EQUIVALENCE BETWEEN FUZZY-LOGIC CONTROLLERS AND PI CONTROLLERS FOR SINGLE-INPUT SYSTEMS

For a single input and single output system, we prove that when a proportional integral (PI) controller is given, one can design a fuzzy logic controller whose output is identical to that of the PI controller. We also prove that if a fuzzy logic controller using specified fuzzy logic operations is given, there is a PI controller whose output is identical to that of the fuzzy logic controller.