A Note on the Simplest Mamdani Fuzzy Two-Term (PI/PD) Controllers
Sadhna Malik, B.M. Mohan · 2024
In view of the large number of publications dealing with mathematical modelling of varieties of fuzzy controllers so far, it is well understood that the model of a controller depends on various factors such as AND operator (commonly used: Algebraic Product – AP and Minimum – Min), OR operator (commonly used: Bounded Sum – BS and Maximum – Max), inference method (commonly used: Larsen Product – LP and Mamdani Minimum – MM), aggregation operator (commonly used: Max), and defuzzification method (commonly used: Weighted Average – WA, Centre of Sums – CoS and Centre of Area – CoA). It is important to note that BS aggregation operator was never used in modelling. What happens if BS aggregation is used? Shall we get unique models for controllers? This important aspect is addressed in this paper. Surprisingly, it is found that the models of the controllers obtained with BS aggregation operator are not unique as they are identical to the models of other known controllers reported in the literature. In order to show this astonishing result, the models of all possible 28 controllers are compared in a particular region of scaled input plane and found that only 20 controllers are unique.