模糊PID控制器的设计与仿真——设计步骤.doc

模糊PID控制器的设计与仿真
设计模糊PID控制器时，一方面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。模糊化的重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涉及以下变量：变化量e ，变化量的变化速率ec 尚有参数整定过程中的输出量ΔKP，ΔKD，ΔKI，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；ΔKP，ΔKD，ΔKI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)需要先验知识来拟定输入变量的范围。就本系统而言，设立语言变量取七个，分别为 NB，NM，NS，ZO，PS，PM，PB。
(2) 语言变量及从属函数
根据控制规定，对各个输入，输出变量作如下划定：
e，ec论域：｛-6，-5，-4，-3，-2，-1，0，1，2，3，4，5，6｝
ΔKP，ΔKD，ΔKI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

式中为经典PID控制器的初始参数。
设立输入变量从属度函数如图2所示，输出变量从属度函数如图3所示。

图2 输入变量从属度函
图3 输出变量从属度函
（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，具体的控制规则如下所示：
1. If (e is NB) and (ec is NB) then (kp is NB)(ki is PB)(kd is NS)(1)
2. If (e is NB) and (ec is NM) then (kp is NB)(ki is PB)(kd is PS)(1)
3. If (e is NB) and (ec is NS) then (kp is NM)(ki is PM)(kd is PB)(1)
4. If (e is NB) and (ec is ZO) then (kp is NM)(ki is PM)(kd is PB)(1)
5. If (e is NB) and (ec is PS) then (kp is NS)(ki is PS)(kd is PB)(1)
6. If (e is NB) and (ec is PM) then (kp is ZO)(ki is ZO)(kd is PM)(1)
7. If (e is NB) and (ec is PB) then (kp is ZO)(ki is ZO)(kd is NS)(1)
8. If (e is NM) and (ec is NB) then (kp is NB)(ki is PB)(kd is NS)(1)
9. If (e is NM) and (ec is NM) then (kp is NB)(ki is PB)(kd is PS)(1)
10. If (e is NM) and (ec is NS) then (kp is NM)(ki is PM)(kd is PB)(1)
11. If (e is NM) and (ec is ZO) then (kp is NS)(ki is PS)(kd is PM)(1)
12. If (e is NM) and (ec is PS) then (kp is NS)(ki is PS)(kd is PM)(1)
13. If (e is NM) and (ec is PM) then (kp is ZO)(ki is ZO)(kd is PS)(1)
14. If (e is NM) and (ec is PB) then (kp is PS)(ki is ZO)(kd is ZO)(1)
15. If (e is NS) and (ec is NB) then (kp is NM)(ki is PB)(kd is ZO)(1)
16. If (e is NS) and (ec is NM) then (kp is NM)(ki is PM)(kd is PS)(1)
17. If (e is NS) and (ec is NS) then (kp is NM)(ki is PS)(kd is PM)(1)
18. If (e is NS) and (ec is ZO) then (kp is NS)(ki is PS)(kd is PM)(1)
19. If (e is NS) and (ec is PS) then (kp is ZO)(ki is ZO)(kd is PS)(1)
20. If (e is NS) and (ec is PM) then (kp is PS)(ki is NS)(kd is PS)(1)
21. If (e is NS) and (ec is PB) then (kp is PS)(ki is NS)(kd is ZO)(1)
22. If (e is ZO) and (ec is NB) then (kp is NM)(ki is PM)(kd is ZO)(1)
23. If (e is ZO) and (ec is NM) then (kp is NM)(ki is PM)(kd is PS)(1)
24. If (e is ZO) and (ec is NS) then (kp is NS)(ki is PS)(kd is PS)(1)
25. If (e is ZO) and (ec is ZO) then (kp is ZO)(ki is ZO)(kd is PS)(1)
26. If (e is ZO) and (ec is PS) then (kp is PS)(ki is NS)(kd is PS)(1)
27. If (e is ZO) and (ec is PM) then (kp is PM)(ki is NM)(kd is PS)(1)
28. If (e is ZO) and (ec is PB) then (kp is PM)(ki is NM)(kd is ZO)(1)
29. If (e is PS) and (ec is NB) then (kp is NS)(ki is PM)(kd is ZO)(1)
30. If (e is PS) and (ec is NM) then (kp is NS)(ki is PS)(kd is ZO)(1)
31. If (e is PS) and (ec is NS) then (kp is ZO)(ki is ZO)(kd is ZO)(1)
32. If (e is PS) and (ec is ZO) then (kp is PS)(ki is NS)(kd is ZO)(1)
33. If (e is PS) and (ec is PS) then (kp is PS)(ki is NS)(kd is ZO)(1)
34. If (e is PS) and (ec is PM) then (kp is PM)(ki is NM)(kd is ZO)(1)
35. If (e is PS) and (ec is PB) then (kp is PM)(ki is NB)(kd is ZO)(1)
36. If (e is PM) and (ec is NB) then (kp is NS)(ki is ZO)(kd is NB)(1)
37. If (e is PM) and (ec is NM) then (kp is ZO)(ki is ZO)(kd is PS)(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 is NS)(1)
40. If (e is PM) and (ec is PS) then (kp is PM)(ki is NM)(kd is NS)(1)
41. If (e is PM) and (ec is PM) then (kp is PM)(ki is NB)(kd is NS)(1)
42. If (e is PM) and (ec is PB) then (kp is PB)(ki is NB)(kd is NB)(1)
43. If (e is PB) and (ec is NB) then (kp is ZO)(ki is ZO)(kd is NB)(1)
44. If (e is PB) and (ec is NM) then (kp is ZO)(ki is ZO)(kd is NM)(1)
45. If (e is PB) and (ec is NS) then (kp is PM)(ki is NS)(kd is NM)(1)
46. If (e is PB) and (ec is ZO) then (kp is PM)(ki is NM)(kd is NM)(1)
47. If (e is PB) and (ec is PS) then (kp is PM)(ki is NM)(kd is NS)(1)
48. If (e is PB) and (ec is PM) then (kp is PB)(ki is NB)(kd is NS)(1)
49. If (e is PB) and (ec is PB) then (kp is PB)(ki is NB)(kd is NB)(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
运用MATLAB软件中的Simulink仿真环境，可以对模糊PID控制器系统进行模拟仿真实验，来检查设计是否达成规定。针对本次控制器设计，我们设立被控对象为，根据被控对象，设立相应的PID参数为：=6;=3;=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。在传统PID控制器中设立相应的PID参数为：=6;=3;=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PID控制器的对比。把图5的输入阶跃信号改为输入正弦信号即可进行正弦信号的跟踪。图7是传统PID与模糊PID控制器在Simulink中的正弦仿真波形比较。

图7 传统PID与模糊PID控制器在Simulink中的正弦仿真波形比较
图7中，黄色线为输入的正弦信号，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，依旧是模糊控制的控制性能要明显好于传统的PID控制效果。