Analysis of controlled CSTR models with fluctuating parameters and uncertain parameters

In this paper, a detailed stability analysis of PI controlled CSTRs has bee n studied, accounting for both fluctuating parameters (i.e. noise) and unce rtain parameters to be present in the model. Noise has been considered in t he inlet temperature and in the temperature measurement made by the control ler, while uncertainty has been taken into account for kinetic parameters, imperfect mixing and bias in the temperature measurement made by the contro ller. As far as uncertain parameters are concerned, a recently presented me thodology to detect the most probable stability regions in the control gain s plane has been applied. Such results are combined with the noise analysis (implemented by applying the Fokker-Planck theory of stochastic differenti al equations), to obtain global criteria for the choice of control gains wh ich guarantee both the stability of the steady state with a given confidenc e and low fluctuations in the reactor induced by noise in the inlet tempera ture and in the temperature measurement made by the controller. Furthermore , attention has been given to how to obtain results minimising the computat ional effort. In this way, it will be shown that the presented techniques, which allow a rigorous analysis of reacting systems, accounting for both un certain and fluctuating parameters, can be very efficient. (C) 2000 Elsevie r Science S.A. All rights reserved.