Closed-loop transfer function

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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.


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:

Closed Loop Block Deriv.png

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:


We define an intermediate signal Z shown as follows:

Closed Loop Block Deriv.png

Using this figure we write:

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