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[fuzzy neural network] simulation of fuzzy neural network based on MATLAB

2022-06-28 02:43:00 【FPGA and MATLAB】

1. Software version

matlab2013b

2. System Overview

· The first model ：

;

· The second model

;,U=13.012

First of all ： Design of membership function

Design of membership function , You can use the blur editor , It can also be designed through the above code .

second ： Design of fuzzy rules

Design by inputting fuzzy rule quantification table , The resulting fuzzy rules are as follows ：

1. If (e is NB) and (ec is NB) then (u is PB) (1)

2. If (e is NB) and (ec is NM) then (u is PB) (1)

3. If (e is NB) and (ec is NS) then (u is PM) (1)

4. If (e is NB) and (ec is Z) then (u is PM) (1)

5. If (e is NB) and (ec is PS) then (u is PS) (1)

6. If (e is NB) and (ec is PM) then (u is PS) (1)

7. If (e is NB) and (ec is PB) then (u is Z) (1)

8. If (e is NM) and (ec is NB) then (u is PB) (1)

9. If (e is NM) and (ec is NM) then (u is PM) (1)

10. If (e is NM) and (ec is NS) then (u is PM) (1)

11. If (e is NM) and (ec is Z) then (u is PS) (1)

12. If (e is NM) and (ec is PS) then (u is PS) (1)

13. If (e is NM) and (ec is PM) then (u is Z) (1)

14. If (e is NM) and (ec is PB) then (u is NS) (1)

15. If (e is NS) and (ec is NB) then (u is PM) (1)

16. If (e is NS) and (ec is NM) then (u is PM) (1)

17. If (e is NS) and (ec is NS) then (u is PS) (1)

18. If (e is NS) and (ec is Z) then (u is PS) (1)

19. If (e is NS) and (ec is PS) then (u is Z) (1)

20. If (e is NS) and (ec is PM) then (u is NS) (1)

21. If (e is NS) and (ec is PB) then (u is NS) (1)

22. If (e is Z) and (ec is NB) then (u is PM) (1)

23. If (e is Z) and (ec is NM) then (u is PS) (1)

24. If (e is Z) and (ec is NS) then (u is PS) (1)

25. If (e is Z) and (ec is Z) then (u is Z) (1)

26. If (e is Z) and (ec is PS) then (u is NS) (1)

27. If (e is Z) and (ec is PM) then (u is NS) (1)

28. If (e is Z) and (ec is PB) then (u is NM) (1)

29. If (e is PS) and (ec is NB) then (u is PS) (1)

30. If (e is PS) and (ec is NM) then (u is PS) (1)

31. If (e is PS) and (ec is NS) then (u is Z) (1)

32. If (e is PS) and (ec is Z) then (u is NS) (1)

33. If (e is PS) and (ec is PS) then (u is NS) (1)

34. If (e is PS) and (ec is PM) then (u is NM) (1)

35. If (e is PS) and (ec is PB) then (u is NM) (1)

36. If (e is PM) and (ec is NB) then (u is PS) (1)

37. If (e is PM) and (ec is NM) then (u is PS) (1)

38. If (e is PM) and (ec is NS) then (u is Z) (1)

39. If (e is PM) and (ec is Z) then (u is NS) (1)

40. If (e is PM) and (ec is PS) then (u is NM) (1)

41. If (e is PM) and (ec is PM) then (u is NM) (1)

42. If (e is PM) and (ec is PB) then (u is NB) (1)

43. If (e is PB) and (ec is NB) then (u is Z) (1)

44. If (e is PB) and (ec is NM) then (u is NS) (1)

45. If (e is PB) and (ec is NS) then (u is NS) (1)

46. If (e is PB) and (ec is Z) then (u is NM) (1)

47. If (e is PB) and (ec is PS) then (u is NM) (1)

48. If (e is PB) and (ec is PM) then (u is NB) (1)

49. If (e is PB) and (ec is PB) then (u is NB) (1)

Third ： Design of control loop

Usually , The closed-loop structure of a traditional fuzzy controller is as follows ：

