Stabilizing An Interconnection System Of A Flexible Beam-cart On An Incline: A Port-hamiltonian Approach

The goal of this paper is to stabilize the interconnection system of a flexible beam-cartmoving on an incline. Firstly, we incorporate the interconnection system into aport-Hamiltonian framework, and model the flexible beam as an infinite dimensionalport-Hamiltonian system and the cart as a finite dimensional one; Then we introduce thenotion of power conserving Dirac structure and interconnect the finite dimensionalport-Hamiltonian system of the cart with the infinite dimensional port-Hamiltonian systemof the flexible beam according to the composition of Dirac structures. Finally, to stabilizethe interconnection system, we propose a finite dimensional stabilizing controller and adoptthe energy Casimir method to accomplish the stability analysis of closed-loop system.