Closed-loop transfer function: Difference between revisions

Revision as of 16:48, 19 April 2024

Latest revision as of 16:38, 7 May 2024

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{{short description|Function describing the effects of feedback on a control system}}

In [[control theory]], a '''closed-loop transfer function''' is a [[mathematical function]] describing the net result of the effects of a [[feedback control loop]] on the input [[signal (information theory)|signal]] to the [[plant (control theory)|plant]] under control.[closed]

== Overview ==

The closed-loop [[transfer function]] is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be [[waveform|waveforms]], [[image|images]], or other types of [[data stream|data streams]].

An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:

[[Image:Closed Loop Block Deriv.png]]

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: <math>\dfrac{Y(s)}{X(s)} = \dfrac{G(s)}{1 + G(s) H(s)}</math>

<math>G(s) </math> is called the [[Feedforward#ControlFeed forward (control)|feedforwardfeed forward]] transfer function, <math>H(s) </math> is called the [[Feedback#Control theory|feedback]] transfer function, and their product <math>G(s)H(s) </math> is called the '''open-loop transfer function'''.

==Derivation==