Control of Translational Motion of Flexible Bodies by “Wave Method”

The motivation for this work is the motion control of flexible mechanical systems, specifically the position control of the shifting parts without the residual vibrations. These systems are for example long robot arms, gantry cranes, some parts of machine tools etc.. The actuators are coupled to the continuum in one point or in its vicinity. The other boundaries are “free”. The goal of the actuators is to position the “important point” of the continuum at the other end through the flexible system and to suppress the vibrations during the motion including the complete elimination of the residual vibrations of the important point at the end of the motion. The wave-based control method for 1D continuum has been developed. This paper shows how to extend this 1D method to 2D continuum. The paper shows how to compute and use the “launched” and “reflected” waves for control. If some strategy is used, the flexible system will be translated to the required position with no residual vibrations.