Structure analysis of three-dimensional fuzzy controller with the simplest rule-base and its relationship to PID controller

This paper presents an approach to the structure analysis of three-dimensional fuzzy controller which is based on Zadeh´s linguistic control strategy and inference process. The authors analytically prove that a typical three-dimensional fuzzy controller with linear control rules is the sum of global nonlinear controller and a local nonlinear incremental PID-like controller. In such a way, we present the reasoning mechanism of three-dimensional fuzzy controller and disclose the nonlinear essence of it.