1、模糊 PID 控制器的設計與仿真設計模糊 PID 控制器時，首先要將精確量轉換為模糊量，并且要把轉換后的 模糊量映射到模糊控制論域當中， 這個過程就是精確量模糊化的過程。 模糊化的 主要功能就是將輸入量精確值轉換成為一個模糊變量的值， 最終形成一個模糊集 合。本次設計系統的精確量包括以下變量：變化量 e ，變化量的變化速率 ec 還 有參數整定過程中的輸出量 KP， KD， KI ，在設計模糊 PID 的過程中，需要 將這些精確量轉換成為模糊論域上的模糊值。 本系統的誤差與誤差變化率的模糊 論域與基本論域為： E=-6,-4,-2,0,2,4,6;Ec=-6,-4,-2,0,2,4,6 。模糊

2、 PID 控制器的設計選用二維模糊控制器。 以給定值的偏差 e 和偏差 變化 ec 為輸入； KP， KD，KI 為輸出的自適應模糊 PID 控制器， 見圖 1。圖 1 模糊 PID 控制器（1）模糊變量選取輸入變量 E和EC的模糊化將一定范圍 （基本論域 ）的輸入變量映射到離散區 間（論域） 需要先驗知識來確定輸入變量的范圍。 就本系統而言， 設置語言變量取 七個，分別為 NB，NM，NS，ZO，PS，PM， PB。（2） 語言變量及隸屬函數 根據控制要求，對各個輸入，輸出變量作如下劃定： e，ec 論域：-6 ，-5，-4 ，-3 ，-2，-1，0，1，2，3，4，5，6 KP， KD，

3、KI 論域：-6 ，-5 ， -4 ， -3 ，-2 ，-1 ，0，1，2，3，4，5，6 應用模糊合成推理 PID 參數的整定算法。第 k 個采樣時間的整定為KP(k) KP0KP(k) , K I(k) KI0 KI(k) , KD(k) KD0 KD(k).式中 KP0,KI0,KD0為經典 PID 控制器的初始參數設置輸入變量隸屬度函數如圖 2 所示，輸出變量隸屬度函數如圖 3 所示圖2 輸入變量隸屬度函圖3 輸出變量隸屬度函3）編輯模糊規則庫根據以上各輸出參數的模糊規則表，可以歸納出 49 條控制邏輯規則，具體 的控制規則如下所示：1. If (e is NB) and (ec is

4、 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

5、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

6、 (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

7、) 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

8、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

9、 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) t

10、hen (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)

11、(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

12、 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)

13、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 i

14、s 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) 4

15、9.If (e is PB) and (ec is PB) then (kp is PB)(ki is NB)(kd is NB)(1)把這 49 條控制邏輯規則，鍵入到模糊規則庫中，如圖4圖 4 模糊規則庫5）模糊 PID 控制器仿真利用 MATLAB軟件中的 Simulink 仿真環境，可以對模糊 PID 控制器系統進行 模擬仿真實驗， 來檢驗設計是否達到要求。 針對本次控制器設計， 我們設置被控 對象為 10 ，根據被控對象，設置相應的 PID 參數 （s 1）（s 2）（ s 3）（s 4）為： KP =6; KI =3; KD =2。圖 5 為控制器系統在 Simulink 中的仿真

16、模型。為了方便與傳統 PID控制器進行比較，在 Simulink 仿真環境中作出傳統 PID 控制以便于對模糊 PID進行比較。在傳統 PID 控制器中設置相應的 PID參數為：KP =6; K I =3; KD =2。圖6是傳統PID與模糊 PID控制器在 Simulink 中的階躍仿 真波形比較。圖 5 傳統 PID 與模糊 PID 控制器在 Simulink 中的仿真模型圖 6 傳統 PID 與模糊 PID 控制器在 Simulink 中的階躍仿真波形比較圖 6 中，黃色線為輸入的階躍信號，紫色為輸出的傳統 PID 控制信號，青色 為輸出的模糊 PID 控制信號，通過圖 1-7 中傳統 PID控制方式與模糊 PID 控制控 制曲線的對比結果可以看出， 模糊控制的控制性能要明顯好于傳統的 PID 控制效 果。我們把輸入信號變為正弦信號再一次進行傳統 PID與模糊