The rotational inverted pendulum (also known as the Furuta pendulum) consists of a rotational servo motor system which drives an independent output gear. A rotational pendulum arm (see Fig. 1(a)) of radius r and mass mr is mounted to the output gear and a pendulum of length 2l and mass m is attached to the hinge (point P). The pivot arm rotates in a horizontal plane XY by means of a servo motor and must be moved in such a way that the pendulum, which rotates in a plane XZ that is always perpendicular to the rotating arm, is in the upright position.