# Feedback control

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**Synonyms**: control circuit, control loop, closed-loop control, feedback interaction

## DefinitionEdit

Information processing structures that comprise a control process with inclosed degenerative feedback (thus forming a loop) are referred to as **feedback control systems**. Feedback control permits that vitally important parameters of body function like osmolality, pH and Oxygen-tension as well as plasma level of hormones and body temperature remain constant or in a compliant range (Homeostasis).

## ExampleEdit

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

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.

## TypesEdit

Selected types of feedback control cover:

- Unity feedback systems
- Linear feedback control
- Subtractive 0th order linear feedback control
- Subtractive 1st order linear feedback control
- Subtractive higher order linear feedback control systems

- Nonlinear feedback control
- Divisive feedback control
- Divisive 0th order feedback control
- Divisive 1st order feedback control
- Divisive higher order feedback control

- Control circuits with Michaelis-Menten-type saturable elements

- Divisive feedback control

Feedback systems are also classified according to their behaviour with regard to a set point. Regulators hold the controlled variable steady, while tracking or servo systems track a reference signal.

## PhysiologyEdit

Feedback control systems play essential roles in the organism. Examples are:

- Osmoregulation
- corticotropic feedback controls
- gonadotropic feedback controls
- thyrotropic feedback control
- homeostasis of blood glucose level
- control of blood pressure
- control of respiration and plasma pH
- thermoregulation in homeotherms
- synchronisation of root and crown growth in plants

## Mathematical description and modellingEdit

Common methods for describing the relation among structure and behaviour of feedback control systems are:

- Time domain analysis (as outlined in the example above)
- Frequency domain analysis (covering transfer functions)
*s*-plane analysis including zero-pole investigation- State space description.

Additionally, the behaviour of control circuits may be studied with simulative methods (in silico modelling).

## BackgroundEdit

Physiological systems theory, a subsection of medical cybernetics deals with mathematical description and analysis of feedback control systems and other information processing structures.