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Physics 566: Inverted pendulum example

We did an elementary version of the inverted pendulum, a classic control theory problem, in class. We found a control law that would enable us to keep the pendulum up indefinitely. We only briefly considered the possibility that the base position, as well as the orientation, could be controlled.

Todd Gelbord found an inverted pendulum video. This is a remarkable video for several reasons:

• The control law works well outside the linear regime.
• The controller can restore the pendulum to inverted equilibrium even when it starts out hanging downward.
• The controller has a finite range of motion, and is apparently optimized to take best advantage of that range of motion.