EXPERIMENT 11 · CART-POLE

Balance is not position

Can the pole stay upright while the cart drifts away?

Try it in the current lab

Pin the angle-only run, then switch to cascade mode.

Open Cart position and compare angle-only and cascade modes after the same kick.

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

Angle feedback keeps the pole up but does not promise a cart position. The outer position loop asks for a small tilt to guide the cart home.

\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 is not position

Can the pole stay upright while the cart drifts away?

Try it in the current lab

Pin the angle-only run, then switch to cascade mode.

Open Cart position and compare angle-only and cascade modes after the same kick.

What the system is doing

Angle feedback keeps the pole up but does not promise a cart position. The outer position loop asks for a small tilt to guide the cart home.

\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}