A port-Hamiltonian approach to modeling and interconnections of canal systems
نویسندگان
چکیده
We show how the port-Hamiltonian formulation of distributed parameter systems, which incorporates energy flow through the boundary of the spatial domain of the system, can be used to model networks of canals and study interconnections of such systems. We first formulate fluid flow with 1-d spatial variable whose dynamics are given by the well-known shallow water equations, with respect to a Stokes-Dirac structure, and then consider a slightly more complicated case where we have a modified (a non-constant) Stokes-Dirac structure. We also explore the existence of Casimir functions for such systems and highlight their implications on control of fluid dynamical systems. Keywords— Shallow water equations, port-Hamiltonian systems, Dirac structures
منابع مشابه
On Interconnections of Infinite-dimensional Port-Hamiltonian Systems
Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving interconnection of Dirac structures is again a Dirac structure. In this paper we study interconnection prop...
متن کاملPort-Hamiltonian Modeling of Systems with Position-Dependent Mass
It is known that straightforward application of the classical Lagrangian and Hamiltonian formalism to systems with mass varying explicitly with position may lead to discrepancies in the formulation of the equations of motion. Systems with mass varying explicitly with position often arise from situations where the partitioning of a closed system of constant mass leads to open subsystems that exc...
متن کاملNetwork Modeling and Control of Physical Systems, DISC Theory of Port-Hamiltonian systems Chapter 1: Port-Hamiltonian formulation of network models; the lumped-parameter case
It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems, ..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamilton...
متن کاملNetwork Modeling and Control of Physical Systems, DISC Theory of Port-Hamiltonian systems Chapter 2: Control of Port-Hamiltonian systems
Port-based network modeling of physical systems directly leads to their representation as portHamiltonian systems. Key feature of port-Hamiltonian systems is that the power-conserving interconnection of port-Hamiltonian systems results in another port-Hamiltonian system, with total state space the product of the state spaces of the components, total Hamiltonian being the sum of the Hamiltonian ...
متن کاملPort-Hamiltonian Systems Theory: An Introductory Overview Port-Hamiltonian Systems Theory: An Introductory Overview
An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief i...
متن کامل