Using energy-based variable structure approach to control the vibrations in a nonlinear beam with large deformations

Nonlinear model for transverse dynamics of a vibrating beam is derived. In this modeling large deformation for beam is considered and consequently, high order curvature terms are not neglected. An adaptation method for applying large moments in the beam tip is developed using FEM. Port Hamiltonian interconnected system modeling is used to model the resulted configuration. The energy-based variable structure method is utilized to develop an interconnected controller with energy function associated with a set of Casimir functions relating to sliding surfaces. The energy function of the controller is chosen to make an attractive sliding surface for closed-loop system. Using this system, vibration of the nonlinear beam is stabilized in the desired shape of the beam.