Passivity-based Boundary Controls of Flexible Beams with Large Deformations

Abstract

This paper discusses passivity-based boundary controls of flexible beams with large deformations in terms of a distributed parameter port-Hamiltonian system. Distributed parameter systems have been mainly studied from the viewpoint of analytical methods. However, analytical solutions cannot be always derived from nonlinear distributed parameter systems such as the flexible beam. A distributed parameter port-Hamiltonian system is a standard control representation that can be applied to such a complex system without model reductions. The passivity-based boundary controls consist of boundary damping assignment and boundary energy shaping. Inputs and outputs for the controls are systematically derived from the system representation. Finally, we illustrate numerical results of the controls for stabilizing the flexible beam and shaping its potential energy.