A NONLINEAR FUZZY CONTROLLER WITH LINEAR-CONTROL RULES IS THE SUM OF A GLOBAL 2-DIMENSIONAL MULTILEVEL RELAY AND A LOCAL NONLINEAR PROPORTIONAL-INTEGRAL CONTROLLER

The author analytically proves that a nonlinear fuzzy controller with linear control rules and N members for input fuzzy sets is the sum of a global two-dimensional multilevel relay and a local nonlinear proportional-integral (PI) controller which adjusts the control action generated by the global multilevel relay. As N increases, the resolution of the global multilevel relay is enhanced but the role of the local nonlinear PI controller in total control action is decreased. As N approaches infinity, the global multilevel relay approaches a regular linear PI controller while the control action from the local nonlinear PI controller approaches zero. The role of the global multilevel relay and the local nonlinear PI controller in total control action is quantitatively described, as is the degree of nonlinearity of the fuzzy controllers with different N.