3HAB6659-1模块备件使用指导

许多模糊控制器都能表示成(1)式的形式，只是控制器的增益随其输入的变化而变化，因此说，模糊控制器是非线性PID控制器。Ying［1］先提出模糊PID控制器的解析结构，并证明了采用两个线性输入模糊集、四条模糊规则、Zadeh模糊逻辑AND和OR操作及重心解模糊器的简单的Mamdani模糊控制器是非线性PI控制器；接着又进一步将其结果推广到采用其它推理方法(如Mamdani小、Larsen乘积、drastic乘积和有界乘积等)的各类Mamdani模糊控制器［2］。更复杂的情况是采用两个输入变量、多个对称或非对称的三角形输入模糊集、线性控制规则、均匀分布的独点输出模糊集、不同推理方法和重心解模糊器的Mamdani模糊控制器，已被证明是一个全局的两维多值继电控制器和一个局部的非线性PI控制器之和［3，4］。这些结果被一般化到采用非线性控制规则的单输入单输出［5］和两输入两输出模糊控制器［6］。其它一些类似的结果见文献［7－10］。
人们已研究了基本Mamdani模糊控制器的各种扩展设计及其结构分析，证明了模糊PID［11－13］、模糊PI＋D［14］、模糊PD＋I［15］、串行模糊PI＋PD［16］、并行模糊PI+PD［17］和模糊(PI+D)2［18］控制器都是非线性PID控制器，并推导出其非线性增益的明晰表达式。另外，一种基于开-关控制技术的时变模糊控制器的结构与非线性PD控制器解析地联系起来，并证明它是一种带有非线性控制偏量的非线性PD控制器［19］。Many fuzzy controllers can be expressed in the form of formula (1), but the gain of the controller changes with the change of its input. Therefore, the fuzzy controller is a nonlinear PID controller. Ying [1] first proposed the analytical structure of fuzzy PID controller, and proved that the simplest Mamdani fuzzy controller using two linear input fuzzy sets, four fuzzy rules, Zadeh fuzzy logic and or operation and barycentric defuzzifier is a nonlinear PI controller; Then, the results are further extended to all kinds of Mamdani fuzzy controllers using other reasoning methods (such as Mamdani minimum, Larsen product, drastic product and bounded product). More complicated is the Mamdani fuzzy controller with two input variables, multiple symmetric or asymmetric triangular input fuzzy sets, linear control rules, uniformly distributed single point output fuzzy sets, different reasoning methods and center of gravity defuzzifier. It has been proved to be the sum of a global two-dimensional multivalued relay controller and a local nonlinear PI controller [3,4]. These results are generalized to single input single output [5] and two input two output fuzzy controllers [6] using nonlinear control rules. Other similar results are shown in literature [7-10].
Various extended designs and structural analysis of the basic Mamdani fuzzy controller have been studied. It is proved that the fuzzy PID [11-13], fuzzy PI + D [14], fuzzy PD + I [15], serial fuzzy PI + PD [16], parallel fuzzy PI + PD [17] and fuzzy (PI + D) 2 [18] controllers are nonlinear PID controllers, and the explicit expression of their nonlinear gain is derived. In addition, the structure of a time-varying fuzzy controller based on on on-off control technology is analytically connected with the nonlinear PD controller, and it is proved that it is a nonlinear PD controller with nonlinear control bias [19].