Analytical Study and Stability Design of a 3-D Fuzzy Logic Controller for Spatially Distributed Dynamic Systems

A novel 3-D fuzzy logic controller (3-D FLC) was presented to control a class of spatially distributed dynamic systems by Li (IEEE Trans. Fuzzy Syst., vol. 15, no. 3, pp. 470–481, Jun. 2007) by utilizing a 3-D fuzzy set and an inference mechanism with 3-D nature for spatial information processing. In this paper, the analytical mathematical model of the 3-D FLC is derived, and the controller structure is explained with the help of the existing conventional control techniques. The graphic analytical method for the traditional two-term FLC can be used for the analytical model derivation. The derived result shows that the 3-D FLC has a global sliding-mode structure over the spatial domain and explains why the 3-D FLC is able to process spatial information more effectively than its traditional counterpart using a few more sensors. Because of its sliding-mode feature, the Lyapunov stability criterion can be developed easily to analyze and design the 3-D FLC. Finally, a catalytic reactor is presented as an example to demonstrate the effectiveness of the 3-D FLC as compared with other controllers.