2 research outputs found
Linear Boundary Port-Hamiltonian Systems with Implicitly Defined Energy
In this paper we extend the previously introduced class of boundary
port-Hamiltonian systems to boundary control systems where the variational
derivative of the Hamiltonian functional is replaced by a pair of reciprocal
differential operators. In physical systems modelling, these differential
operators naturally represent the constitutive relations associated with the
implicitly defined energy of the system and obey Maxwell's reciprocity
conditions. On top of the boundary variables associated with the Stokes-Dirac
structure, this leads to additional boundary port variables and to the new
notion of a Stokes-Lagrange subspace. This extended class of boundary
port-Hamiltonian systems is illustrated by a number of examples in the
modelling of elastic rods with local and non-local elasticity relations.
Finally it shown how a Hamiltonian functional on an extended state space can be
associated with the Stokes-Lagrange subspace, and how this leads to an energy
balance equation involving the boundary variables of the Stokes-Dirac structure
as well as of the Stokes-Lagrange subspace.Comment: 23 page
Dissipativity-based boundary control of linear distributed port-Hamiltonian systems
The main contribution of this paper is a general synthesis methodology of exponentially stabilising control laws for a class of boundary control systems in port-Hamiltonian form that are dissipative with respect to a quadratic supply rate, being the total energy the storage function. More precisely, general conditions that a linear regulator has to satisfy to have, at first, a well-posed and, secondly, an exponentially stable closed-loop system are presented. The methodology is illustrated with reference to two specific stabilisation scenarios, namely when the (distributed parameter) plant is in impedance or in scattering form. Moreover, it is also shown how these techniques can be employed in the analysis of more general systems that are described by coupled partial and ordinary differential equations. In particular, the repetitive control scheme is studied, and conditions on the (finite dimensional) linear plant to have asymptotic tracking of generic periodic reference signals are determined