Takagi-Sugeno fuzzy PI controllers: Analytical equivalence and tuning

This paper derives the analytical structure of a simple class of Takagi-Sugeno PI controller with respect to conventional control theory. It is well-known that fuzzy controllers are nonlinear systems but the underlying analytic model of the nonlinearities is generally difficult to derive. Specializing to a class of Takagi-Sugeno PI controllers described by a simple rule base, these nonlinearities are determined explicitly then leading to familiar conventional representations of these controllers. The derived conventional structures provide a basis for controller tuning. An illustrative example is also given to show the effectiveness of the analytical structure towards a systematic tuning approach to Takagi-Sugeno fuzzy PI controllers.