Modelling and Analysis of the Simplest Fuzzy PI/PD Controllers of Takagi-Sugeno Type

In this paper analytical structures of the simplest fuzzy PI/PD controllers of Takagi-Sugeno (TS) type are found with a modified rule base. The rule base contains only two rules which greatly reduce the tuning parameters of the controllers. These controllers are the simplest since minimal number (two) of fuzzy sets is employed on each input variable. The triangular norms and co-norms are chosen as algebraic product/minimum and bounded sum/maximum, respectively. It is shown that the fuzzy controller with modified TS rule base is equivalent to a nonlinear variable gain PI/PD controller. The gain variations and computational aspects are also studied.