Reduced Order Bilinear Models for Distillation Columns

Abstract

The distillation columns are considered as compartmental systems. Because the inputs act linearly upon the transports matter flows, it is possible to include this type of system in the class of bilinear systems. By considering as output the distillate concentration of one of the produc contained in the distilled mixture, the distillation column can be assimilated to a compartmental system with three compartments each of them replacing a set of distillation plates. These considerations allows finally to characterize a distillation column by a minimal bilinear model having three state variables and eight structural parameters.An identification algorithm allowing to identify such a reduced order bilinear model is presented and is based on the minimization of the output error. Simulation results obtained by using as reference a complete nonlinear model of a distillation column are presented. These results illustrate the validity of the approach proposed as well as the performance of the identification method. The reduced order bilinear model obtained is robust and valid for large variations of the inputs and of the working points.The resulting bilinear model can be used either for designing new control algorithms as well as for deriving a set of linear models around an equilibrium point using only one identification procedure.