Closed-loop transfer function: Difference between revisions

Revision as of 02:22, 30 June 2016

Revision as of 19:30, 14 September 2017

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: <math>Z(s) = X(s)-Y(s)H(s)</math>

: <math>XY(s) = Z(X(s)-Y(s)H(s))G(s) += X(s)G(s) - Y(s)H(s)G(s)</math>

: <math>XY(s) = Z+Y(s) + ZH(s)G(s)H = X(s)G(s)</math>

: <math>\Rightarrow \dfrac{Y(s)}{X(s)} = \dfrac{Z1+H(s)G(s)}{Z(s) += ZX(s)G(s) H(s)}</math>

: <math>\Rightarrow \dfrac{Y(s)}{X(s)} = \dfrac{G(s)}{1 + GH(s) HG(s)}</math>

==See also==