3HAB7178-1模块备件

近，我们开始讨论TS模糊控制器的解析结构，将一种简单的2×2模糊规则集结构用于分析一类TS模糊PI(或PD)控制器的非线性［20］。推导了TS模糊PI(或PD)控制器增益的明晰表达式，并研究了其增益变化的范围和几何形状等特性。TS模糊PI(或PD)控制器实际上是一种非线性PI(或PD）控制器。上述简单的TS模糊PI(或PD）控制器结构的解析结果还被推广到更典型和复杂的各类TS模糊控制器［21－23］。这些TS模糊控制器由三个或多个梯形(或任意)输入模糊集、带有线性后项的TS模糊规则、Zadeh模糊逻辑AND操作和重心解模糊器构成。
模糊控制器与线性PID控制器相联系的解析结构，一方面揭示了模糊控制器在非线性、时变和纯滞后等系统的应用中比线性PID控制器优越的机理，同时也提供了根据它们之间的增益关系来解析设计模糊控制系统并确保其稳定性的一种方法。
3.2　模糊控制器作为滑模变结构控制器
对于一大类非线性系统，模糊控制器是由与状态x(n)和（n）相对应的偏差e(n)和偏差变化率（n）确定的相平面来设计的。对于二维模糊控制器，一般设计方法是通过一个开关线将相平面划分为两个半平面。其开关函数定义为
（2）
二维控制规则集的零对角线上的控制输入为零。在工作原理上，模糊控制器类似于滑模变结构控制器［10，24－28］。Wu和Liu将模糊控制表示成一类变结构控制，滑模用于确定模糊控制规则中的好参数值［29］。若采用变结构类型的规则集，则模糊控制器具有语义和定量两方面的变结构特性，对于二维和三维模糊控制器，已推导出其具体的数学表达式［30］。与通常的滑模控制相比，模糊控制具有更强的鲁棒性，且模糊控制器的变结构特性有助于人们设计鲁棒稳定的模糊控制器。Recently, we began to discuss the analytical structure of TS fuzzy controller × 2 fuzzy rule set structure is used to analyze the nonlinearity of a class of TS fuzzy PI (or PD) controllers [20]. The explicit expression of the gain of TS fuzzy PI (or PD) controller is derived, and the variation range and geometry of the gain are studied. TS fuzzy PI (or PD) controller is actually a nonlinear PI (or PD) controller. The analytical results of the above simple TS fuzzy PI (or PD) controller structure are also extended to more typical and complex TS fuzzy controllers [21-23]. These TS fuzzy controllers are composed of three or more trapezoidal (or arbitrary) input fuzzy sets, TS fuzzy rules with linear afterterms, Zadeh fuzzy logic and operation and barycentric defuzzifier.
The analytical structure of fuzzy controller and linear PID controller not only reveals the superior mechanism of fuzzy controller over linear PID controller in the application of nonlinear, time-varying and pure delay systems, but also provides a method to analyze and design fuzzy control system and ensure its stability according to the gain relationship between them.
3.2 fuzzy controller as sliding mode variable structure controller
For a large class of nonlinear systems, the fuzzy controller is designed by the phase plane determined by the deviation e (n) and the deviation change rate (n) corresponding to the states X (n) and (n). For two-dimensional fuzzy controller, the general design method is to divide the phase plane into two half planes through a switch line. Its switching function is defined as
（2）
The control input on the zero diagonal of the two-dimensional control rule set is zero. In working principle, fuzzy controller is similar to sliding mode variable structure controller [10, 24-28]. Wu and Liu expressed the fuzzy control as a kind of variable structure control, and the sliding mode is used to determine the best parameter value in the fuzzy control rules [29]. If the rule set of variable structure type is adopted, the fuzzy controller has semantic and quantitative variable structure characteristics. For two-dimensional and three-dimensional fuzzy controllers, its specific mathematical expression has been derived [30]. Compared with the usual sliding mode control, fuzzy control has stronger robustness, and the variable structure characteristics of fuzzy controller help people to design robust and stable fuzzy controller.