Analysis of control structures for a Petlyuk distillation column by partial relative gains

Abstract

In multiloop SISO control, decentralized integral controllability (DIC) is usually a desired feature. Necessary conditions for DIC can be expressed by the relative gains of the full system and its various subsystems. The author has previously introduced a controllability measure, the partial relative gain (PRG), that defines relative gains for partially controlled systems, i.e., situations when part of the system is under closed-loop integral control. Thus, this measure directly addresses the desired DIC properties. The measure is more reliable for variable pairing than the conventional relative gain array (RGA). In addition, it can be inferred from the PRG analysis when block-decentralized (or full MIMO) control should be considered. A review of relevant controllability measures for DIC is given in the paper. The PRG is applied to the analysis of control structures for a Petlyuk distillation column.