A Survey for the Selection of Control Structure for Distillation Columns Based on Steady State Controllability Indexes

One of the important aspects of distillation control design is the choice of a good control structure since improper choice of manipulated/controlled variable pairing can lead to poor control performance. In this paper, comparison and selection of structures is mainly based on the plant condition number. Columns with reflux ratios less than unity or greater than five show large condition numbers. For the ratio structures, the results show that double-ratio structures such as the (D/(L+D))(V/B)-structure have smaller values of the relative gain array element (λ11) compared with single-ratio structures, such as the (D/(L+D))V-structure. In addition, the relative values of λ11 corresponding to the values of minimized condition number (γmin), instead of condition number (γ), provides a better basis for comparison. It has also been shown that the maximum singular value (σmax) of the relative gain array (RGA) is a good criteria between ratio and non-ratio structures, and also between various ratio structures selection. At a constant reflux ratio, columns with smaller values of σmax show small values of γmin. Finally, a frequency-based analysis is performed for the selection of the appropriate structure. The analyses show that although the DV-structure has a relatively small value of condition number with respect to other structures, the value of λ11 is far from unity. In contrast, ratio structures have λ11 values near unity. Frequency-based behavior of ratio structures show small oscillations at higher frequencies (> 1 rad/min), while the conventional LV-structures show large oscillations for smaller values of λ11 at higher frequencies