An Example of a Digital Feedback Control System.

A free swinging pendulum is inverted so the hinge is at the bottom. The challenge is to move the bottom of the pendulum back and forth to keep the pendulum from falling over.

The hinge at the bottom of the pendulum is attached to a cart which moves back and forth on a track. The cart is connected to wires which are connected to an electric motor. The voltage applied to the electric motor is controlled by a computer. The observable properties are the current pendulum's angle from vertical and the current cart position.

Below is a diagram of the setup:

This paper derives all the characteristic equations of motion for an inverted pendulum, all the transfer functions, Bode plots, state space representations, and concludes with an example of controlling a real setup.

After mastering this 2-dimensional problem you can expand this to a 3-dimensional problem. If you can master the task of controlling an inverted pendulum free to fall in any direction, then you can launch a rocket into outer space, controlling the thrust angle at the bottom so it doesn't fall over.

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