Generalized availability function for the control of chemical reactors

In this paper we derive from the thermodynamic availability function, a set of generalized availability functions that can advantageously be used as Lyapunov functions for the control of Chemical Reactors. This generalization is given by using a translation of the entropy function of the system along singular lines. The convexity and the positivity of the generalized availability are proved by using the concavity property of the entropy function. These generalized availability functions are parameterized by some homogeneity coefficient which recovers the original thermodynamic availability at infinity. We show the advantage of the use of the generalized availability functions as Lyapunov functions for control and how it reduces the transient high control input obtained by using the original one.