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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 (telecommunication)|loop]] on the input [[signal (information theory)|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.
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:
: <math>\dfrac{Y(s)}{X(s)} = \dfrac{G(s)}{1 + G(s) H(s)}</math>
==Derivation==
Let's define an intermediate signal Z shown as follows:
[[Image:Closed Loop Block Deriv.png]]
Using this figure we can write
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