Modelling and control of the motion of a rolling disk: effect of motor dynamics on the dynamical model

This work deals with the modelling and control of a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the disk's center and two overhead rotors with their axes fixed in the upper part of the rod (see Figs. 1 and 2). The rod is controlled in such a manner that it is always aligned along the line passing through the points O and C, where O denotes the center of the disk and C denotes the point of contact between the disk and the plane. Each of the rotors is being driven by a DC motor. In addition, a third DC motor, located at the center of the disk, is generating a pedalling torque applied to the disk's motion. The aim of this work is first to obtain a set of dynamic equations of the disk's motion that includes the motors dynamics. Then, a control strategy is proposed under which the disk's inclination is stabilized about its vertical position and the disk's motion is able asymptotically to track any given smooth ground trajectory.