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PID Control — tune it live
A cart on a track wants to reach a setpoint. Tune the Proportional, Integral, and Derivative gains until it lands smoothly. Click the track to move the setpoint.
PID gains
Plant disturbance
Live state
What each term does
P — Proportional
Force ∝ current error. Pull harder when far away. High Kp → fast response but overshoot & oscillation. Low Kp → slow, often steady-state error.
I — Integral
Force ∝ accumulated error over time. Kills steady-state offset (e.g. friction holding the cart back). Too much Ki → wind-up & slow oscillation.
D — Derivative
Force ∝ rate of change of error. Acts like a brake when approaching the target. Damps overshoot & oscillation, but amplifies sensor noise.
u(t) = Kp·e(t) + Ki·∫e dt + Kd·(de/dt) e(t) = setpoint − position
Tuning hint — Start with Kp only (set Ki = Kd = 0). Increase Kp until you see oscillation, then back off ~30%. Add Kd to damp the oscillation. Add a little Ki last to eliminate any remaining offset. This is the classic Ziegler-Nichols heuristic.