A new approach to fuzzy control using the distending function

Here, we develop a fuzzy controller using fuzzy arithmetics and a new type of membership function. The proposed new fuzzy control technique is simple, fast and computationally efficient, compared to the classical techniques (Mamdani, Takagi Sugeno) and it can also adapt to the process dynamics. The unique features are: 1) A new class of parametric membership function called the Distending Function (DF) is introduced; 2) A general parametric operator system is used. It utilizes most of the fuzzy operator systems for evaluating the knowledge base; 3) Inference is based on fuzzy arithmetic operations; 4) This leads to a computationally efficient single-step defuzzification. With these concepts, the paradigm of fuzzy control design changes radically. Using this technique with an optimization method, an adaptive fuzzy controller is designed. This adaptive controller adjusts to the changing dynamics of the non-linear processes by tuning our new type of membership function. The effectiveness of the proposed methodology is demonstrated on two industrial processes (a water tank system and continuously stirred tank reactor system).