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Closed Loop

In a feedback control system a measured value is compared with a reference, and the error drives a controller that affects the process. The relationship between the reference and the output for a negative-feedback loop with forward gain $G$ and feedback $H$ is a simple, widely used expression.

\dfrac{Y}{R}=\dfrac{G}{1+GH}

closed-loop transfer function, negative feedback

Symbols

$G$	forward gain (controller and process)
$H$	the feedback's transfer function
$Y$	output
$R$	reference

Example

$G=10$ , $H=1$ :

$Y/R=10/(1+10)\approx0.909$ .

Set up

G/(1+GH)

and simplify before finding poles or the final value.

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