A reduced bilinear model of a binary distillation column is presented. This model has as control inputs the reflux rate and the heat flow of the reboiler, as perturbations the feed stream and its concentration, and as outputs the distillate and residual concentrations. A bilinear model is simpler than a non-linear one, and more exact than a linear model. Furthermore, its structure allows the design of a control structure via optimal control theory. In this paper, two optimal control schemes designed by the reduced bilinear model have been applied to a column simulated by an analytical model, obtaining a robust control of the process even in the presence of disturbances.