Analysis and performance evaluation of linear-like fuzzy PI and PID controllers

Abstract

A fuzzy controller output surface based on linearity defined fuzzy regions in a linguistic error state space is used to define a general two input linear-like fuzzy logic controller (LLFLC). The output behavior of a LLFLC is generated using triangular membership functions to create a linear-like controller output surface in the normalized error state space and its properties are thus identified. A non-fuzzy equivalent linear controller (ELC) is established to generate a truly linear controller output surface. Two input linear-like fuzzy PI and PID control implementations and their ELC actions are presented. A first-order temperature control process with transport delay is used to test the performance of the above fuzzy and non-fuzzy, controllers. Fuzzy PI and PID controllers and their ELC structures are tested with different fuzzy resolutions. Results show that a LLFLC with fine fuzzy resolution and a non-fuzzy ELC behave similarly. As well, a LLFLC with coarse fuzzy resolution has the benefit of the anti-symmetric, non-linearity property of the fuzzy controller output surface to produce better performance. Overall, a linear-like fuzzy PID controller with coarse fuzzy resolution gives the best performance.