Closed-loop transfer function

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.

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:

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

Derivation

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

Using this figure we can write

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

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

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

See also

• Federal Standard 1037C
• Open-loop controller

References

•  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Applied mathematics stubs Control theory Cybernetics Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Closed captioning Coasting mode Look at other dictionaries: closed-loop transfer function — uždarosios sistemos perdavimo funkcija statusas T sritis automatika atitikmenys: angl. closed loop transfer function vok. Ausgangsübertragungsfunktion, f rus. передаточная функция замкнутой системы, f pranc. transmittance en boucle fermée, f …   Automatikos terminų žodynas Closed-loop pole — Closed loop poles are the positions of the poles (or eigenvalues) of a closed loop transfer function in the s plane. The open loop transfer function is equal to the product of all transfer function blocks in the forward path in the block diagram …   Wikipedia Closed loop — may refer to: A feedback loop, often found in: Control theory#Closed loop transfer function, where a closed loop controller may be used Electronic feedback loops in electronic circuits PID controller, a commonly used closed loop controller Closed …   Wikipedia Phase-locked Loop — Eine Phasenregelschleife, auch als Phase locked loop (PLL) bezeichnet, ist eine elektronische Schaltungsanordnung, die die Phasenlage und damit zusammenhängend die Frequenz eines veränderbaren Oszillators über einen geschlossenen Regelkreis so… …   Deutsch Wikipedia Phase-locked loop — Eine Phasenregelschleife, auch als englisch Phase locked loop (PLL) bezeichnet, ist eine elektronische Schaltungsanordnung, die die Phasenlage und damit zusammenhängend die Frequenz eines veränderbaren Oszillators über einen geschlossenen… …   Deutsch Wikipedia Control theory — For control theory in psychology and sociology, see control theory (sociology) and Perceptual Control Theory. The concept of the feedback loop to control the dynamic behavior of the system: this is negative feedback, because the sensed value is… …   Wikipedia Nyquist stability criterion — The Nyquist plot for . When designing a feedback control system, it is generally necessary to determine whether the closed loop system will be stable. An example of a destabilizing feedback control system would be a car steering system that… …   Wikipedia Root locus — In control theory, the root locus is the locus of the poles and zeros of a transfer function as the system gain K is varied on some interval. The root locus is a useful tool for analyzing single input single output (SISO) linear dynamic systems.… …   Wikipedia PID controller — A block diagram of a PID controller A proportional–integral–derivative controller (PID controller) is a generic control loop feedback mechanism (controller) widely used in industrial control systems – a PID is the most commonly used feedback… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”