Fuzzy frequency response estimation: A case study for the pH neutralization process

Fuzzy frequency response estimation: a case study for the pH neutralization process is proposed in this paper. A fuzzy c-Means clustering algorithm is used to organize the output experimental data of pH neutralization process into groups based on similarities among the data. Starting from the fuzzy clustering a methodology for identification of the linear sub-models, in terms of transfer function, that represent the pH neutralization process in operation regions is developed and these linear sub-models are organized according to Takagi-Sugeno (TS) fuzzy representation. A fuzzy frequency estimation of pH neutralization process is determined through the frequency response function. The main contribution of this paper is to demonstrate through the proposal of a Theorem, that fuzzy frequency response estimation is a region in the magnitude and phase Bode plots.