Abstract: Absolute Vibration Suppression (AVS) is a control method for
flexible structures governed by the wave equation. Such system may be a
rotating shaft, a rod in tension or a crane for which the cable mass is not
negligible. First an accurate, infinite dimension, transfer function, relating
arbitrary actuation and measurement points, with general boundary conditions,
is derived. The transfer function consists of time delays, due to the wave
motion, and low order rational terms, which correspond to the reflection from
the boundary. Thus the compact mathematical representation has a clear physical
interpretation. Furthermore, it leads to the special structure of the AVS
controller which is a collocated, rate to force feedback that completely
eliminates the vibration. The paper investigates the properties of the AVS
controller and its robustness to modeling errors, in particular small
non-collocation.
