Feedback control

From Biomedical Cybernetics

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

[edit] Definition

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).

[edit] Example

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

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

y_S(t) = G₁ e(t) = G₁ [x(t) - y_R(t)]

y(t) = y_S(t) + z(t) = G₁ [x(t) - y_R(t)] + z(t)

y_R(t) = G₂ y(t)

y(t) = G₁ x(t) - G₁ G₂ y(t) + z(t)

y = [G₁ x + z] / [1 + G₁ G₂]

x: set point, e: error, y: controlled variable, y_S: 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.

[edit] Types

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
  - MiMe-NoCoDI models

[edit] Physiology

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

[edit] Mathematical description and modelling

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)
Zero-pole analysis
State space description.

Additionally, the the behaviour of control circuits may be studied with simulative methods.

[edit] Background

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

[edit] External Links