The basic structure of fuzzy controller ：

3. Part of the source code

addpath 'func\'

title_function

% initialization 
fnn_parameter;

% The object of the charge 
a1        = 1.2;
b1        = 1;
b2        = 0.8;
b3        = 0;

ta        = 40;
sys       = tf(a1,[b1,b2,b3]);
dsys      = c2d(sys,0.1,'z');
[num,den] = tfdata(dsys,'v');
ts        = 0.1;% Sampling time T=0.1

% Closed loop controller 
for k=1:SIM_times
    k
    time(k) = k*ts;
    % Define the input signal 
    yd(k)   = 2;  
    % Define output signal 
    if k < ta
       yn = 0; 
    else
       yn = -den(2)*y1 - den(3)*y2 + num(2)*u1 + num(3)*u2;
    end    
    
    y2   = y1;
    y1   = yn;
    y(k) = yn;
    u2   = u1;
    e2   = e1;
    e1   = yd(k)-yn;
    e(k) = e1;
    ec   =(e1-e2);
    
    x1   =(1-exp(-10*e1))/(1+exp(-10*e1));
    x2   =(1-exp(-ec))/(1+exp(-ec));
    
    % The first 1 Layer output 
    for i=1:7
        o11(i) = x1;
        o12(i) = x2;
    end
    o1=[o11;o12];
    
    % The first 2 Layer output 
    for i=1:2
        for j=1:7
            z1(i,j)  =-((o1(i,j)-a(i,j))^2)/(b(i,j));
            o2(i,j)  =  exp(z1(i,j));
        end
    end
    
    % The first 3 Layer output 
    for j=1:7
        for l=1:7
            o3((j-1)*7+l)=o2(1,j)*o2(2,l);
        end
    end
    
    % The first 4 Layer output 
    I=0;
    for i=1:49
        I = I + o3(i)*Weight(i)/4;
    end

    o4   = I/(sum(o3));
    u(k) = o4;
    u1   = o4;
    % Gradient descent method to adjust the weight 
    for i=1:49
        dwp       =  e1*du*o3(i)/(sum(o3));
        % iteration 
        Weight(i) =  Weight(i) + eta*dwp;
    end

    % Center value update 
    da11=zeros(1,7);
    for j=1:7
        for l=1:7
            da11(j) =  da11(j)+(o2(2,l)*((Weight((j-1)*7+l)*sum(o3))-I));
        end
        da12(1,j)   = -e1*du*(2*(o1(1,j)-a(1,j))*(o2(1,j)))/((b(1,j)^2)*(sum(o3))^2);
        da1(j)      = (da12(1,j))*(da11(j));
    end
    da21 = zeros(1,7);
    for j=1:7
        for l=1:7
            da21(j) = da21(j)+(o2(1,l)*((Weight((l-1)*7+j)*sum(o3))-I));
        end
        da22(2,j) = -e1*du*(2*(o1(2,j)-a(2,j))*(o2(2,j))/((b(2,j)^2)*(sum(o3))^2));
        da2(j)    = (da22(2,j))*(da21(j));
    end      
    da=[da1;da2];
    for i=1:2
        for j=1:7
            a(i,j)=a(i,j)-eta*da(i,j);
        end
    end             
    a_s(:,:,k) = a;
    
    if k == 1
       a_(:,:,k) = a_s(:,:,1);
    else
       for i = 1:2
           for j = 1:7
               dist_tmp(i,j) = (a_s(i,j,k) - a_(i,j))^2;
           end
       end
       dist = sqrt(sum(sum(dist_tmp))); 
       
       if dist < 0.1
           
          tmps(:,:,1) = a_(:,:,k-1);
          tmps(:,:,2) = a_s(:,:,k);
           
          a_(:,:,k) = mean(tmps(:,:,1:2),3);
       else
          a_(:,:,k) = a_(:,:,k-1);
       end
    end
    
    a = a_(:,:,k);
    
