I did a little experimenting with my wife’s Canon camera that also shoots video, and I made some pretty decent videos of the pendulum in action.
These are links to WMV files. They should start playing in a separate window when you click on them. These are much smaller and faster than the original versions that I posted.
This first video shows a swing up, stable inversion, and a swing down. In the hanging position, it is programmed to move to the center with no pendulum swing.
Pendulum Swing Up Video
This second video shows how stable the pendulum is while inverted. It recovers quickly from small pushes and allows the pendulum to swing down and back up if the push is large. It also tries to stay close to the center of the track.
Inverted Pendulum Stability Video
This third video shows how stable the pendulum is while hanging. Notice the pendulum stops swinging quickly and moves to back to center when pushed.
Hanging Pendulum Stability Video