Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics

In this paper, the thermodynamic availability function is used as a Lyapunov function for the practical derivation of non linear control laws for the stabilization of a large class of CSTRs far from the equilibrium. The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed. In this study, we consider liquid mixture with constant volume, the constraint on the volume being insured by perfect regulation of the outlet flow of the CSTR. Several control laws are then derived which insure global asymptotic stability, exponential stability or simple asymptotic stability. These control laws are discussed regarding the magnitude and the dynamic variations of the control variable. It is shown that the availability function can be split into two parts : one corresponds to the mixing term and depends on mole numbers only and the other depends on both temperature and mole numbers. The two parts are positive and the second one is chosen as a new Lyapunov function. The use of this new Lyapunov function insures smooth variations of the control variable. An exothermal, first order chemical reaction leading to multiple steady-state operating points of the CSTR illustrates the proposed theory.