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📐 Root Locus Explorer

Drag a gain slider and watch closed-loop pole locations trace root-locus branches across the complex plane, crossing into instability in real time.

Engineering & Materials3DModerate60 FPS

An interactive 3D complex plane where dragging a feedback-gain slider slides closed-loop pole markers along pre-traced root-locus branches, showing exactly when a control system tips from stable into oscillatory or unstable behaviour.

🔬 What It Demonstrates

Each branch is the path traced by a root of the characteristic equation 1 + K·G(s)H(s) = 0 as gain K sweeps from zero to infinity. Branches start at open-loop poles (✕) and end at zeros (○) or run off along asymptotes.

🎮 How to Use

Pick a pole/zero configuration, then drag the gain slider to move the glowing closed-loop pole markers along the branches. Watch the damping ratio and stability readout change, and see branches turn red once they cross the imaginary axis.

💡 Did You Know?

Walter R. Evans devised the root locus method in 1948 specifically so control engineers could sketch this entire family of curves by hand, decades before anyone could simulate a closed-loop step response on a computer.

⚙ Under the hood

Interactive 3D complex-plane where dragging a gain slider shows how closed-loop pole locations trace root-locus branches and cross into instability.

root-locuscontrol-theorypole-zero-analysissystem-stabilityfeedback-gaincomplex-planeengineering

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install