Linear fuzzy controller: It is a linear nonfuzzy controller

Abstract

We consider a process controlled, by a controller described by an nth-order linear ordinary differential equation, towards its target output. As a special case, the controller is a proportional-integral-derivative (PID) controller. We show how to construct a linear fuzzy controller that gives precisely the same control as the PID controller. We speculate that nonfuzzy controllers and fuzzy controllers may coincide on an unsuspectingly large class of control problems.