1、切換式模糊控制器一.前言 本篇文章提出一種具有切換能力的模糊控制器架構,藉由不同的切換區域,使模糊控制器能在不同的目標區域中,切換到適當的輸入輸出比例因數(Scaling factors),使系統達到滿意的響應,即小的超越量(overshoot),小的穩態誤差(steady state error ),與快速的上升時間(rise time).二.切換式模糊控制器的架構圖1.切換式模糊控制器(1)參數說明:k:取樣間隙s:設定點,追蹤目標值e(k):誤差量ce(k):誤差變化量cce(k):誤差變化量的變化量u(k):控制輸入訊號cu(k):增加的控制輸入訊號:比例因數u(k)=u(k-1)+c

2、u(k)Plant:(2)模糊控制器模糊化界面: 圖2.(a) 為e,ce,cce前提部之歸屬函數.模糊控制規則:(圖2.Table 1) IF e is Ei and ce is CEi and cce is CCEi THEN cu is Cui解模糊化界面: vi為結論部之值如圖2.(b) 為圖2.(2)切換器設計: 由受控程序輸出y(k)與設定目標s的距離大小設定了五個切換區域如下:(1) y(k)<0.2s (大加速區)(2) 0.2s<y(k)<0.5s (小加速區)(3) 0.5s<y(k)<0.7s (大減速區)(4) 0.7s<y(k)&l

3、t;0.9s (小減速區)(5) 0.9s<y(k) (穩定區)並由Table 2,Table 3.得到控制器的輸入Ke,Kce,Kcce與輸出Kcu ,4個比例參數.三.模擬結果圖3.依照本篇提供的所有參數表所得結果圖4.將Table 3.的設定值s換成誤差e所得結果 觀察圖3.與圖4.的結果有些不同,因為由Table 3.可知在s=0時,Ku=0,cu(k)=0,不能反映真正的誤差,輸出所要求的值到Plant的輸入,所以將Table 3.設定值s換成誤差e ,可得與本篇較相同的模擬結果.圖2.模擬結果之t,u,y,e數據如下所示tuye0002010.8891726.71E-0519

4、.99993217.090068.60843111.39157319.8409818.485751.514254420.0009420.29544-0.29544519.7707520.40507-0.40507619.6047120.21366-0.21366719.5305920.08165-0.08165819.5055920.02365-0.02365919.4994620.00432-0.004321019.4988219.999670.0003341119.4991919.999230.0007691219.4995219.999560.0004411319.4997119.999

5、790.000211419.4997619.999972.67E-051519.4997619.999972.67E-051619.4997619.999972.67E-051719.4997619.999972.67E-051819.4997619.999972.67E-051919.4997619.999972.67E-052019.4997619.999972.67E-052119.0274419.99994-19.9999228.77845115.51663-15.5166233.0017676.833609-6.83361240.7548322.327366-2.32737250.0

6、872590.573206-0.5732126-0.042020.060828-0.0608327-0.02964-0.034670.034665280.001973-0.016120.016117290.0060520.004046-0.00405300.0031690.004826-0.00483310.001210.002501-0.0025320.0003490.000941-0.00094336.34E-050.000268-0.0002734-5.08E-064.69E-05-4.69E-0535-1.10E-05-4.98E-064.98E-0636-1.81E-06-7.15E

7、-067.15E-06371.68E-06-1.55E-071.55E-07381.09E-061.39E-06-1.39E-06394.63E-078.61E-07-8.61E-07401.50E-073.62E-07-3.62E-07411.7783430.00013439.999874234.1801217.2168622.783144339.6819536.97153.0285034440.0018740.59089-0.590894539.5371140.80677-0.806774639.2071540.42382-0.423824739.0603340.16153-0.16153

8、4839.0109540.04665-0.046654938.9988840.00845-0.008455038.9976539.99930.000698穩態誤差小於1E-45138.9983939.998470.001534穩態誤差小於1E-45238.9990539.999130.0008745338.9994339.999580.0004165438.9995239.999955.34E-055538.9995239.999955.34E-055638.9995239.999955.34E-055738.9995239.999955.34E-055838.9995239.999955.3

9、4E-055938.9995239.999955.34E-056038.9995239.999955.34E-056138.0548739.99988-39.99996217.556931.03326-31.0333636.00353413.66722-13.6672641.5096644.654731-4.65473650.1745191.146412-1.1464166-0.084040.121655-0.1216667-0.05928-0.069330.06933680.003947-0.032230.032234690.0121030.008093-0.00809700.0063390

