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By treating the positioning control problem of a cautilever-type arm rotating horizontally, the digital optimal control problem of an elastic structure system is theoretically and experimentally considered in this study. Especially, a method for examining the influence of spillover due to a finite dimensional approximation of the elastic structure and a calculation delay in the digital control is presented. By the practical development of control equipment and the various control experiments, the usefulness of the proposed design method is verified, and important information about this kind of control is obtained. Furthermore, the influence of the friction in the DC servo-motor is investigated, mainly by digital simulations.