Proportionelle

Proportionelle is an attributive form of the German adjective meaning proportional or proportionate. It is used in technical and scientific language to describe relationships in which one quantity scales directly with another. The feminine form appears before feminine nouns, as in proportionelle Regelung (proportional control) or proportionelle Beziehung (proportional relationship).

In mathematics and physics, a proportionelle relationship means that one variable changes in direct proportion to another. A common representation is y = kx, where k is the Proportionalitätskonstante, or constant of proportionality. The concept of proportionality is central to many formulas, such as V ∝ I for a fixed resistance, expressed by V = IR in Ohm’s law.

In engineering and control theory, the term occurs in the context of proportional control. A proportional controller, often abbreviated as P-Regler, applies an output that is proportional to the error e(t). The control action is commonly written as u(t) = Kp · e(t), where Kp is the proportional gain. This approach emphasizes the proportion between the error and corrective action, though it can be combined with integral or derivative components in PID controllers to address steady-state error and dynamic response.

Etymologically, proportionelle derives from proportion, with the German suffix -ell indicating an adjective form. The concept is closely related to proportionalität (proportionality) and proportionalitätskonstante (constant of proportionality). While "proportionelle" is a German-language form, the underlying idea of proportionality is universal across mathematics, physics, and engineering.