On the extraction of the boundary conditions and the boundary ports in second-order field theories

Abstract

In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This has also consequences on the derivation of the boundary conditions when non trivial variations are allowed on the boundary. By posing extra conditions on the set of possible boundary terms we exploit the degree of freedom in the Cartan form to extract physical meaningful boundary expressions. The same mathematical machinery will be applied to derive the boundary ports in a Hamiltonian representation of the partial differential equations which is crucial for energy based control approaches. Our results will be visualized for mechanical systems such as beam and plate models.

Cited by in corpus (5)

• Port-Hamiltonian formulation and symplectic discretization of Plate models. Part I : Mindlin model for thick plates
• Port-Hamiltonian formulation and symplectic discretization of plate models. Part II : Kirchhoff model for thin plates
• Energy-Based In-Domain Control of a Piezo-Actuated Euler-Bernoulli Beam
• Energy-based Control and Observer Design for higher-order infinite-dimensional Port-Hamiltonian Systems
• On Structural Invariants in the Energy-Based Control of Infinite-Dimensional Port-Hamiltonian Systems with In-Domain Actuation