High purity distillation control of a binary mixture in a tray column is considered in the paper at hand. The approach is based on an inferential control idea: dynamics within the column may be described as movements of concentration waves; the position of the wave front on the one hand side can be inferred from few temperature measurements, on the other hand the position implies the product concentrations. Dynamics of wave propagation is derived by simplification of a first principles model of the column. The resulting descriptor model is the basis for a recent LMI based controller design scheme that provides general quadratic performance for descriptor systems.