proportionnel

Proportionnel is a French adjective meaning proportional, relating to proportion. The term is widely used in mathematics, physics, and engineering to describe relationships in which one quantity changes in a constant ratio to another.

In mathematics, a direct proportion means a variable y varies directly with x, written as y = kx, where k is the constant of proportionality. The ratio y/x remains constant in this case. An inverse proportion describes a relation where y is proportional to 1/x, expressed as y = k/x, so that the product xy is constant. Proportionality concepts underpin many formulas and unit conversions.

In physics and engineering, proportional relationships appear in laws that link quantities under constant conditions. In control theory, a proportional controller, or P-controller, outputs a signal proportional to the error between a desired setpoint and the measured process variable, using a gain Kp. P-controllers are simple and fast-acting but can leave a steady-state error, which is why they are often combined with integral or derivative components in PID controllers.

Etymology and usage: proportionnel derives from the Latin proportionalis, through French. The term is synonymous with proportional in English and is used in technical and mathematical contexts to denote direct proportionality or related concepts.

See also: proportionality, constant of proportionality, direct proportion, inverse proportion, proportional controller.