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.