Inverted Pendulum

One of the coolest things I did during my education was implement a controller for an inverted pendulum. See the following video.

There was only one problem. While I implementd the controller to control the inverted pendulum, I did not derive the model. That was given to me by my instructor. Even though implementing the controller was cool, it was somewhat unsatisfying. After all, I really had no idea how the model was derived. It was a black box that I took for granted to be true and correct. In order to better understand this black box, I decided to sit down and derive the model of the inverted pendulum myself. And oh man, I now understand why my instructor decided to just give it to me. Below is my derivation for the model of the inverted pendulum. I tried to make the derivation as approachable as possible and link to other resouces when I felt appropriate. Enjoy.