Modelling and control of a class of lumped beam with distributed control

A simple lumped port-Hamiltonian model for an actuated flexible beam is proposed. The flexible beam is modelled as a n-DOF actuated beam, and the port-Hamiltonian model is constructed by a systematic interconnection of the links of the beam. The proposed model is then instrumental to derive a stabilizing controller using interconnection and damping assignment - passivity based control considering an underactuated scenario. The work has been developed motivated by the practical application to a medical endoscope with distributed actuation by electro-active polymers. The lumped parameter model offers the possibility of having input/output ports in every joint between successive links, this permits to easily model the action of the actuators as an input force applied to a specific joint