10、.009651-0.00965四.結論 本篇的切換式模糊控制器在誤差很大時,能有較大的輸出,且在誤差很小時,也能反應較小輸出到Plant,而達到更佳的性能.本篇文章提到未來研究方向,是如何找到最佳的參數使控制器有更好的效果.主要程式列表:/-/定義歸屬函數圖形/enum Shape Triangle,ShoulderR,ShoulderL,Singleton,Gaussian,NoShape;/* | (p1,1) |/ Triangle: +- 中心值p1, 展幅:p1-begin,end-p1, begin<p1<end begin end |_(p1,1) ShoulderR

11、:| begin=-00(d)< 轉折點 p1 <end +- end |(p1,1)_ ShoulderL:| / begin< 轉折點 p1< end=00(d) +-/- begin (p1,1) | . | | Singleton: +-+- begin=end=0 , p1 單點 (p1,1) | . | | | 展幅約 2倍 sigma /if sigma=1 then (2,0.018315)(3,0.000123409) Gaussian: +-/-+- begin=sigma, p1 中心值 */class FuzzySet protected: Sh

12、ape MbsFun;/歸屬函數形狀Membership public: float Begin,P1,End; AnsiString LgV; /Linguistic Variables 語言變數 void IniSet(AnsiString lgv,Shape Mbsfun,float begin,float p1,float end);/設定歸屬函數的語言.形狀.開始點.p1.結束點 float Fuzzifier(float Input);/計算輸入值之歸屬度輸出至MbsValue float MbsValue;/歸屬值;void FuzzySet:IniSet(AnsiString

13、lgv,Shape Mbsfun,float begin,float p1,float end) LgV=lgv; MbsFun=Mbsfun; Begin=begin; P1=p1; End=end;float FuzzySet:Fuzzifier(float Input) switch(MbsFun) case Triangle: if( (Begin>Input)|(Input>End) ) MbsValue=0;break; if( (Begin<=Input)&&(Input<=P1) ) if (Begin=P1) MbsValue=1; e

14、lse MbsValue=(Input-Begin)/(P1-Begin);break; if( (P1<Input)&&(Input<=End) ) if (End=P1) MbsValue=1; else MbsValue=(Input-End)/(P1-End);break; break; case ShoulderR: if(Input<P1) MbsValue=1;break; if( (P1<Input)&&(Input<=End) ) MbsValue=(Input-End)/(P1-End);break; if(En

15、d<Input)MbsValue=0;break; break; case ShoulderL: if(P1<Input) MbsValue=1;break; if( (Begin<Input)&&(Input<P1) ) MbsValue=(Input-Begin)/(P1-Begin);break; if(Input<Begin)MbsValue=0;break; break; case Singleton: if( (P1-TOLERANCE)<=Input)&&(Input<=(P1+TOLERANCE) ) M

16、bsValue=1;else MbsValue=0; break; case Gaussian: MbsValue=exp(-1*(Input-P1)*(Input-P1)/(Begin*Begin); break; return(MbsValue);class FuzzyController /容納一組Fuzzy Set 的控制器 protected: FuzzySet *Fuzzy1; FuzzySet *Fuzzy2; FuzzySet *Fuzzy3; float *U13; float *U23; float *U33; float RuleValue333; float MbsSu

17、m; float Output; public: void IniSet(FuzzySet *fuzzy1,FuzzySet *fuzzy2,FuzzySet *fuzzy3,float (*u1)3,float (*u2)3,float (*u3)3); float Compute(float Input1,float Input2,float Input3);void FuzzyController:IniSet(FuzzySet *fuzzy1,FuzzySet *fuzzy2,FuzzySet *fuzzy3,float (*u1)3,float (*u2)3,float (*u3)3

18、) Fuzzy1=fuzzy1; Fuzzy2=fuzzy2; Fuzzy3=fuzzy3; for(int i=0;i<3;i+) *(U1+i)=*(u1+i); for(int i=0;i<3;i+) *(U2+i)=*(u2+i); for(int i=0;i<3;i+) *(U3+i)=*(u3+i); for(int i=0;i<3;i+) for(int j=0;j<3;j+) RuleValue0ij=U1ji; for(int i=0;i<3;i+) for(int j=0;j<3;j+) RuleValue1ij=U2ji; for

