PPolySim OS

Cart-Pole Balance

The hello-world of control theory. A controller nudges a cart back and forth to keep a pole balanced upright — switch it off and gravity wins instantly.

Cart-Pole BalanceLive

Controls

Presets

Balancing a pole on a moving cart is the classic control benchmark. A state-feedback controller senses the pole angle and cart position and pushes the cart to keep the pole upright. Turn the controller off and it topples instantly; add disturbance to test how hard it can fight back.

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Data Inspector

Pole angle8.6°
Cart position0.00
Statusbalanced

Governing equation

Reading this result: The state-feedback law F = -K·state pushes the cart under the falling pole; with gain above the disturbance it recovers from each nudge.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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How it works

The cart-pole, or inverted pendulum, is an unstable system stabilized by feedback. A state-feedback controller measures the pole angle and cart position and applies a force to keep the pole vertical. It is the standard benchmark for control and reinforcement learning. Turn the controller off, or crank up the disturbance, to watch it fail.

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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.

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Frequently asked questions

Is this cart pole inverted pendulum tool really free?
Yes. Cart-Pole Balance runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.