Chapter

Conservation Laws and Lumped System Dynamics

DOI: 10.1007/978-1-4419-0895-7_3

ABSTRACT Physical systems modeling, aimed at network modeling of complex multi-physics systems, has especially flourished in the fifties
and sixties of the 20-th century, see e.g. [11, 12] and references provided therein. With the reinforcement of the ’systems’
legacy in Systems & Control, the growing recognition that ’control’ is not confined to developing algorithms for processing
the measurements of the system into control signals (but instead is concerned with the design of the total controlled system),
and facing the complexity of modern technological and natural systems, systematic methods for physical systems modeling of
large-scale lumpedand distributed-parameter systems capturing their basic physical characteristics are needed more than ever.

0 Bookmarks
 · 
95 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we suggest a class of quasi-port-Hamiltonian systems called Irreversible port-Hamiltonian Systems, that expresses simultaneously the first and second principle of thermodynamics as a structural property. These quasi-port-Hamiltonian systems are defined with respect to a structure matrix and a modulating function which depends on the thermodynamic relation between state and co-state variables of the system. This modulating function itself is the product of some positive function γγ and the Poisson bracket of the entropy and the energy function. This construction guarantees that the Hamiltonian function is a conserved quantity and simultaneously that the entropy function satisfies a balance equation containing an irreversible entropy creation term. In the second part of the paper, we suggest a lift of the Irreversible Port-Hamiltonian Systems to control contact systems defined on the Thermodynamic Phase Space which is canonically endowed with a contact structure associated with Gibbs' relation. For this class of systems we have suggested a lift which avoids any singularity of the contact Hamiltonian function and defines a control contact system on the complete Thermodynamic Phase Space, in contrast to the previously suggested lifts of such systems. Finally we derive the formulation of the balance equations of a CSTR model as an Irreversible Port-Hamiltonian System and give two alternative lifts of the CSTR model to a control contact system defined on the complete Thermodynamic Phase Space.
    Chemical Engineering Science 02/2013; 89:223–234. DOI:10.1016/j.ces.2012.12.002 · 2.61 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. In this paper we show how to perform Kron reduction for a class of electrical networks without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.
    Automatica 07/2012; 50(10). DOI:10.1016/j.automatica.2014.08.017 · 3.13 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and outflows. As a preparatory result it is shown how a distributed proportional-integral controller structure, associating with every edge of the graph a controller state, will regulate the state variables of the vertices, irrespective of the unknown constant inflows and outflows, in the sense that the storage variables converge to the same value (load balancing or consensus). This will be proved by identifying the closed-loop system as a port-Hamiltonian system, and modifying the Hamiltonian function into a Lyapunov function, dependent on the value of the vector of constant inflows and outflows. In the main part of the paper the same problem will be addressed for the case that the input flow variables are {\it constrained} to take value in an interval. We will derive sufficient and necessary conditions for load balancing, which only depend on the structure of the network in relation with the flow constraints.
    Systems & Control Letters 03/2013; 62(11). DOI:10.1016/j.sysconle.2013.08.001 · 1.89 Impact Factor

Preview (3 Sources)

Download
0 Downloads
Available from