STABILIZATION OF NON ISOTHERMAL CHEMICAL REACTORS USING TWO THERMODYNAMIC LYAPUNOV FUNCTIONS

Abstract

The main goal of this paper is to introduce a link between the thermodynamics and control systems theory. More precisely, the paper focuses on Lyapunov based control of process systems, specially the non isothermal Continuous Stirred Tank Reactors in a thermodynamic framework, using either the jacket temperature or the inlet molar flow rate as the only control input. As soon as the constraint on the total mass is considered and the reaction kinetics is a Lipschitz continuous function with respect to the temperature, it shows that the stabilization of thermal solicitations reciprocally entails the one of matter using La Salle’s invariance principle. As a consequence, these control problems can be solved if the closed loop Lyapunov functions are chosen to be proportional to the thermal part or material part of the so called thermodynamic availability function. Some numerical simulations for a first order chemical reaction with multiple steady states are given to validate our theoretical developments. The performance of the obtained nonlinear controllers with regard to the conversion rate is also discussed.