Interaction analysis and loop pairing for MIMO processes described by T–S fuzzy models

This paper presents a loop pairing method for determining the control configuration for multi-input–multi-output (MIMO) processes represented by Takagi–Sugeno (T–S) fuzzy models. The method is simple with straightforward calculation and it provides more accurate results compared with existing fuzzy pairing approaches, since both steady-state and dynamic information for the system is utilized. Each individual loop in the MIMO process is represented by a T–S fuzzy model based on the data and the models are then assembled to form the MIMO model. Simple formulae are derived to calculate the steady-state and dynamic information for the loops. In this way, interactions among the loops can be assessed and loop pairing can be determined according to the relative normalized gain array (RNGA) criterion. Two examples are provided to show that loop pairing decisions obtained from T–S fuzzy models are the same as those obtained from precise mathematical models. This demonstrates the effectiveness of the proposed interaction measure and the loop pairing method.