Closed-loop transfer function: Difference between revisions

Revision as of 09:23, 27 May 2018

Revision as of 16:09, 12 March 2019

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Using this figure we write:

: <math>Y(s) = ZG(s)GZ(s) </math>

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

: <math>Y(s) = (XG(s)-Y(X(s)-H(s))GY(s)) = XG(s)GX(s) - YG(s)H(s)GY(s)</math>

: <math>Y(s)+YG(s)H(s)GY(s) = XG(s)GX(s)</math>

: <math>Y(s)(1+HG(s)GH(s)) = XG(s)GX(s)</math>

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

==See also==