Industrial & Systems
Control Loop Lab
What does turning up the gain actually do? Drag the damping ratio ζ and natural frequency ωn of a standard second-order system and the unit-step response redraws, with the overshoot peak, the ±2% settling band and the transient metrics (overshoot %, peak/rise/settling time) updating live. Underdamped systems overshoot and ring; critical damping is the fastest rise with no overshoot; overdamped is sluggish. It's the intuition equations can't give you.
16.3 %
Overshoot
1.81 s
Peak time
1.21 s
Rise time
4.00 s
Settling (2%)
Underdamped — it overshoots and rings. Lower ζ ⇒ bigger overshoot, more oscillation. ωn sets the speed: higher ωn ⇒ everything happens sooner.
How to use this simulation
What does turning up the gain actually do? Drag the damping ratio ζ and natural frequency ωn of a standard second-order system and the unit-step response redraws, with the overshoot peak, the ±2% settling band and the transient metrics (overshoot %, peak/rise/settling time) updating live. Underdamped systems overshoot and ring; critical damping is the fastest rise with no overshoot; overdamped is sluggish. It's the intuition equations can't give you.
Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.