Tuesday, June 23, 2009

Inverted Pendulum

We know what a pendulum is. It's a great device for producing regular periods, which is especially useful in mechanical clocks, when you want to break down fast power into smaller intervals (like seconds).

Galileo Galilei discovered it around 1602 and Christiaan Huygens was the first to use it in a clock for accurate escapement in 1656.

But what if you turned it upside down? It's easy to do by hand. Take a long rod and balance it on the palm of your hand. In order to keep it up, it requires finite adjustments by your hand. A little to the left... right... forward... Don't let it fall!

Your brain accepts input from your eyes and feel of the weight on your hand to see which way the rod begins to fall, and tells your arm and hand to adjust as necessary to keep the bottom of the rod under the top... keeping it balanced. It's not that difficult to do for someone as intelligent as ourselves.

Could that control be synthesized? Imagine the possibility...

...or, just look it up on YouTube...

From Wikipedia, "An inverted pendulum is a pendulum which has its mass above its pivot point. It is often implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright, either by applying a torque at the pivot point or by moving the pivot point horizontally as part of a feedback system."

Check out this pendulum clock:

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