Boundary Damping for Mixed Finite/Infinite Dimensional Systems

In this paper we study two mixed (finite-dimensional and infinite dimensional) systems - a flexible beam on a moving cart and a fluid tank mounted on a moving cart. The cart is connected to ordinary dampers, which dissipate the energy. The ultimate objective of this work is to ensure that all the energy of the infinite dimensional system (due to any disturbances) flows into the dampers and gets dissipated. We show that this is possible under certain conditions and that boundary damping alone is sufficient to bring the composite system to rest. We adopt the port-Hamiltonian approach (van der Schaft and Maschke (2002)) for our analysis, which allows us to look at the composite plant as a power conserving interconnection of infinite and finite dimensional systems.