Markus Schöberl, Kurt Schlacher,
"Port-Hamiltonian formulation for Higher-order PDEs"
: Proceedings, 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, 2015
Port-Hamiltonian formulation for Higher-order PDEs
Sprache des Titels:
Proceedings, 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control
In this paper we consider partial differential equations in a port-Hamiltonian setting. A crucial property of this system class, especially
for control purposes,
is the property to be able to link a power balance relation to the structure of the equations. However, to derive
this power balance relation
one has to take into account also the effects of energy flows via the boundary. This can be handled in a straightforward manner when
the Hamiltonian depends on derivative variables of first order, e.g. by using integration by parts. If higher-order derivatives
appear (higher-order field theory) then integration by parts cannot be used without due care, thus we suggest an approach by
using the so-called Cartan-form. In this paper we concentrate on second-order theories in a port-Hamiltonian framework
and we visualize the derivation of a power balance relation by using mechanical examples such
as plates modeled as a first-order and as second-order field theory.