Balance a broom on your palm. Your hand makes constant corrections — not because it knows the broom's equations of motion, but because it sees the angle tilt and responds. Here the cart is the "hand," the pole is the broom, and the controller is a linear feedback law on the four states .
Try this: click and drag the pole tip sideways to knock it. While you're dragging, physics is paused — release and watch the controller fight to bring it back to vertical. If the controller can't recover, the sim auto-resets so you can try new gains. The four sliders are the gains on each state; bigger gain = controller cares more about that thing.
Drag the pole, let go, watch it recover
x (cart) —
θ (angle) —
u (force) —
status balanced
what to try
- First — leave defaults alone and click small knock a few times. The pole wobbles but the controller pulls it back. Status stays "balanced." This is stabilizing an open-loop-unstable plant.
- Drag the pole tip sideways and release. With defaults you can usually recover from ~25° tilt. Push past that and it falls — the linearization breaks down too far from upright, and the controller can't catch it.
- Click "no derivative (watch it ring)" — sets Kθ̇ = 0. Now knock the pole. It oscillates uncontrollably and falls. This is classical "P without D": the controller knows where the pole is, but not where it's going. Restore Kθ̇ and the ring vanishes.
- Set Kx and Kẋ to 0. Knock the pole. It balances but the cart slides off-screen. The controller doesn't care about cart position — only the pole. Add both gains back; the cart returns home while the pole stays vertical.
- Set Kθ = 0. The pole has no feedback at all. It falls immediately. Reset.