    
    % Width update 
    db11=zeros(1,7);
    for j=1:7
        for l=1:7
            db11(j)=db11(j)+(o2(2,l)*((Weight((j-1)*7+l)*sum(o3))-I));
        end
        db12(1,j)=-e1*du*(2*(o1(1,j)-a(1,j))^2)*(o2(1,j))/((b(1,j)^3)*(sum(o3))^2);
        db1(j)=(db12(1,j))*(db11(j));
    end
    db21=zeros(1,7);
    for j=1:7
        for l=1:7
            db21(j)=db21(j)+(o2(1,l)*((Weight((l-1)*7+j)*sum(o3))-I));
        end
        db22(2,j)=-e1*du*(2*(o1(2,j)-a(2,j))^2)*(o2(2,j))/((b(2,j)^3)*(sum(o3))^2);
        db2(j)=(db22(2,j))*(db21(j));
    end      
    db=[db1;db2];
    for i=1:2
        for j=1:7
            b(i,j)=b(i,j)-eta*db(i,j);
        end
    end      
    b_s(:,:,k) = b;
    
    if k == 1
       b_(:,:,k) = b_s(:,:,1);
    else
       for i = 1:2
           for j = 1:7
               dist_tmp(i,j) = (b_s(i,j,k) - b_(i,j))^2;
           end
       end
       dist = sqrt(sum(sum(dist_tmp))); 
       
       if dist < 0.1
          tmps(:,:,1) = b_(:,:,k-1);
          tmps(:,:,2) = b_s(:,:,k);
           
          b_(:,:,k) = mean(tmps(:,:,1:2),3);
       else
          b_(:,:,k) = b_(:,:,k-1);
       end
    end    
    
    
    b = b_(:,:,k);
    
    % Algorithm 
    s11 = y1;
    s12 = y2;
    s13 = u1;
    s14 = u2;
    s1  =[s11;s12;s13;s14];
    
    for i=1:5
        net2(i) = w2(i,:)*s1 + theta2(i);
        s2(i)   = (1-exp(-net2(i)))/(1+exp(-net2(i)));
    end
    
    net3  = w3*s2+theta3;
    yg    = am*(1-exp(-net3))/(1+exp(-net3));

    for i=1:5
        delta2(i)=0.5*(1-s2(i))*(1+s2(i));
    end
    
    delta3=0.5*am*(1-yg/am)*(1+yg/am);
    
    for i=1:5
        theta22(i) = theta2(i)-theta21(i);
        theta21(i) = theta2(i);
        theta2(i)  = theta2(i)+eta1*(yn-yg)*delta3*w3(i)*delta2(i)+beta1*theta22(i);
    end
    
    theta32 = theta3-theta31;
    theta31 = theta3;
    theta3  = theta3+eta1*(yn-yg)*delta3+beta1*theta32;
    
    for i=1:5
        for j=1:4
            w22(i,j) = w2(i,j)-w21(i,j);
            w21(i,j) = w2(i,j);
            w2(i,j)  = w2(i,j)-eta1*(yn-yg)*delta3*w3(i)*delta2(i)*s1(j)+beta1*w22(i,j);
        end
        w32(i) = w3(i)-w31(i);
        w31(i) = w3(i);
        w3(i)  = w3(i)-eta1*(yn-yg)*delta3*s2(i)+beta1*w32(i);
    end
    a2   = am-a1;
    a1   = am;
    am   = am+eta1*(yn-yg)*yg/am+beta1*a2;
    sum1 = 0;
    for i=1:5
        sum1 = sum1 + w3(i)*delta2(i)*w2(i,3);
    end
    du = delta3*sum1;
    
end            

figure;
plot(time,y,'r', time,yd,'b');
grid on

figure;
subplot(121);
plot(a_s(1,:,SIM_times),a_s(2,:,SIM_times),'o'); 
grid on
axis square
subplot(122);
plot(b_s(1,:,SIM_times),b_s(2,:,SIM_times),'o'); 
grid on
axis square

save Simu_Results\fnn_result.mat time y

save Simu_Results\nfis.mat a b

This paper mainly introduces the design of fuzzy neural network controller ,

First of all ： The structure design of four layered neural network layer ：

The first 1 layer ：