Interaction Measures for Control Configuration Selection Based on Interval Type-2 Takagi–Sugeno Fuzzy Model

Interaction measure determines decentralized and sparse control configurations for a multivariable process control. This paper investigates interval type-2 Takagi-Sugeno fuzzy (IT2TSF) model based interaction measures using two different criteria, one is controllability and observability gramians, the other is relative normalized gain array (RNGA). The main contributions are: first, a data-driven IT2TSF modeling method is introduced; second, explicit formulas to execute the two measures based on IT2TSF models are given; third, two interaction indexes are defined from RNGA to select sparse control configuration; fourth, the calculations to derive sensitivities of the two measures with respect to parametric variations in the IT2TSF models are developed; and fifth, the discussion to compare the two measures is presented. Three multivariable processes are used as examples to show that the results calculated from IT2TSF models are more accurate than that from their type-1 counterparts, and compared to gramian-based measure, RNGA selects more reasonable control configurations and is more robust to the parametric uncertainties.