Analysis and Comparison of Port-Hamiltonian Formulations for Field Theories - demonstrated by means of the Mindlin plate

Abstract

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known Lagrangian framework. Then it is of interest to reformulate the equations of motion in a port-Hamiltonian setting, where we compare the approach based on Stokes-Dirac structures to a Hamiltonian setting that makes use of the involved bundle structure similar to the one on which the variational approach is based. We will use the Mindlin plate, a distributed parameter system with spatial domain of dimension two, as a running example.

arXiv comment6 pages, submitted

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• Energy-Based In-Domain Control and Observer Design for Infinite-Dimensional Port-Hamiltonian Systems
• On Structural Invariants in the Energy-Based Control of Infinite-Dimensional Port-Hamiltonian Systems with In-Domain Actuation