغير حالة

de
Zustandsgröße, f

es
variable de estado, f

fi
tilasuure

it
variabile di stato

ko
상태 변수

ja
状態変数

pl
zmienna stanu

pt
variável de estado

zh
状态变量

Publication date: 2013-11
Copyright © IEC 2019. All Rights Reserved.