Limits to Energy Conversion
Authors
Arjan van der Schaft, Dimitri Jeltsema
Abstract
The Second Law of thermodynamics implies that no thermodynamic system with a single heat source at constant temperature can convert heat into mechanical work in a recurrent manner. First, we note that this is equivalent to cyclo-passivity at the mechanical port of the thermodynamic system, while the temperature at the thermal port of the system is kept constant. This leads to the question, which general systems with two power ports have similar behavior: when is a system cyclo-passive at one of its ports, while the output variable at the other port (such as the temperature in the thermodynamic case) is kept constant? This property is called “one-port cyclo-passivity,” and entails, whenever it holds, a fundamental limitation to energy transfer from one port to the other. Sufficient conditions for one-port cyclo-passivity are derived for general multiphysics systems formulated in port-Hamiltonian form. This is illustrated by a variety of examples from different (multi-)physical domains; from coupled inductors and capacitor microphones to synchronous machines.
Citation
- Journal: IEEE Transactions on Automatic Control
- Year: 2022
- Volume: 67
- Issue: 1
- Pages: 532–538
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tac.2021.3075652
BibTeX
@article{van_der_Schaft_2022,
title={{Limits to Energy Conversion}},
volume={67},
ISSN={2334-3303},
DOI={10.1109/tac.2021.3075652},
number={1},
journal={IEEE Transactions on Automatic Control},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={van der Schaft, Arjan and Jeltsema, Dimitri},
year={2022},
pages={532--538}
}
References
- Desoer, Basic Circuit Theory (1969)
- Fermi, Thermodynamics (1937)
- Fiaz, S., Zonetti, D., Ortega, R., Scherpen, J. M. A. & van der Schaft, A. J. A port-Hamiltonian approach to power network modeling and analysis. European Journal of Control vol. 19 477–485 (2013) – 10.1016/j.ejcon.2013.09.002
- Hill, Cyclo-dissipativeness, dissipativeness, and losslessness for nonlinear dynamical systems. (1975)
- Hill, D. J. & Moylan, P. J. Dissipative Dynamical Systems: Basic Input-Output and State Properties. Journal of the Franklin Institute vol. 309 327–357 (1980) – 10.1016/0016-0032(80)90026-5
- Kondepudi, D. & Prigogine, I. Modern Thermodynamics. (2014) doi:10.1002/9781118698723 – 10.1002/9781118698723
- Kundur, Power System Stability and Control. New York, NY, USA: Mc-Graw-Hill Engineering (1993)
- Lanczos, C. The Variational Principles of Mechanics. (University of Toronto Press, 1949). doi:10.3138/9781487583057 – 10.3138/9781487583057
- Lobontiu, N. Dynamics of Microelectromechanical Systems. Microsystems (Springer US, 2007). doi:10.1007/978-0-387-68195-5 – 10.1007/978-0-387-68195-5
- van der Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer International Publishing, 2017). doi:10.1007/978-3-319-49992-5 – 10.1007/978-3-319-49992-5
- van der Schaft, A. Cyclo-Dissipativity Revisited. IEEE Transactions on Automatic Control vol. 66 2920–2924 (2021) – 10.1109/tac.2020.3013941
- van der Schaft, A. Classical Thermodynamics Revisited: A Systems and Control Perspective. IEEE Control Systems vol. 41 32–60 (2021) – 10.1109/mcs.2021.3092809
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. (2014) doi:10.1561/9781601987877 – 10.1561/9781601987877
- van der Schaft, A. & Stegink, T. Perspectives in modeling for control of power networks. Annual Reviews in Control vol. 41 119–132 (2016) – 10.1016/j.arcontrol.2016.04.017
- Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
- Willems, J. C. Qualitative Behavior of Interconnected Systems. Annals of Systems Research 61–80 (1974) doi:10.1007/978-1-4613-4555-8_4 – 10.1007/978-1-4613-4555-8_4