Thermodynamic Analysis and Feedback Stabilization for Irreversible Liquid–Vapor Systems

In this paper, we investigate the stability analysis and the feedback stabilization design problem for multiphase chemical systems using a nonequilibrium thermodynamics formalism. We first present a compartmental model for multiphase systems far from thermodynamic equilibrium. The modeling framework allows us to describe irreversible multiphase systems as a differential-algebraic equation (DAE) system. The differential part of the model corresponds to macroscopic balance equations. The algebraic system of equations represents the interface thermodynamic subsystem that occurs between bulk phases. Integrating the DAE model is equivalent to fixing the degrees of freedom prescribed by the Gibbs phase rule. A linear stability analysis and numerical simulations for the resulting differential-algebraic model are presented. We stabilize the system by fixing the pressure to a constant value. Following this result, we present a feedback structure that fixes the pressure of the system using the proposed modeling framework.