Structure analysis of three-dimensional fuzzy controller and its relationship to PID controller

Three-dimensional fuzzy controller (error, rate, rate of change of rate) has attracted extensive attention due to its advantages over conventional two-dimensional fuzzy controller in applications. In SISO system, it is reasonable to consider that a three-dimensional fuzzy controller may probably be related to nonlinear PID controllers. In this paper, the structure analysis methodology given by Ying (1993) is extended towards three-dimensional fuzzy controllers. The result shows that a typical three-dimensional fuzzy controller with linear control rules is the sum of a global three-dimensional multilevel relay and a local nonlinear PID-like controller