Interaction analysis for MIMO nonlinear systems based on a fuzzy basis function network model

This paper describes an interaction analysis method for a general multi-input multi-output (MIMO) nonlinear system based on its fuzzy rule-based model. Most real-world multivariable systems are nonlinear, complex and time varying. The multiple system input–output variables interact and sometime even fight against each other, causing significant challenges for system control and optimization. Especially in many practical applications, the accurate quantitative system model is not available or difficult to obtain, which subsequently makes it impossible to analyze the system multivariable interaction characteristics. In this paper, the nonlinear MIMO system is first modeled by fuzzy basis function networks (FBFN) based on a set of linguistic IF–THEN rules or data. The multivariable interaction property is analyzed locally around the operating point based on the relative gain Array (RGA), which is systematically formulated using the system steady-state gain values. Two simulation examples of chemical distillation columns illustrate the system interaction degree obtained by the proposed method is in a sufficient accuracy compared with the result calculated from the system explicit mathematical model, which indicates the applicability of the proposed method as an alternative way to derive the system multivariable interaction when the system mathematical model is not available.