模糊PID控制器的设计与仿真——设计步骤

1、模糊PID控制器的设计与仿真设计模糊 PID 控制器时，首先要将精确量转换为模糊量，并且要把转换后的 模糊量映射到模糊控制论域当中， 这个过程就是精确量模糊化的过程。 模糊化的 主要功能就是将输入量精确值转换成为一个模糊变量的值， 最终形成一个模糊集 合。本次设计系统的精确量包括以下变量：变化量 e ，变化量的变化速率 ec 还 有参数整定过程中的输出量 Kp,AKD,AK,在设计模糊 PID 的过程中，需要 将这些精确量转换成为模糊论域上的模糊值。 本系统的误差与误差变化率的模糊 论域与基本论域为： E=-6,-4,-2,0,2,4,6;Ec=-6,-4,-2,0,2,4,6 。模糊 PID

2、 控制器的设计选用二维模糊控制器。 以给定值的偏差 e 和偏差 变化ec 为输入；AKP,AKD, AK 为输出的自适应模糊PID 控制器，见图 1。图 1 模糊 PID 控制器(1 )模糊变量选取输入变量 E 和 EC 的模糊化将一定范围(基本论域)的输入变量映射到离散区 间(论域)需要先验知识来确定输入变量的范围。 就本系统而言， 设置语言变量取 七个，分别为 NB， NM， NS， ZO， PS， PM， PB。(2) 语言变量及隶属函数根据控制要求，对各个输入，输出变量作如下划定：e, ec 论域：-6 , -5 , -4 , -3 , -2 , -1 , 0, 1, 2, 3, 4,

3、 5, 6A &,AKD,AK 论域：-6 , -5 , -4 , -3 , -2 , -1 , 0, 1 , 2 , 3 , 4 , 5 , 6 应用模糊合成推理 PID 参数的整定算法。第 k 个采样时间的整定为KP(k) KP0KP(k) , KI(k)KI0KI(k) , KD(k) KD0KD(k).式中KPO,K|O,KDO为经典 PID 控制器的初始参数。设置输入变量隶属度函数如图 2 所示 输出变量隶属度函数如图 3 所示。图 2 输入变量隶属度函 图 3 输出变量隶属度函3)编辑模糊规则库根据以上各输出参数的模糊规则表，可以归纳出 49 条控制逻辑规则，具体的控制规则

4、如下所示：1. If(e isNB) and (ec is NB) then (kp isNB)(kiis PB)(kd is NS)(1)2.If(e isNB) and (ec is NM) then (kp is NB)(kiis PB)(kd is PS)(1)3.If(e isNB) and (ec is NS) then (kp is NM)(kiis PM)(kd is PB)(1)4.If(e isNB) and (ec is ZO) then (kp is NM)(kiis PM)(kd is PB)(1)5.If(e isNB) and (ec is PS) then (k

5、p is NS)(kiis PS)(kd is PB)(1)6.If(e isNB) and (ec is PM) then (kp is ZO)(kiis ZO)(kd is PM)(1)7.If(e isNB) and (ec is PB) then (kp is ZO)(kiis ZO)(kd is NS)(1)8.If(e isNM) and (ec is NB) then (kp is NB)(kiis PB)(kd is NS)(1)9.If(e isNM) and (ec is NM) then (kp is NB)(kiis PB)(kd is PS)(1)10.If (e i

6、s NM) and (ec is NS) then (kp is NM)(ki is PM)(kd isPB)(1)11.If (e is NM) and (ec is ZO) then (kp is NS)(ki is PS)(kd isPM)(1)12.If (e is NM) and (ec is PS) then (kp is NS)(ki is PS)(kd isPM)(1)13.If (e is NM) and (ec is PM) then (kp is ZO)(ki is ZO)(kd isPS)(1)14.If (e is NM) and (ec is PB) then (k

7、p is PS)(ki is ZO)(kd isZO)(1)15.If (e is NS) and (ec is NB) then (kp is NM)(ki is PB)(kd isZO)(1)16.If (e is NS) and (ec is NM) then (kp is NM)(ki is PM)(kd isPS)(1)17.If (e is NS) and (ec is NS) then (kp is NM)(ki is PS)(kd isPM)(1)18.If (e is NS) and (ec is ZO) then (kp is NS)(ki is PS)(kd isPM)(

8、1)19.If (e is NS) and (ec is PS) then (kp is ZO)(ki is ZO)(kd isPS)(1)20.If (e is NS) and (ec is PM) then (kp is PS)(ki is NS)(kd isPS)(1)21.If (e is NS) and (ec is PB) then (kp is PS)(ki is NS)(kd isZO)(1)22.If (e is ZO) and (ec is NB) then (kp is NM)(ki is PM)(kd isZO)(1)23.If (e is ZO) and (ec is

