Inverted Pendulum Controls

The problem is to move the cart supporting a rod so that the rod does not fall, or—even better—so that the rod stays vertical. This classic problem appears in the control of the Segway invented by Dean Kamen. The solution shown here uses a proportional derivative controller. Other parameters can be examined using this example, but at some point it becomes too complicated for a simple visualization. You can vary several parameters to demonstrate the stability of the device, which can be instructive. The problem includes free body diagrams and variables that can be included in future versions.