About Some System-Theoretic Properties of Port-Thermodynamic Systems

Recently a class of Hamiltonian control systems was introduced for geometric modeling of open irreversible thermodynamic processes. These systems are defined as ordinary Hamiltonian input-output systems on a symplectic manifold, with the special property that the Hamiltonian is homogeneous in the generalized momentum variables, and that there is an invariant homogeneous Lagrangian submanifold characterizing the state properties of the thermodynamic system. After recalling the basic framework we study the passivity, controllability and observability properties of such systems.

[1]  M. Krüger,et al.  On a variational principle in thermodynamics , 2013 .

[2]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[3]  Christoph Kawan,et al.  Invariance entropy for a class of partially hyperbolic sets , 2017, Math. Control. Signals Syst..

[4]  D. Mart'in de Diego,et al.  New insights in the geometry and interconnection of port-Hamiltonian systems , 2018, Journal of Physics A: Mathematical and Theoretical.

[5]  Arjan van der Schaft,et al.  Generalized port-Hamiltonian DAE systems , 2018, Syst. Control. Lett..

[6]  Arjan van der Schaft,et al.  Geometry of Thermodynamic Processes , 2018, Entropy.

[7]  Miroslav Grmela,et al.  Contact Geometry of Mesoscopic Thermodynamics and Dynamics , 2014, Entropy.

[8]  A. Schaft,et al.  Homogeneous Hamiltonian Control Systems Part I: Geometric Formulation , 2018 .

[9]  R. MrugaŁa,et al.  Geometrical formulation of equilibrium phenomenological thermodynamics , 1978 .

[10]  A. Schaft,et al.  Homogeneous Hamiltonian Control Systems Part II: Application to thermodynamic systems , 2018 .

[11]  Daniel Sbarbaro,et al.  Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR , 2013 .

[12]  Denis Dochain,et al.  An entropy-based formulation of irreversible processes based on contact structures , 2010 .

[13]  Antonio A. Alonso,et al.  Process systems and passivity via the Clausius-Planck inequality , 1997 .

[14]  Charles-Michel Marle,et al.  Symplectic geometry and analytical mechanics , 1987 .

[15]  Bernhard Maschke,et al.  An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes , 2007 .

[16]  Hans Zwart,et al.  Linear port-Hamiltonian descriptor systems , 2018, Math. Control. Signals Syst..

[17]  A. Schaft,et al.  Port-controlled Hamiltonian systems : modelling origins and systemtheoretic properties , 1992 .

[18]  Miroslav Grmela,et al.  Reciprocity relations in thermodynamics , 2002 .

[19]  Hans Zwart,et al.  Port-Hamiltonian descriptor systems , 2017, 1705.09081.

[20]  J. Keenan Availability and irreversibility in thermodynamics , 1951 .

[21]  R. Mrugaa̵,et al.  On a special family of thermodynamic processes and their invariants , 2000 .

[22]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[23]  R. Mrugala,et al.  Continuous contact transformations in thermodynamics , 1993 .

[24]  A. Schaft L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[25]  J. Willems Dissipative dynamical systems part I: General theory , 1972 .

[26]  R. Balian,et al.  Hamiltonian structure of thermodynamics with gauge , 2000 .