Inverted pendulums can be a pretty cool testbed for controls stuff. They’re relatively simple, but very non-linear systems, and there are a lot of approaches to swinging up and stabilizing the pendulum. The Furuta pendulum style of machine is particularly interesting, I think. If built right, they can be very small but have unlimited travel, unlike the car-pole style of inverted pendulum, which eventually runs out of track for the cart. Although the full non-linear equations of motion are much more gnarly, for small motions the behavior is largely the same, so it’s not actually any harder to stabilize.
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