Flexible structures moving using "wave-based method"

The motivation for this work is the 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 cutting machines etc. The actuators are coupled to the continuum close to one point. The other boundaries are “free”. The actuators are attempting to position the “important point” at the far end through the flexible system and eliminate the vibrations during the motion also at the end of the motion. The wave-based control method was developed. This paper shows how to apply this published 1D method [1] to 2D continuum. The paper shows how to compute and use the “launch” and “reflected” waves for control. If some strategy is used, the flexible system will be transposed to the required position with no residual vibrations. Some ambiguities still exist. If the superposition principle is valid, many motions will be able to control simultaneously.