Analytical structure of a class of product & interval-type-2 fuzzy controllers
LONG Zu-qiang
XU Yue-bing
LI Long
Abstract：The difficulties in deriving the analytical structure of IT2 (interval type-2) fuzzy controllers chiefly come from the iterative computation in type-reduction algorithms. In this paper, we propose a novel technique for deriving the analytical structure of the IT2 fuzzy controllers based on product AND operators. The controllers are configured with triangle IT2 input fuzzy sets, T1 output fuzzy singletons, center-of-sets type reducer, centroid defuzzifier, and product AND operators in precedent parts of fuzzy rules. In comparison to the analytical structure of traditional PID controllers, it is proven that such IT2 fuzzy controllers are equivalent to the sum of two nonlinear PI (or PD) controllers. By means of the iteration-stopping conditions of KM algorithm, an IC-partitioning approach with six steps is presented, which guarantees that a fired subspace can be partitioned correctly. Superimposing all subspaces can produce an overall figure of IC partitions. To avoid solving the symbolic mathematical equations repeatedly, a direct method is given to determine IC boundaries, which facilitates the six-step approach of IC partitioning. Our approach sidesteps the iterative computation in type-reducing algorithm, and guarantees that the closed-loop analytical expression of the IT2 fuzzy controllers can be obtained.
Keywords：fuzzy systemsfuzzy setsfuzzy controllersmembership functionsIT2 fuzzy logicanalytical structure
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 929-935 )