Überschwingen

Überschwingen is a term used in physics, engineering and related disciplines to describe a transient phenomenon in which a system’s response temporarily exceeds its final steady-state value after a disturbance or change in input. The verb überschwingen means to overswing or overshoot; the noun Überschwingung (more common in technical literature) denotes the overshoot itself.

In control theory and mechanics, Überschwingen occurs mainly in underdamped systems. For a standard second-order system with natural frequency ω_n and damping ratio ζ, the maximum overshoot M_p is given by M_p = exp(-ζπ/√(1−ζ^2)). The percent overshoot is 100%·M_p. Overshoot increases as damping decreases and typically vanishes for ζ ≥ 1 (overdamped). It is a key metric for assessing transient performance alongside rise time and settling time.

Implications and design: Überschwingen can cause mechanical stress, actuator saturation, or instability in control loops if excessive. Designers seek to minimize it by increasing damping, retuning controllers, or shaping inputs. In some applications a controlled amount of overshoot may be acceptable or even desirable for speed, but it must be kept within safe limits.

Context and usage: The term appears across engineering disciplines, including servo systems, structural dynamics and electronics. While Überschwingung is the standard term for the phenomenon in German, Überschwingen is used as the verb form or in some texts as a nominal variant. In English-language literature, the phenomenon is commonly called overshoot. See also: damping ratio, overshoot, second-order systems, control theory.