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 compose d of a disk rolling on a plane, a controlled slender rod that is pivoted th rough its center of mass about the disk's center and two overhead rotors wi th their axes fixed in the upper part of the rod (see Figs. 1 and 2). The r od 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 bring driven by a DC motor. in addition, a third DC motor, lo cated at the center of the disk, is generating a pedalling torque applied t o the disk's motion. The aim of this work is first to obtain a set of dynam ic equations of the disk's motion that includes the motors dynamics. Then, a control strategy is proposed under which the disk's inclination is stabil ized about its vertical position and the disk's motion is able asymptotical ly to track ally given smooth ground trajectory. (C) 2000 Elsevier Science S.A. All rights reserved.