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A key problem in process control is to decide which inputs should controlwhich outputs. There are multiple ways to solve this problem, among them usinggramian based measures, which include the Hankel interaction index array, theparticipation matrix and the $\Sigma_{2}$ method. The gramian based measureshowever have issues with input and output scaling. Generally, this is resolvedby scaling all inputs and outputs to have equal range. However, we demonstratehow this can result in an incorrect pairing and examine alternative methods ofscaling the gramian based measures, using either row or column sums, or byutilizing the Sinkhorn-Knopp algorithm. The benefits of these scalingstrategies are first illustrated by applying them to the control structureselection for a heat exchanger network. Then, to more systematically analyzethe benefits of the scaling schemes, a multiple input multiple output modelgenerator is used to test the different schemes on a large number of systems.This, along with implementation of automatic controller tuning, allows for astatistical comparison of the scaling methods. This assessment showsconsiderable benefits to be gained from the alternative scaling of the gramianbased measures, especially when using the Sinkhorn-Knopp algorithm. The use ofthis method also has the advantage that the results are completely independentof the original scaling of the inputs and outputs.

Resolving issues of scaling for gramian based input-output pairing methods