On the interconnection of irreversible port-Hamiltonian systems
Authors
Hector Ramirez, Yann Le Gorrec
Abstract
Different from mechanic or reversible systems, such as port-Hamiltonian systems (PHS), which preserves the energy or the Hamiltonian, irreversible PHS (IPHS) also satisfy the second law of Thermodynamics, i.e., the internal entropy production of the system is always greater or equal to zero. Hence, when considering the interconnection of IPHS, it must be so that the first and second laws of Thermodynamics are satisfied, implying that the interconnection must be power-preserving and entropy-increasing. In this work the conditions for a thermodynamic admissible interconnection of IPHS have been studied and characterized. The interconnection law is given by a state modulated input-output feedback, in which each modulating function is related and defined by the corresponding irreversible thermodynamic driving force induced by the interconnection. The interconnection law also encompasses the reversible interactions, and can be interpreted as a generalization of a power-preserving interconnection to deal with thermodynamic systems. The result has been illustrated on the abstract interconnection of purely thermodynamic and thermo-mechanic systems, and on the examples of an ideal heat-exchanger and a gas-piston system.
Keywords
Irreversible port-Hamiltonian systems; passivity; irreversible thermodynamics
Citation
- Journal: IFAC-PapersOnLine
- Year: 2023
- Volume: 56
- Issue: 1
- Pages: 114–119
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2023.02.020
- Note: 12th IFAC Symposium on Nonlinear Control Systems NOLCOS 2022- Canberra, Australia, January 4-6, 2023
BibTeX
@article{Ramirez_2023,
title={{On the interconnection of irreversible port-Hamiltonian systems}},
volume={56},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2023.02.020},
number={1},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Ramirez, Hector and Gorrec, Yann Le},
year={2023},
pages={114--119}
}
References
- Brugnoli, A., Alazard, D., Pommier-Budinger, V. & Matignon, D. Port-Hamiltonian formulation and symplectic discretization of plate models Part I: Mindlin model for thick plates. Applied Mathematical Modelling vol. 75 940–960 (2019) – 10.1016/j.apm.2019.04.035
- Caballeria, J., Ramirez, H. & Gorrec, Y. L. An irreversible port-Hamiltonian model for a class of piezoelectric actuators. IFAC-PapersOnLine vol. 54 436–441 (2021) – 10.1016/j.ifacol.2021.10.393
- Callen, (1985)
- Cardoso-Ribeiro, F. L., Matignon, D. & Lefèvre, L. A partitioned finite element method for power-preserving discretization of open systems of conservation laws. IMA Journal of Mathematical Control and Information vol. 38 493–533 (2020) – 10.1093/imamci/dnaa038
- Couenne, F., Jallut, C., Maschke, B., Breedveld, P. C. & Tayakout, M. Bond graph modelling for chemical reactors. Mathematical and Computer Modelling of Dynamical Systems vol. 12 159–174 (2006) – 10.1080/13873950500068823
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- Maschke, Port controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
- Maschke, B. M., van der Schaft, A. J. & Breedveld, P. C. An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 42 73–82 (1995) – 10.1109/81.372847
- Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
- Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
- Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
- Ramirez, H., Maschke, B. & Sbarbaro, D. Modelling and control of multi-energy systems: An irreversible port-Hamiltonian approach. European Journal of Control vol. 19 513–520 (2013) – 10.1016/j.ejcon.2013.09.009
- Ramirez, H. & Le Gorrec, Y. An Overview on Irreversible Port-Hamiltonian Systems. Entropy vol. 24 1478 (2022) – 10.3390/e24101478
- Ramirez, H., Gorrec, Y. L. & Maschke, B. Boundary controlled irreversible port-Hamiltonian systems. Chemical Engineering Science vol. 248 117107 (2022) – 10.1016/j.ces.2021.117107
- Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
- Ramirez, H., Sbarbaro, D. & Gorrec, Y. L. Irreversible Port-Hamiltonian Formulation of some Non-isothermal Electrochemical Processes. IFAC-PapersOnLine vol. 52 19–24 (2019) – 10.1016/j.ifacol.2019.07.004
- Rashad, R., Califano, F., van der Schaft, A. J. & Stramigioli, S. Twenty years of distributed port-Hamiltonian systems: a literature review. IMA Journal of Mathematical Control and Information vol. 37 1400–1422 (2020) – 10.1093/imamci/dnaa018
- Trenchant, V., Ramirez, H., Le Gorrec, Y. & Kotyczka, P. Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct. Journal of Computational Physics vol. 373 673–697 (2018) – 10.1016/j.jcp.2018.06.051
- van der Schaft, (2000)
- van der Schaft, The Hamil-tonian formulation of energy conserving physical systems with external ports. Archiv für Elektronik und Übertragungstechnik (1995)
- Van der Schaft, A. & Maschke, B. Geometry of Thermodynamic Processes. Entropy vol. 20 925 (2018) – 10.3390/e20120925
- Villalobos, I., Ramírez, H. & Gorrec, Y. L. Energy shaping plus Damping injection of Irreversible Port Hamiltonian Systems. IFAC-PapersOnLine vol. 53 11539–11544 (2020) – 10.1016/j.ifacol.2020.12.630