Contents I. Introduction
Modeling and control of the pH process is considered to be a difficult task because one needs to have knowledge about the components and their nature in the process stream in order to model its dynamics using conventional techniques. In the modeling aspect, rigorous models from first principles involving the material balance and equilibrium equations were established in [1] and later extended in [2] through the concept of the reaction invariant, and more complicated situations were considered in [3]. Due to the susceptibility to change in operating point, varying gain and load disturbances, the performance of the practical processes deviates from conventional modeling output [4]. Fuzzy identification is an effective tool for the approximation of uncertain nonlinear systems on the basis of measured data [5]. Among the different fuzzy modeling techniques, the Takagi-Sugeno (TS) model [6] has attracted the most attention. Fuzzy models can be seen as rule-based systems suitable for formalizing the knowledge of experts, and at the same time they are flexible mathematical structures, which can represent complex nonlinear mappings [7]. Membership functions can be defined by the model developer (expert), using prior knowledge, or by experimentation, which is a typical approach in knowledge-based fuzzy control [8]. Knowledge acquisition however is, a cumbersome task, and for (partially) unknown systems, human experts are not available. Therefore, data-driven construction of fuzzy membership function and rules from measured input/output data has received a lot of attention. Such modeling approaches typically seek to optimize some numerical objective function, while less attention is paid to the complexity of the resulting model in terms of the number of membership functions and rules [9].
