Interaction measures and pairing of controlled and manipulated variables for multiple-input-multiple-output systems: a survey

This article presents a survey of a set of interaction measures for multiple-input-multiple-output (MIMO) linear systems, and discusses their use to determine the best pairing of manipulated and controlled variables. Criteria to decide whether a multiloop control strategy can be applied successfully to a given process are also described. The classical approaches, such as Bristol's relative gain array and Niederlinski's theorem are reviewed in the first sections. Next, less common methods based on the Jacobi eigenvalue criterion, the direct Nyquist array, and singular value analysis are introduced. Finally, examples are used to illustrate the usefulness of each approach and criterion.