Abstract
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).
Highlights
We develop a fuzzy controller using fuzzy arithmetics and a new type of membership function
If the input is in the interval [−, ], the value of the Distending Function (DF) is greater than ν and δε(λ,ν)(ε) = ν
Our design methodology is motivated by our previous study where a fuzzy control was designed using fuzzy arithmetic operations [32]
Summary
Fuzzy theory has been an area of extensive research since its inception, nearly half a century ago, by Lotfi A. An adaptive fuzzy controller organizes the rule base (type and number of rules) and it tunes the parameters of the membership functions if the process dynamics changes over time [15,16]. It consists of tuning the DF parameters using gradient descent optimization. The antecedent and consequent parts of the rule base are fuzzy sets, so it is very close to direct human linguistic inputs. There are two main differences with our approach: 1) Product inference (operator and implication) is used for evaluating the fuzzy rules and designing controller in [14]; 2) Adaptivity is achieved using Retractable Membership Functions (RMFs) in [13], which are symmetric membership functions. Namely the symmetric and asymmetric DF and both can be utilized for control system design
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
