A CLOSED LOOP APPROACH TO TANK REACTOR MODEL SIMPLIFICATION Veronica Olesen, Torsten Wik and Claes Breitholtz Control and Automation Laboratory, Chalmers University of Technology, G¨ oteborg, Sweden e-mail: veronica@s2.chalmers.se, tw@s2.chalmers.se, cb@s2.chalmers.se Abstract: Stirred tank reactors are widely used in the chemical process industry and in many of them there are problems and constraints related to the temperature control. In order to achieve a model suitable for temperature control of such a system a number of ad hoc assumptions and approximations are generally made. Here, a method to systemat- ically evaluate the validity of such simplifications based on the resulting performance of the controlled closed loop system is proposed. The method is applied to a two- compartment model of a reactor with an exothermic reaction. It is then shown that many standard assumptions are reasonable but some assumptions are clearly not advisable because of possibly deteriorated closed loop performance. Copyright c  2005 IFAC Keywords: Non-Ideally Stirred Tank Reactor, Compartmental Model, Sensitivity Functions, Model Simplification 1. INTRODUCTION An exothermic reaction in a reactor can easily run out of control, since a rise in temperature will make the reaction go faster and the reaction itself produces heat. To avoid instability many of these reactions are run today with highly diluted components and reaction temperatures well below optimal operating temper- atures. Thus, an efficient temperature control would increase the productivity of such processes, since the reactant concentration and operating temperature can be higher. In order to determine a non-trivial temper- ature controller, reactor models suitable for controller design are required. Preferably, the models should be of low order, but with variables still having a direct physical interpretation. There are many tank reactor models suitable for in- vestigation of special phenomena or specific con- trol strategies, see for instance (Lagerberg and Bre- itholtz, 1997; Abel and Marquardt, 2003) and ref- erences therein. However, in many of these models, assumptions have been made that might not be valid in general. For example, one commonly used approx- imation in tank reactor modelling is to ignore the tem- perature dependence of the specific heat capacities. In many models all heat capacities are also set to the heat capacity of water when water is used as liquid solvent. There are also many ways to reduce and simplify a complex first principles model, for example by nonlin- ear identification as described by Vargas and Allg¨ ower (2004). In this paper, we begin the modelling and model reduction with a detailed compartmental model of a non-ideally stirred tank reactor and then we pro- pose a method to systematically evaluate the validity of such simplifications based on the resulting per- formance of the controlled closed loop system. The key steps are (i) a linearization of the compartmental model, (ii) a preliminary controller design for the sim- plified and for the detailed model, (iii) determination of the closed loop sensitivity functions and stability measures, and (iv) an evaluation of the deviation of these closed loop measures resulting from the model simplifications.