# Subtractive 0th order linear feedback control

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Synonyms: proportional controller, proportional feedback system, linear feedback system without memory

## DefinitionEdit

A Subtractive 0th order linear feedback control is a linear memoryless control system. Proportional control circuits are examples for LTI-systems.

## Processing structureEdit

Example of a 0th order linear feedback control system with load:

## Mathematical modelEdit

e(t) = x(t) - yR(t)

yS(t) = G1 e(t) = G1 [x(t) - yR(t)]

y(t) = yS(t) + z(t) = G1 [x(t) - yR(t)] + z(t)

yR(t) = G2 y(t)

y(t) = G1 x(t) - G1 G2 y(t) + z(t)

$y = G1x + z / (1 + G1 G2)$

x: set point, e: error, y: controlled variable, yS: manipulated variable, yR: measured variable, z: load, disturbance variable, G1: amplification factor of direct branch, G2: amplification factor of feedback path.

See the legend for an explanation of symbols.

## PhysiologyEdit

Linear feedback control systems are not very common in living organisms. An example for a proportional feedback circuit is binding of hormones to plasma proteins.