9、 NM) then (kp is NM)(ki is PM)(kd isPS)(1)24.If (e is ZO) and (ec is NS) then (kp is NS)(ki is PS)(kd isPS)(1)25.If (e is ZO) and (ec is ZO) then (kp is ZO)(ki is ZO)(kd isPS)(1)26.If (e is ZO) and (ec is PS) then (kp is PS)(ki is NS)(kd isPS)(1)27.If (e is ZO) and (ec is PM) then (kp is PM)(ki is N

10、M)(kd isPS)(1)28.If (e is ZO) and (ec is PB) then (kp is PM)(ki is NM)(kd isZO)(1)29.If (e is PS) and (ec is NB) then (kp is NS)(ki is PM)(kd isZO)(1)30.If (e is PS) and (ec is NM) then (kp is NS)(ki is PS)(kd isZO)(1)31.If (e is PS) and (ec is NS) then (kp is ZO)(ki is ZO)(kd isZO)(1)32.If (e is PS

11、) and (ec is ZO) then (kp is PS)(ki is NS)(kd isZO)(1)33.If (e is PS) and (ec is PS) then (kp is PS)(ki is NS)(kd isZO)(1)34.If (e is PS) and (ec is PM) then (kp is PM)(ki is NM)(kd isZO)(1)35.If (e is PS) and (ec is PB) then (kp is PM)(ki is NB)(kd isZO)(1)36.If (e is PM) and (ec is NB) then (kp is

12、 NS)(ki is ZO)(kd isNB)(1)37.If (e is PM) and (ec is NM) then (kp is ZO)(ki is ZO)(kd isPS)(1)38.If (e is PM) and (ec is NS) then (kp is PS)(ki is NS)(kd is NS)(1)39.If (e is PM) and (ec is ZO) then (kp is PM)(ki is NS)(kd isNS)(1)40.If (e is PM) and (ec is PS) then (kp is PM)(ki is NM)(kd isNS)(1)4

13、1.If (e is PM) and (ec is PM) then (kp is PM)(ki is NB)(kd isNS)(1)42.If (e is PM) and (ec is PB) then (kp is PB)(ki is NB)(kd isNB)(1)43.If (e is PB) and (ec is NB) then (kp is ZO)(ki is ZO)(kd isNB)(1)44.If (e is PB) and (ec is NM) then (kp is ZO)(ki is ZO)(kd isNM)(1)45.If (e is PB) and (ec is NS

14、) then (kp is PM)(ki is NS)(kd isNM)(1)46.If (e is PB) and (ec is ZO) then (kp is PM)(ki is NM)(kd isNM)(1)47.If (e is PB) and (ec is PS) then (kp is PM)(ki is NM)(kd isNS)(1)48.If (e is PB) and (ec is PM) then (kp is PB)(ki is NB)(kd isNS)(1)49.If (e is PB) and (ec is PB) then (kp is PB)(ki is NB)(

15、kd isNB)(1)把这 49 条控制逻辑规则，键入到模糊规则库中，如图4。图 4 模糊规则库(5)模糊 PID 控制器仿真利用 MATLAB件中的 Simulink 仿真环境，可以对模糊 PID 控制器系统进行 模拟仿真实验， 来检验设计是否达到要求。 针对本次控制器设计， 我们设置被控对象为，根据被控对象，设置相应的 PID 参数(s 1)( s 2)( s 3)( s 4)为：KP=6;K|=3;KD=2。图 5 为控制器系统在 Simulink 中的仿真模型。为了方便与传统 PID 控制器进行比较， 在 Simulink 仿真环境中作出传统 PID 控制以便于对模糊 PID 进行比较

16、。在传统 PID 控制器中设置相应的 PID 参数为：KP=6;KI=3;心=2。图 6 是传统 PID 与模糊 PID 控制器在 Simulink 中的阶跃仿 真波形比较。图 5 传统 PID 与模糊 PID 控制器在 Simulink 中的仿真模型图 6 传统 PID 与模糊 PID 控制器在 Simulink 中的阶跃仿真波形比较图 6 中，黄色线为输入的阶跃信号，紫色为输出的传统 PID 控制信号，青色 为输出的模糊 PID 控制信号，通过图 1-7 中传统 PID 控制方式与模糊 PID 控制控 制曲线的对比结果可以看出，模糊控制的控制性能要明显好于传统的 PID 控制效 果。我们把输入信号变为正弦信号再一次进行传统 PID 与模糊 PI