Type-II T-S fuzzy model-based predictive control

Type-II fuzzy model is useful to handle the influence of uncertainties. This paper presents an algorithm of Type-II T-S fuzzy (T2TSF) modeling based on data clustering and two approaches to design T2TSF model-based predictive controllers. As the T2TSF model is an extension of T1TSF (Type-I T-S fuzzy) model, the T2TSF modeling algorithm divides the input-output data set into several Type-I fuzzy sets by G-K clustering algorithm at first. As for antecedent in each T2TSF rule, the fluctuation range of the memberships is computed by averaging the membership differences among the similar data, and the Type-I fuzzy set can then be expanded to Type-II fuzzy set. As for consequent in each T2TSF rule, the fluctuation range of the data output sections is computed by averaging the output differences of the data with similar input sections, the crisp coefficients of linear polynomials can then be expanded to interval Type-I fuzzy sets. T2TSF model has two kinds of outputs: crisp value and type-reduced set. Based on these two kinds of outputs and predictive control algorithm, two types of controllers are designed. Controller I is based on crisp output to compute crisp control variable. Controller II is based on the type-reduced set to compute a control variable set, and then the crisp control variable is derived by defuzzifying this set. Simulation results of pH neutralization with uncertainties are provided to confirm that the proposed T2TSF modeling is superior to the T1TSF modeling in terms of accuracy, and Controller I and II can achieve better performance than the predictive controller based on T1TSF model.