Reduced order bilinear models for distillation columns

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 products 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 finally permit a characterization of a distillation column by a minimal bilinear model having only three state variables and eight structural parameters. An identification algorithm permitting the identification of 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 non-linear 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 use of the resulting bilinear model for control purposes is discussed.