Analytical approach to evaluation of distillation control structures by frequency-dependent relative gains

Abstract

It is known that control structure selection based on the relative gain array (RGA) may be unreliable for systems larger than 2 × 2. To obtain useful information by the RGA, it is often advantageous, or even necessary, to consider the system with some control loops closed. In distillation, it is necessary to close the inventory control loops. In the paper, analytical relationships useful for frequency-dependent relative gain analysis of distillation control structures are developed. An expression that relates the RGA for an arbitrary control structure to the transfer functions for the so-called LV-structure is derived. Relationships that directly relate the relative gains for different control structures to one another are also derived. The usefulness of the relationships is illustrated by calculation of frequency-dependent relative gains for nine different control structures for a distillation column. Based on these relative gains, the most promising control structures can be selected for further study.