step response
The step response is what a system does when you suddenly slam its command from one steady value to another — like flooring the gas pedal from a standstill or jumping a thermostat from 18 to 22 °C. It's the single most-used test in control because that abrupt jump excites every dynamic in the system at once, and watching the output recover tells you almost everything: how fast it reacts, whether it overshoots, how much it wobbles, and where it finally settles.
Engineers read a handful of numbers off the step-response curve. Rise time: how quickly it first reaches the target (a fast servo might be milliseconds). Overshoot: how far it sails past before turning back — 10% overshoot means it briefly hit 110% of the goal. Settling time: how long until it stays within, say, ±2% of final value. Steady-state error: the gap it never closes. These come straight from the closed-loop poles: lightly damped poles (ζ small) give big overshoot and ringing; well-damped poles (ζ ≈ 0.7) give a fast response with little overshoot — the sweet spot most designs aim for.
There's a fundamental trade-off baked into the step response: you cannot make a loop both lightning-fast and overshoot-free and disturbance-rejecting all at once — push one and another gives. The art of tuning is choosing which compromise fits the job.