EXPERIMENT 10 · CART-POLE

Balance the pole

Which way should the cart move when the pole leans right?

Try it in the current lab

Change the initial angle and test the recovery limit.

Watch pole angle in the response plot, cart position beside the animation, and force in Control effort.

The lab recalculates after a setting changes. Pin a run before changing one variable; the response and control-effort plots share the same replay time. PID experiments also show the P/I/D terms; estimator experiments show measured and estimated states.

What the system is doing

The cart accelerates toward a falling pole so the pivot catches up. This model covers balance near the upright position.

\ddot{x}=\frac{F+m\sin\theta(l\dot{\theta}^2-g\cos\theta)-b\dot{x}}{M+m\sin^2\theta},\qquad \ddot{\theta}=\frac{g\sin\theta-\ddot{x}\cos\theta}{l}

Open this experiment →Model and method →

Balance the pole

Which way should the cart move when the pole leans right?

Try it in the current lab

Change the initial angle and test the recovery limit.

Watch pole angle in the response plot, cart position beside the animation, and force in Control effort.

What the system is doing

The cart accelerates toward a falling pole so the pivot catches up. This model covers balance near the upright position.

\ddot{x}=\frac{F+m\sin\theta(l\dot{\theta}^2-g\cos\theta)-b\dot{x}}{M+m\sin^2\theta},\qquad \ddot{\theta}=\frac{g\sin\theta-\ddot{x}\cos\theta}{l}