Abstract
This paper solves the stabilization problem for a flexible beam with both ends free using a boundary control technique. The boundary controller is designed according to the standard method for designing passivity-based controllers. For set point problems, the potential energy shaping that assigns the desired configuration to an equilibrium point of the closed-loop system is sufficient. The potential energy shaping is therefore completed by adding the artificial potential energy that specifies the displacement of the both ends of the flexible beam. Numerical simulations confirm the stability of the equilibrium configuration of the closed-loop system formed by the flexible beam together with the proposed controllers.
