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A closed-loop transfer function in control theory is a mathematical expression (algorithm) describing the net result of the effects of a closed (feedback) loop on the input signal to the circuits enclosed by the loop.
## Overview

The closed-loop transfer function is measured at the output. The output signal waveform can be calculated from the closed-loop transfer function and the input signal waveform.## Derivation

Let's define an intermediate signal Z shown as follows:## See also

## References

An example of a closed-loop transfer function is shown below:

The summing node and the G(s) and H(s) blocks can all be combined into one block, which would have the following transfer function:

- $dfrac\{Y(s)\}\{X(s)\}\; =\; dfrac\{G(s)\}\{1\; +\; G(s)\; H(s)\}$

Using this figure we can write

- $Y(s)\; =\; Z(s)G(s)\; Rightarrow\; Z(s)\; =\; dfrac\{Y(s)\}\{G(s)\}$

- $X(s)-Y(s)H(s)\; =\; Z(s)\; =\; dfrac\{Y(s)\}\{G(s)\}\; Rightarrow\; X(s)\; =\; Y(s)\; left[\{1+G(s)H(s)\}\; right]/G(s)$

- $Rightarrow\; dfrac\{Y(s)\}\{X(s)\}\; =\; dfrac\{G(s)\}\{1\; +\; G(s)\; H(s)\}$

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Last updated on Thursday May 08, 2008 at 05:02:41 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Thursday May 08, 2008 at 05:02:41 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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