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Retroalimentación

De por WikiMatematica.org

EnsambleRetro.jpg

\[X(P)=(Y+U)G_{1}(P)\]

\[X(P)=Y(P)*G_{1}(P)+U*G_{1}(P)\]

\[U=X(P)*G_{2}(P)\]



Sustituimos U en X(P):

\[X(P)=Y*(P)G_{1}(P)+[X(P)*G_{2}(P)]*G_{1}(P)\]

\[X(P)=Y(P)*G_{1}(P)+X(P)*G_{2}(P)*G_{1}(P)\]

\[X(P)-X(P)*G_{2}(P)*G_{1}(P)=Y(P)*G_{1}(P)\]

\[X(P)[1-G_{2}(P)*G_{1}(P)]=Y(P)*G_{1}(P)\]

\[\frac{X(P)}{Y(P)}=\frac{G_{1}(P)}{1-G_{2}(P)*G_{1}(P)}\]

\[G_{E}(P)=\frac{X(P)}{Y(P)}=\frac{G_{1}(P)}{1-G_{2}(P)*G_{1}(P)}\]

\[G_{E}(P)=\frac{G_{1}(P)}{1-G_{2}(P)*G_{1}(P)}\]

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