Linear Strong Structural Controllability for an n-Link Inverted Pendulum in a Cart

Abstract

A multilink inverted pendulum connected to a cart moving in a same vertical plane is typical underactuated mechanical system studied in both control and robotic communities. This paper presents the motion equation for an n-link inverted pendulum in a cart without any assumption on the physical parameters of the pendulum. Based on the motion equation and some properties of the physical parameters of the pendulum, this paper proves that such a system is linearly controllable around its upright equilibrium point (all its links in the upright position and the cart in the origin) for all its possible physical parameters; that is, such a system is linearly strongly structurally controllable around the point. This paper validates the above result via two existing physical systems of 3-link inverted pendulum in a cart.