Stability Analysis of Thermodynamic Systems: Heat Conduction in Solids

Daming Lou; Siep Weiland

doi:10.1016/j.ifacol.2020.12.629

Stability Analysis of Thermodynamic Systems: Heat Conduction in Solids

Daming Lou (Corresponding author), Siep Weiland (Corresponding author)

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

20 Downloads (Pure)

Abstract

This paper addresses the fundamental difference between equilibria of thermodynamic systems and equilibria of autonomous state space systems. The notion of stability of thermodynamic equilibria is analyzed in terms of an entropy generating function that classifies as a Lyapunov function to prove asymptotic stability of thermal equilibria. The stability analysis is performed for both finite and infinite dimensional systems. It is shown how the proposed Lyapunov function naturally extends to assess stability of interconnected thermal systems. A number of examples is given to demonstrate the time evolution of the Lyapunov function.

Original language	English
Pages (from-to)	11533-11538
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	53
Issue number	2
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.629
Publication status	Published - 2020
Event	21st World Congress of the International Federation of Aufomatic Control (IFAC 2020 World Congress) - Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020 Conference number: 21 https://www.ifac2020.org/

Keywords

Lyapunov functions
Thermal equilibria
Thermal stability

Access to Document

10.1016/j.ifacol.2020.12.629

published versionFinal published version, 651 KB

Cite this

@article{e830070b7ec8419bb4779bed55472e15,

title = "Stability Analysis of Thermodynamic Systems: Heat Conduction in Solids",

abstract = "This paper addresses the fundamental difference between equilibria of thermodynamic systems and equilibria of autonomous state space systems. The notion of stability of thermodynamic equilibria is analyzed in terms of an entropy generating function that classifies as a Lyapunov function to prove asymptotic stability of thermal equilibria. The stability analysis is performed for both finite and infinite dimensional systems. It is shown how the proposed Lyapunov function naturally extends to assess stability of interconnected thermal systems. A number of examples is given to demonstrate the time evolution of the Lyapunov function.",

keywords = "Lyapunov functions, Thermal equilibria, Thermal stability",

author = "Daming Lou and Siep Weiland",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.629",

language = "English",

volume = "53",

pages = "11533--11538",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "2",

note = "21st World Congress of the International Federation of Aufomatic Control (IFAC 2020 World Congress), IFAC 2020 ; Conference date: 12-07-2020 Through 17-07-2020",

url = "https://www.ifac2020.org/",

}

TY - JOUR

T1 - Stability Analysis of Thermodynamic Systems: Heat Conduction in Solids

AU - Lou, Daming

AU - Weiland, Siep

N1 - Conference code: 21

PY - 2020

Y1 - 2020

N2 - This paper addresses the fundamental difference between equilibria of thermodynamic systems and equilibria of autonomous state space systems. The notion of stability of thermodynamic equilibria is analyzed in terms of an entropy generating function that classifies as a Lyapunov function to prove asymptotic stability of thermal equilibria. The stability analysis is performed for both finite and infinite dimensional systems. It is shown how the proposed Lyapunov function naturally extends to assess stability of interconnected thermal systems. A number of examples is given to demonstrate the time evolution of the Lyapunov function.

AB - This paper addresses the fundamental difference between equilibria of thermodynamic systems and equilibria of autonomous state space systems. The notion of stability of thermodynamic equilibria is analyzed in terms of an entropy generating function that classifies as a Lyapunov function to prove asymptotic stability of thermal equilibria. The stability analysis is performed for both finite and infinite dimensional systems. It is shown how the proposed Lyapunov function naturally extends to assess stability of interconnected thermal systems. A number of examples is given to demonstrate the time evolution of the Lyapunov function.

KW - Lyapunov functions

KW - Thermal equilibria

KW - Thermal stability

UR - http://www.scopus.com/inward/record.url?scp=85105085457&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.629

DO - 10.1016/j.ifacol.2020.12.629

M3 - Conference article

VL - 53

SP - 11533

EP - 11538

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 2

T2 - 21st World Congress of the International Federation of Aufomatic Control (IFAC 2020 World Congress)

Y2 - 12 July 2020 through 17 July 2020

ER -

Stability Analysis of Thermodynamic Systems: Heat Conduction in Solids

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this