Sløjfegain

Sløjfegain is a term used in control theory to denote the gain around a feedback loop, i.e., the product of gains in the forward path and the feedback path. For a system with forward transfer function G(s) and feedback transfer function H(s), the loop gain is L(s) = G(s)H(s). The magnitude and phase of L(s) across frequencies determine stability via Nyquist or Bode analyses. The term is sometimes distinguished from the overall closed-loop gain, which is 1/(1+L(s)) for negative feedback.

The word is formed from sløjfe (Danish for loop or feedback) and gain. In mid-20th century Danish and international control literature, sløjfegain was used to describe loop gain, paralleling the English term. The concept reflects how amplification around a loop can reinforce or attenuate signals depending on frequency and phase shifts.

Applications and interpretation: Sløjfegain is central to the design and analysis of servo systems, audio amplifiers, regulators, and robotics, where maintaining stability under parameter variation is critical. In practice, engineers compute the forward path G and the feedback path H, multiply them to obtain L, and assess stability margins using Nyquist plots or Bode plots. The gain margin and phase margin derived from L indicate how much gain or phase change the system can tolerate before becoming unstable.

Variants and notes: Open-loop gain refers to the forward path G, while the loop gain includes the feedback path. In nonlinear systems, effective gain may depend on signal amplitude, time delay, or saturation effects.

See also: Feedback, Nyquist criterion, Bode plot, gain margin, phase margin.