Trajectory Control of a Cart-inverted Pendulum System in the Presence of a Jet Force for an Open Loop Stabilization

Abstract

This paper presents an investigation on the stabilization and the tracking problem of an inverted pendulum-cart system. An open loop subsystem is augmented to the original components which comprises an auxiliary stable pendant pendulum, (P.P.), and a jet force component. The latter is attached firmly to the auxiliary pendulum in such a way to keep the jet force acting in an alignment to this pendulum. The dynamic equations of the system are derived using Lagrange formulation. The jet force locates the inverted pendulum in the up-right position and holds it stable. A scheme based on model reference and error driven control is proposed to track the system along a pre-specified trajectory, while the inverted pendulum, (I.P.), maintains it's up-right position with fairly negligible oscillation. Real-time dynamic simulation is performed and the results of which are presented to illustrate the validity of the proposed approach.