Optimization problem in inverted pendulum system with oblique track

Abstract

Abstract. This paper studies an optimization problem, i.e., the optimal tracking error control problem, on an inverted pendulum model with oblique track. We characterize the minimum tracking error in term of pendulum’s parameters. Particularly, we derive the closed form expression for the pendulum length which gives minimum error. It is shown that the minimum error can always be accomplished 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.