19、(int i=0;i<3;i+) for(int j=0;j<3;j+) RuleValue2ij=U3ji;float FuzzyController:Compute(float Input1,float Input2,float Input3) float Mbs1,Mbs2,Mbs3,Mbs,ResultSum=0,Result; MbsSum=0; for(int i=0;i<3;i+) for(int j=0;j<3;j+) for(int k=0;k<3;k+) Mbs1=Fuzzy12-i.Fuzzifier(Input1); Mbs2=Fuzzy2

20、2-j.Fuzzifier(Input2); Mbs3=Fuzzy3k.Fuzzifier(Input3); /if (Mbs1>Mbs2) Mbs=Mbs2;else Mbs=Mbs1; /Mbs=(Mbs1+Mbs2)/2;/( 2-(Mbs1+Mbs2+Mbs1*Mbs2) ); Mbs=(Mbs1*Mbs2*Mbs3); Result=Mbs*RuleValueijk; ResultSum+=Result; MbsSum+=Mbs; Output=ResultSum/MbsSum; return(Output);/-float _fastcall TForm1:f_1(float

21、 t,float x1,float x2,float x3)return(x2);float _fastcall TForm1:f_2(float t,float x1,float x2,float x3) return(x3);float _fastcall TForm1:f_3(float t,float x1,float x2,float x3) return(-6.3383*x3-27.6256*x2-40.6229*x1);/void _fastcall TForm1:StartRun() AnsiString str4; GridToArray3(u1Grid,u1a); Grid

22、ToArray3(u2Grid,u2a); GridToArray3(u3Grid,u3a); Controller.IniSet(e,ce,cce,u1a,u2a,u3a); ResultSeries->Clear(); RSeries->Clear(); eSeries->Clear(); uSe->Clear(); float ek,cek,ccek; float ek_1,cek_1,y; float sek,scek,sccek,scuk,cuk,uk,uk_1; float eSum=0; uk=0;uk_1=0;ek_1=0;cek_1=0; y=0; c

23、ek=0; ccek=0; float t,dt,x1=0,x2=0,x3=0,h=0.01,u; float k43; float Int_t=0; ResultGrid->RowCount=2; dt=0.96; for(t=0;t<70;t+=h) u=uk; k00=f_1(t,x1,x2,x3); k01=f_2(t,x1,x2,x3); k02=f_3(t,x1,x2,x3)+41.665*u; k10=f_1(t+h/2,x1+h*k00/2,x2+h*k01/2,x3+h*k02/2); k11=f_2(t+h/2,x1+h*k00/2,x2+h*k01/2,x3+

24、h*k02/2); k12=f_3(t+h/2,x1+h*k00/2,x2+h*k01/2,x3+h*k02/2)+41.665*u; k20=f_1(t+h/2,x1+h*k10/2,x2+h*k11/2,x3+h*k12/2); k21=f_2(t+h/2,x1+h*k10/2,x2+h*k11/2,x3+h*k12/2); k22=f_3(t+h/2,x1+h*k10/2,x2+h*k11/2,x3+h*k12/2)+41.665*u; k30=f_1(t+h,x1+h*k20,x2+h*k21,x3+h*k22); k31=f_2(t+h,x1+h*k20,x2+h*k21,x3+h*

25、k22); k32=f_3(t+h,x1+h*k20,x2+h*k21,x3+h*k22)+41.665*u; x1=x1+(k00+2*k10+2*k20+k30)/6*h; x2=x2+(k01+2*k11+2*k21+k31)/6*h; x3=x3+(k02+2*k12+2*k22+k32)/6*h; y=x1; /y=Plant(uk); SwitchType(y,Ym(t-dt)-y); ek=Ym(t-dt)-y; cek=(ek-ek_1); ek_1=ek; ccek=(cek-cek_1); cek_1=cek; sek=ek/Ke; scek=cek/Kce; sccek=

26、ccek/Kcce; scuk=Controller.Compute(sek,scek,sccek); cuk=scuk*Kcu; uk=uk_1+cuk; uk_1=uk; ResultSeries->AddXY(t,y,"",clTeeColor); RSeries->AddXY(t,Ym(t),"",clTeeColor); if (t<dt) eSeries->AddXY(t,20,"",clTeeColor); else eSeries->AddXY(t,ek,"",clTe

27、eColor); if( (Int_t-0.01)<t)&&(t<(Int_t+0.01) ) ) str0=FloatToStr(Int_t); str1=FloatToStr(uk_1); str2=FloatToStr(y); str3=FloatToStr(ek); Result.LinesAdd(4,str); Int_t+; uSe->AddXY(t,uk_1,"",clTeeColor); / cuSe->AddXY(t,cuk,"",clTeeColor); / scukSe->AddXY(t,scuk,"&