Selection of controlled variables: A novel perspective based on the singular energy of weighted graphs

Abstract

The optimal selection of controlled variables is a well-known plant-wide control subproblem. In this paper, a novel approach based on spectral graph theory is proposed. This strategy is useful from both graphical and mathematical point of views. It is shown here that if the closed-loop process is represented by a specific weighted graph, deviations in plant variables are bounded by the graph singular energy. Moreover, this graph-based methodology supports the fast interpretation of the magnitude and direction of influences between process variables at steady state. The suggested spectral approach is compared with the recently proposed minimum square deviation (MSD) methodology in detail. Indeed, both strategies have strong structural and behavioral resemblances, i.e. reducing specific deviations and improving the conditions of the subprocess to be controlled. The introduced graph representation is tested in the Shell oil fractionator process, giving a complete set of evaluations and results.