一类乘积型区间二型模糊控制器的解析结构

摘要

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.%区间二型模糊控制器的降型算法需要使用迭代计算，是导致其解析结构推导困难的主要原因。针对乘积型区间二型模糊控制器，本文提出了一种新的解析结构推导方法。区间二型模糊控制器的配置为：三角形输入模糊集，一型输出模糊单值，集合中心法降型器，平均法解模糊器和基于乘积型“与”操作的规则前件。通过对比传统PID控制器的解析结构，证明了区间二型模糊控制器等效于两个PI(或PD)控制器之和。利用KM算法的迭代终止条件，提出了6步骤IC划分法，保证了激活子空间的正确划分。叠加各个子空间，即可得出全局IC划分图。为了避免重复求解符号数学方程，提出了IC边界线的直接定义法，改进了6步骤IC划分法的便利性。本文方法避开了降型算法的迭代计算，可以保证推导出区间二型模糊控制器的闭环解析表达式。