Editing Closed-loop transfer function (section)

==Derivation==
We define an intermediate signal Z (also known as [[error signal]]) shown as follows:

Using this figure we write:

: <math>Y(s) = G(s)Z(s) </math>

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

Now, plug the second equation into the first to eliminate Z(s):

:<math>Y(s) = G(s)[X(s)-H(s)Y(s)]</math>

Move all the terms with Y(s) to the left hand side, and keep the term with X(s) on the right hand side:

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

Therefore,

:<math>Y(s)(1+G(s)H(s)) = G(s)X(s)</math>

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