From Statistical Mechanics to Process Control: A Tutorial

B. Erik Ydstie, Michael Hartmann, Leyla Özkan

Research output: Contribution to journalConference articlepeer-review

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Abstract

A system-theoretic basis for process control is developed using statistical mechanics as our point of departure. Specifically we show that control of a thermodynamic system can be discussed within the framework of passive systems theory. Using Boltzmann's definition of the entropy S = kB ln(Ω) and assuming that the distribution of states is uniformly distributed close to the equilibrium manifold we demonstrate the existence of a Lyapunov function based on the concept of available work. The LaSalle invariance principle now applies and we conclude that the microscopic (quantum) state converges to an ω-limit set close to the equilibrium manifold. The support of the measure V, interpreted as the volume of the system, defines the phase distribution in a multi-phase system. To connect such ideas with process control we define (approximate) balance equations, force, and flux variables.
Original languageEnglish
Pages (from-to)33-38
Number of pages6
JournalIFAC-PapersOnLine
Volume55
Issue number18
DOIs
Publication statusPublished - 1 Jul 2022

Keywords

  • Convex Analysis
  • Equilibrium
  • Process Control
  • Stability

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