Pendulum PID

Key Insight

A pendulum is the smallest system where you can watch every term of a PID controller earn its keep: the proportional term pulls the pole back toward the upright setpoint, the derivative term damps the swinging so it stops overshooting, and the integral term erases any steady lean left by gravity or a miscalibrated model. This project stabilizes the pole once it is already near upright — holding a balance point, which PID does well — rather than the harder swing-up from hanging, where a weak motor must pump energy in over several swings and plain PID is not enough on its own. Plotting the step response — how the angle reacts when you suddenly command a new target — is how you read off, in one picture, whether your gains are too sluggish, too twitchy, or just right.