Controlling an Inverted Pendulum.
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.
You are the person to balance the inverted pendulum.