# 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)

y_{S}(t) = G_{1} e(t) = G_{1} [x(t) - y_{R}(t)]

y(t) = y_{S}(t) + z(t) = G_{1} [x(t) - y_{R}(t)] + z(t)

y_{R}(t) = G_{2} y(t)

y(t) = G_{1} x(t) - G_{1} G_{2} y(t) + z(t)

x: set point, e: error, y: controlled variable, y_{S}: manipulated variable, yR: measured variable, z: load, disturbance variable, G_{1}: amplification factor of direct branch, G_{2}: 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.