Industrial & Systems
Root Locus Lab
The root locus shows where a feedback system's poles go as you crank the gain. Drag the two open-loop poles and the gain K: the closed-loop poles slide together along the real axis, meet at the breakaway point, then split off vertically into a complex-conjugate pair. Watch the damping ratio fall and the response get ringier as K rises — the core intuition behind tuning any control loop, drawn directly on the s-plane.
-2.00 ± 1.00j
Closed-loop poles
0.89
Damping ζ
Underdamped
Regime
✓ yes
Stable
Turn up the gain K and the two poles slide together along the real axis, meet at the breakaway (K = 1.00), then split off vertically — staying on the line Re = −(p₁+p₂)/2. More gain ⇒ less damping and more ringing, but this 2nd-order loop never actually goes unstable (the poles never cross into the right half-plane).
How to use this simulation
The root locus shows where a feedback system's poles go as you crank the gain. Drag the two open-loop poles and the gain K: the closed-loop poles slide together along the real axis, meet at the breakaway point, then split off vertically into a complex-conjugate pair. Watch the damping ratio fall and the response get ringier as K rises — the core intuition behind tuning any control loop, drawn directly on the s-plane.
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.