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A common closed-loop controller architecture is the [[PID controller]].
===Closed-loop transfer function===
{{details|closed-loop transfer function}}
The output of the system ''y''(''t'') is fed back through a sensor measurement ''F'' to a comparison with the reference value ''r''(''t''). The controller ''C'' then takes the error ''e'' (difference) between the reference and the output to change the inputs ''u'' to the system under control ''P''. This is shown in the figure. This kind of controller is a closed-loop controller or feedback controller.
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The expression <math>H(s) = \frac{P(s)C(s)}{1 + F(s)P(s)C(s)}</math> is referred to as the ''closed-loop transfer function'' of the system. The numerator is the forward (open-loop) gain from ''r'' to ''y'', and the denominator is one plus the gain in going around the feedback loop, the so-called loop gain. If <math>|P(s)C(s)| \gg 1</math>, i.e., it has a large [[norm (mathematics)|norm]] with each value of ''s'', and if <math>|F(s)| \approx 1</math>, then ''Y''(''s'') is approximately equal to ''R''(''s'') and the output closely tracks the reference input.
===PID feedback control===
{{main|PID controller}}
[[File:PID en.svg|right|thumb|400x400px|A [[block diagram]] of a PID controller in a feedback loop, {{math|''r''(''t'')}} is the desired process value or "set point", and {{math|''y''(''t'')}} is the measured process value.]]
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