自适应模糊PID控制器的设计与仿真 - 图文(6)

图4-7 ?ki的隶属函数

图4-8 ?kd的隶属函数

4.7 建立模糊规则表

根据人的直觉思维推理，由系统输出的误差和误差的变化趋势来设计消除系统误差的模糊控制规则。模糊控制规则语句构成了描述众多被控过程的模糊模型。例如，卫星的姿态与作用关系、飞机或舰船航向与舵偏角的关系、工业锅炉中的压力与加热的关系等，都可以用模糊规则来描述。在条件语句中，误差、误差变化率及控制量对于不同的被控对象有着不同的意义。模糊控制的核心是模糊推理，它利用某种模糊推理算法和模糊规则进行推理，得出最终的控制量。本文总结工程设计人员的技术知识和实际操作经验，建立合适的模糊规则表。根据以上所述的PID参数调整原则，一种针对kp、ki、kd3个参数分别整定的模糊控制表如表4-1、表4-2和表4-3所示

[3][9]

。

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表4-1 ?kp的模糊控制规则表

?kp e NB NM NS ZO PS PM PB ec NB PB PB PM PM PS PS ZO NM PB PB PM PM PS ZO ZO NS PM PM PM PS ZO NS NM ZO PM PS PS ZO NS NM NM PS PS PS ZO NS NS NM NM PM ZO ZO NS NM NM NM NB PB ZO NS NS NM NM NB NB

表4-2 ?ki的模糊控制规则表

?ki e NB NM NS ZO PS PM PB ec NB NB NB NB NM NM ZO ZO NM NB NB NM NM NS ZO ZO NS NM NM NS NS ZO PS PS ZO NM NS NS ZO PS PS PM PS NS NS ZO PS PS PM PM PM ZO ZO PS PM PM PB PB PB ZO ZO PS PM PB PB PB

表4-3 ?kd的模糊控制规则表

?kd e NB NM NS ZO PS PM PB ec NB PS PS ZO ZO ZO PB PB NM NS NS NS NS ZO NS PM NS NB NB NM NS ZO PS PM ZO NB NM NM NS ZO PS PM PS NB NM NS NS ZO PS PS PM NM NS NS NS ZO PS PS PB PS ZO ZO ZO ZO PB PB

合并三表可以得出下面49条模糊控制规则：

1. If (e is NB) and (ec is NB) then (kp is PB)(ki is NB)(kd is PS)(1) 2. If (e is NB) and (ec is NM) then (kp is PB)(ki is NB)(kd is NS)(1) 3. If (e is NB) and (ec is NS) then (kp is PM)(ki is NM)(kd is NB)(1) 4. If (e is NB) and (ec is Z) then (kp is PM)(ki is NM)(kd is NB)(1) 5. If (e is NB) and (ec is PS) then (kp is PS)(ki is NS)(kd is NB)(1)

