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

Michael Valasek, Ondrej Marek


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
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.


flexible body; planar motion; residual vibration

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ISSN 1801-1217 (Print)
ISSN 1805-9422 (Online)
Published by the Czech Technical University in Prague, Faculty of Mechanical Engineering