Closed-loop transfer function: Difference between revisions

Revision as of 22:27, 11 July 2014

Revision as of 19:20, 13 April 2015

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Using this figure we write:

: <math>Y(s) = Z(s)G(s) \Rightarrow Z(s) = \dfrac{Y(s)}{G(s)} </math>

: <math>X(s)-Y(s)H(s) = Z(s) = \dfrac{Y(s)}{G(s)} \Rightarrow X(s) = -Y(s) \left[{1+G(s)H(s)} \right]/G(s)</math>

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

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

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

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

==See also==