Poles and step response

ENGR5001. Drag a pole on the s-plane, or set zeta and wn, and watch the step response change. Overshoot, peak time and settling time are marked.

InteractivePoles and step response

Damping ratio zeta0.4Natural frequency wn (rad/s)4

Response: underdamped
Poles: s = -1.6 +- j3.67
Overshoot: 25.4%
Peak time tp: 0.857 s
Settling time (2%): 2.1 s
4 / (zeta wn): 2.5 s
Rise time (10-90%): 0.366 s
Damped frequency wd: 3.67 rad/s

G(s) = wn^2 / (s^2 + 2 zeta wn s + wn^2). Drag a pole (or tap the plane) to move the pair. Settling time is read off the curve; the 4 / (zeta wn) envelope rule is the one used in exams and is only close for zeta below about 0.7. Poles further left settle faster; poles further from the real axis oscillate faster.

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