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6. If (e is NB) and (ec is PM) then (kp is Z)(ki is Z)(kd is NM)(1) 7. If (e is NB) and (ec is PB) then (kp is Z)(ki is Z)(kd is PS)(1) 8. If (e is NM) and (ec is NB) then (kp is PB)(ki is NB)(kd is PS)(1) 9. If (e is NM) and (ec is NM) then (kp is PB)(ki is NB)(kd is NS)(1) 10. If (e is NM) and (ec is NS) then (kp is PM)(ki is NM)(kd is NB)(1) 11. If (e is NM) and (ec is Z) then (kp is PS)(ki is NS)(kd is NM)(1) 12. If (e is NM) and (ec is PS) then (kp is PS)(ki is NS)(kd is NM)(1) 13. If (e is NM) and (ec is PM) then (kp is Z)(ki is Z)(kd is NS)(1) 14. If (e is NM) and (ec is PB) then (kp is NS)(ki is Z)(kd is Z)(1) 15. If (e is NS) and (ec is NB) then (kp is PM)(ki is NB)(kd is Z)(1) 16. If (e is NS) and (ec is NM) then (kp is PM)(ki is NM)(kd is NS)(1) 17. If (e is NS) and (ec is NS) then (kp is PM)(ki is NS)(kd is NM)(1) 18. If (e is NS) and (ec is Z) then (kp is PS)(ki is NS)(kd is NM)(1) 19. If (e is NS) and (ec is PS) then (kp is Z)(ki is Z)(kd is NS)(1) 20. If (e is NS) and (ec is PM) then (kp is NS)(ki is PS)(kd is NS)(1) 21. If (e is NS) and (ec is PB) then (kp is NS)(ki is PS)(kd is Z)(1) 22. If (e is Z) and (ec is NB) then (kp is PM)(ki is NM)(kd is Z)(1) 23. If (e is Z) and (ec is NM) then (kp is PM)(ki is NM)(kd is NS)(1) 24. If (e is Z) and (ec is NS) then (kp is PS)(ki is NS)(kd is NS)(1) 25. If (e is Z) and (ec is Z) then (kp is Z)(ki is Z)(kd is Z)(1) 26. If (e is Z) and (ec is PS) then (kp is NS)(ki is PS)(kd is NS)(1) 27. If (e is Z) and (ec is PM) then (kp is NM)(ki is PM)(kd is NS)(1) 28. If (e is Z) and (ec is PB) then (kp is NM)(ki is PM)(kd is Z)(1) 29. If (e is PS) and (ec is NB) then (kp is PS)(ki is NM)(kd is Z)(1) 30. If (e is PS) and (ec is NM) then (kp is PS)(ki is NS)(kd is Z)(1) 31. If (e is PS) and (ec is NS) then (kp is Z)(ki is Z)(kd is Z)(1) 32. If (e is PS) and (ec is Z) then (kp is NS)(ki is PS)(kd is Z)(1) 33. If (e is PS) and (ec is PS) then (kp is NS)(ki is PS)(kd is Z)(1) 34. If (e is PS) and (ec is PM) then (kp is NM)(ki is PM)(kd is Z)(1) 35. If (e is PS) and (ec is PB) then (kp is NM)(ki is PB)(kd is Z)(1) 36. If (e is PM) and (ec is NB) then (kp is PS)(ki is Z)(kd is PB)(1) 37. If (e is PM) and (ec is NM) then (kp is Z)(ki is Z)(kd is PS)(1) 38. If (e is PM) and (ec is NS) then (kp is NS)(ki is PS)(kd is PS)(1) 39. If (e is PM) and (ec is Z) then (kp is NM)(ki is PS)(kd is PS)(1) 40. If (e is PM) and (ec is PS) then (kp is NM)(ki is PM)(kd is PS)(1) 41. If (e is PM) and (ec is PM) then (kp is NM)(ki is PB)(kd is PS)(1) 42. If (e is PM) and (ec is PB) then (kp is NB)(ki is PB)(kd is PB)(1)

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43. If (e is PB) and (ec is NB) then (kp is Z)(ki is Z)(kd is Z)(1) 44. If (e is PB) and (ec is NM) then (kp is Z)(ki is Z)(kd is PM)(1) 45. If (e is PB) and (ec is NS) then (kp is NM)(ki is PS)(kd is PM)(1) 46. If (e is PB) and (ec is Z) then (kp is NM)(ki is PM)(kd is PM)(1) 47. If (e is PB) and (ec is PS) then (kp is NM)(ki is PM)(kd is PS)(1) 48. If (e is PB) and (ec is PM) then (kp is NB)(ki is PB)(kd is PS)(1) 49. If (e is PB) and (ec is PB) then (kp is NB)(ki is PB)(kd is PB)(1)

在MATLAB命令窗口运行Fuzzy函数进入模糊逻辑编辑器，并建立一个新的FIS文件，选择控制器类型Mamdani型，根据上面的分析分别输入e、ec、?kp、?ki、?kd的隶属函数和量化区间，可得隶属函数图形如图4-9所示。打开Ruler Editor窗口，以If?then的形式输入模糊控制规则，与方式(And method)为min；或方式(0r method)为max；推理(Implication)为min；合成(Aggregation)为max；去模糊(Defuzzification)为最大隶属度平均法(mom)

[10][12][13]

。这样就建立了一个FIS文件，取名为fuzzpid.fis。

在MATLAB的M文件编辑器里建立一个名为fuzzypid.m的文件，其内容见附录；这样就完成了模糊工具箱与SIMULINK的链接，为整个系统的建立打下基础。

图4-9 模糊系统fuzzy.fis的结构

在在线运行的过程当中，控制系统通过对模糊逻辑规则的结果处理、查表以及运算，完成对PID参数的在线自校正，从而保持系统的灵活性、整定性、控制精度更好。而其工作的流程图如图4-10所示。

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