Pendulum System with Elevated track: Length of Pendulum With Minimum Tracking Error

Abstract

This paper studies an optimization problem, i.e., the optimal tracking error control problem, on an inverted pendulum model with elevated track. We characerize the minimum tracking error in term of pendulum's parameters. Prticularly, we derive the close-form expression for the pendulum length which gives minimum error. It is shown that the minimum error can always be accomplised as long as the ratio between the mass of the pendulum and that of the cart satisfies a certain constancy, regardless the type of material we use for the pendulum.