A new controller for the inverted pendulum on a cart

Abstract

This paper presents a complete solution to the problem of swinging-up and stabilization of the inverted pendulum on a cart, with a single control law. The resulting law has two parts: first, an energy-shaping law is able to swing and maintain the pendulum up. Then, the second part introduces additional control to stop the cart and it is based on forwarding control with bounded input. The resulting control law is the sum of both parts and does not commute between different laws although there exist switches inside the controller.