stegsrespons

Stegsrespons, in control theory and signal processing, is the time-domain response of a dynamic system to a step input. It describes how the system output y(t) evolves after a unit step is applied at time t = 0. For linear time-invariant systems with transfer function G(s), the step response is y(t) = L^{-1}{G(s)/s}, the inverse Laplace transform of the transfer function divided by s.

Common examples illustrate the idea. A first-order system with G(s) = K/(τs + 1) has a step response y(t) = K(1 − e^{−t/τ}) for t ≥ 0, approaching the final value K. A standard second-order system with G(s) = ω_n^2/(s^2 + 2ζω_n s + ω_n^2) produces a step response depending on the damping ratio ζ. For 0 < ζ < 1 (underdamped), the response rises with possible overshoot and oscillations and approaches the final value; for ζ ≥ 1, the response is slower and without overshoot.

Key characteristics used to describe step responses include rise time (time to go from a defined lower to a defined upper value), peak time, overshoot, settling time (time to remain within a small error band around the final value), and steady-state error. These metrics help evaluate dynamic performance and guide controller design.

Practical considerations include time delays, nonlinearities, and nonminimum-phase behavior, which can distort the ideal step response. Experimentally, a unit step is applied and the resulting output is recorded to extract the response and relevant performance metrics.