Resolving issues of scaling for gramian-based input–output pairing methods
Journal article, 2022

A key problem in process control is to decide which inputs should control which outputs. There are multiple ways to solve this problem, among them using gramian-based measures, which include the Hankel interaction index array, the participation matrix and the (Formula presented.) method. The gramian-based measures, however, have issues with input and output scaling. Generally, this is resolved by scaling all inputs and outputs to have equal range. However, we demonstrate how this can result in an incorrect pairing and examine alternative methods of scaling the gramian-based measures, using either row or column sums or by utilising the Sinkhorn-Knopp algorithm. To systematically analyse the benefits of the scaling schemes, a multiple-input multiple-output model generator is used to test the different schemes on a large number of systems. This assessment shows considerable benefits to be gained from the alternative scaling of the gramian-based measures, especially when using the Sinkhorn-Knopp algorithm.

input-output pairing

sparse control

Decentralised control

gramian based interaction measures

control configuration selection


Fredrik Bengtsson

Chalmers, Electrical Engineering, Systems and control

Torsten Wik

Chalmers, Electrical Engineering, Systems and control

Elin Svensson

CIT Industriell Energi AB

International Journal of Control

0020-7179 (ISSN)

Vol. 95 3 679-691

Subject Categories

Control Engineering

Signal Processing

Other Electrical Engineering, Electronic Engineering, Information Engineering



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Latest update

7/4/2022 1