Modeling and control of flexible second order systems with damped boundaries

This paper considers the problem of modeling and control of non-conservative flexible systems, whose dynamics is described by the wave equation. Classical modal analysis failed so far when the boundaries included dampers. A new insight into the problem was obtained by infinite dimension transfer functions models, developed in previous works. Their special structure, consisting of delays and low order rational terms lead to the time domain interpretation of traveling waves. In this paper the Laplace modeling approach is used to represent the solution in a modal like fashion, i.e. an infinite sum of products of spatial and temporal functions. While this form is closely related to standing waves, it was shown to lead also to a traveling wave representation. The response is then used to investigate the behavior of the system under control with the absolute vibration suppression (AVS) controller, which was originally designed for tracking control. It is shown that the vibration suppression properties of this controller apply also to nonzero initial conditions.