Pseudo-equivalence of fuzzy PID controllers

This paper presents a pseudo-equivalence of digital fuzzy PID controllers with linear PID controllers in the continuous time domain. Transfer functions and equivalence relations between controller's parameters are obtained for the common structures of the fuzzy PID controllers. The pseudo-equivalence is made using a graphic analytical analysis based on the input-output transfer characteristics of the fuzzy block, the linear characteristic of the fuzzy block around the origin and the usage of the gain in origin obtained as an origin limit of the variable gain of the fuzzy block. An algorithm of equivalence is presented. The paper presents a unitary theory, which may be applied to the most general fuzzy PID controllers, developed using all kind of membership functions, rule bases, inference methods and defuzzification methods. The term pseudo-equivalence is emphasized because there is no straight equivalence between the non-linear fuzzy controllers and the linear PID controllers. A case study of a control system using linear and fuzzy controllers is presented. The action mode of the fuzzy controller is analyzed. Based on the transient characteristics a comparison analyses is done. Better control quality criteria are demonstrated for control systems using fuzzy controllers.