Computing the Relative Gains for Pressure and Composition Control of a Single Distillation Tower

This paper treats calculation of the steady-state relative gains for controlling a single distillation tower. A detailed mathematical model is formulated and solved by a modified Wang and Henke method. Three columns of 90%-10%, 95%-5%, and 99%-1% end product compositions for a benzene-toluene system are considered. The computational results show that the size of the perturbation used to calculate the partial derivatives for the relative gain and the convergence tolerance should be smaller for high purity columns than for low purity columns. Two consistency tests of the computational results are also presented.