Nonlinear Control of an Inverted Pendulum on a Cart by a Single Control Law

Abstract

Stabilization at the top vertical position of an inverted pendulum on a cart, while bringing the cart to a desired position, by applying a force to the cart is considered. This is an underactuated mechanical system for which the main nonlinear control scheme, feedback linearization, fails. A single control law producing the force on the cart using cart velocity, and position and velocity of the pendulum is developed and shown, by numerical experiments, to asymptotically stabilize the pendulum at the top position while bringing the cart to its origin, although no attemp is made for a proof of global stability.