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Analysis and comparison of port-Hamiltonian formulations for field theories - demonstrated by means of the Mindlin plate | IEEE Conference Publication | IEEE Xplore

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...Show More

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.
Date of Conference: 17-19 July 2013
Date Added to IEEE Xplore: 02 December 2013
Electronic ISBN:978-3-033-03962-9
Conference Location: Zurich, Switzerland

I. Introduction

Distributed parameter systems described by partial differential equations arise in systems theory from a modeling and a control theoretic point of view and are without doubt a challenging research problem, where lot of progress has been achieved in the last years. Also the port-Hamiltonian setting, originally developed in the finite dimensional scenario has been transfered to infinite-dimensional systems, where e.g. the well-known approach based on (Stokes-)Dirac structures (also known from the lumped parameter scenario) is available, see e.g. [1], [2], [3], [4], [5], [6] and references therein.

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References

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