Analytical structure of a two-input two-output fuzzy controller

This study investigates the analytical structure of a two-input two-output fuzzy controller which employs triangular-shaped input fuzzy sets, trapezoidal-shaped output fuzzy sets, linear control rules, probabilistic AND fuzzy logic, Lukasiewcz OR fuzzy logic, Mamdani´s minimum inference method and a center of gravity defuzzification algorithm. The structure of the fuzzy controller is proven to be the sum of global 4D multilevel relays and local nonlinear proportional-integral (PI) controllers with variable gains continuously changing with process outputs. The global multilevel relays play a major role in determining control action of the fuzzy controller while the local PI controllers locally fine tune the control action of the relays. As the number of control rules approaches ∞, each global 4D multilevel relay becomes the sum of two global linear PI controllers while the local PI controllers disappear