Nonlinear Multivariable System Identification: A Novel Method Integrating T-S Identification and Multidimensional Membership Functions

Abstract

In this paper, a new multidimensional Takagi–Sugeno (T-S) identification technique is proposed for multivariable nonlinear systems. In this technique, multidimensional membership functions are designed using concepts from solid mechanics. The design of membership functions is carried out in multidimensional space, defining the principal axes from the eigenvectors of the inertia matrix, and it has the characteristic of dividing the space into regions with the same inertia. These regions are analyzed to define the center of gravity for each rule. Illustrative examples of multivariable nonlinear systems, such as a thermal mixing process and a binary distillation column, are selected to evaluate the effectiveness of the proposed method. The proposed method is compared with traditional T-S identification that uses one-dimensional membership functions and shows a reduction in the relative identification error and the algorithm execution time. Additionally, the proposed method prevents rules from being positioned outside the system’s range, thereby avoiding the generation of unnecessary rules.