Using 3 dimensional array to 2d-plot????

I need to use this 3 arrays into 2 equations to 2d-plot

w=0:1:100;
mu4=0:0.01:1;       
lam4=0:0.01:1;

the equation is given below

code for the above equation is given below

            th1=cos(lam4*(pmr/2));
            th2=cos((1+lam4)*(pmr/2));
            th3=cos((lam4+mu4)*(pmr/2));
            th4=sin(mu4*(pmr/2));
            th5=sin(lam4*(pmr/2));

            ki=((-w^(3+lam4))+(42.46*(w^(1+lam4)))+(100*w^(mu4+lam4)*th4))/(250*th5)

            kp=(-1/(250*(w^lam4)*th1))*(((-w^(3+lam4))*th2)+((42.46*w^(1+lam4))*th2)...
            -(15.88*(w^(2+lam4))*th1)+(106.2*(w^lam4)*th1)+(100*(w^(lam4+mu4))*th3)...
            +250*ki)

all the three array need to used together into the equation and get plot as the graph given below

How can i use the 3 dimensional array to plot the graph above.. please help me or suggest me some hints.

Thank you.

Nitesh

Answer 1

[Star Strider]

At the very least you need to vectorise your equations to get vectors of ‘ki’ and ‘kp’:

ki=((-w.^(3+lam4))+(42.46*(w.^(1+lam4)))+(100*w.^(mu4+lam4).*th4))./(250*th5);

kp=(-1./(250*(w.^lam4).*th1)).*(((-w.^(3+lam4)).*th2)+((42.46*w.^(1+lam4)).*th2)...
    -(15.88*(w.^(2+lam4)).*th1)+(106.2*(w.^lam4).*th1)+(100*(w.^(lam4+mu4)).*th3)...
    +250*ki);

You did not provide ‘pmr’, and the values for your variables (and your equations) will not give you the full loop in the image. I leave that to you to sort out.

[Nitesh]

Hello

pmr = 180 which is the pi value.

This is my codes im working on.

clear all; close all; clf; clc

%Fractional Order PID
i=1;
j=1;
k=1;
pmr=180;  %Value of PI

i=1;
for w=0:1:100; % Omega Value Set Range

      j=1;
      for mu4=0:0.1:1; % Mu Value Set Range

          k=1;
          for lam4=0:0.1:1;  % Lambda Value Set Range

   % Short Hand calcalution for Theta values of cos and sin
              th1=cos(lam4*(pmr/2));
              th2=cos((1+lam4)*(pmr/2));
              th3=cos((lam4+mu4)*(pmr/2));
              th4=sin(mu4*(pmr/2));
              th5=sin(lam4*(pmr/2));

              ki(i,j,k)=((-w^(3+lam4))+(42.46*(w^(1+lam4)))+(100*w^(mu4+lam4)*th4))/(250*th5)

              kp(i,j,k)=(-1/(250*(w^lam4)*th1))*(((-w^(3+lam4))*th2)+((42.46*w^(1+lam4))*th2)...
              -(15.88*(w^(2+lam4))*th1)+(106.2*(w^lam4)*th1)+(100*(w^(lam4+mu4))*th3)...
              +250*ki)   

              i=i+1; % for next update

          end % End loop for Lambda

          j=j+1; % for next update

      end % End loop for mu

      k=k+1; % for next update

end % End loop for Omega

figure(1)
plot(ki,kp,'r', 'Linewidth',0.5)

Im using the above coding using 3 dimensional array for loop. However, im having a error which i cant resolve..

Assignment has more non-singleton rhs dimensions than non-singleton subscripts

Your help will be appreciated. Thank you.

Nitesh

[Star Strider]

The impression I get is that you are calculating ‘kp’ and ‘ki’ from your three vectors, then plotting them:

plot(ki, kp)

The plot you show is not a surface plot.

[Nitesh]

Yes im calculating kp and ki from the 3 vectors. But the loop isnt working as expected. I need help to operate the loop to obtain values. Can you suggest me on my codes i have provided??

Thnk you

Nitesh

[Star Strider]

I have no idea why your code is not reproducing the 2D plot you posted. (I have no idea what you are even doing.) I vectorised your ‘kp’ and ‘ki’ assignments and got them to work.

I must leave it to you to be sure they — and the rest of your code — are otherwise correct.

Answer 2

[arich82]

At the very least, you need to switch your i=i+1 and k=k+1 statements: you have k indexing the inner-most loop, and i indexing the outer-most, but the increments are swapped. You also need to change ki in you statement for kp to ki(i, j, k).

You might also want to try plotting using

plot(ki(:), kp(:), '.')

I'm not sure this is going to give you what you want. I'm pretty sure that a fair number of your roughly 1 million data points will be inf and NaN...

Consider the following, which should be equivalent:

n = 100;
omega = linspace(0, 100, n + 1);
mu = linspace(0, 1, n + 1);
lambda = linspace(0, 1, n + 1);
[Omega, Mu, Lambda] = ndgrid(omega, mu, lambda);

K_i = -(...
    -(Omega.^(3 + Lambda)) + ...
    42.46*(Omega.^(1 + Lambda)) + ...
    100*(Omega.^(Lambda + Mu)).*sin(Mu*pi/2)...
    )./(250*sin(Lambda*pi/2));

K_p = -(...
    -(Omega.^(3 + Lambda)).*cos((1 + Lambda)*pi/2) + ...
    42.46*(Omega.^(1 + Lambda)).*cos((1 + Lambda)*pi/2) + ...
    -15.88*(Omega.^(2 + Lambda)).*cos(Lambda*pi/2) + ...
    106.2*(Omega.^(Lambda)).*cos(Lambda*pi/2) + ...
    100*(Omega.^(Lambda + Mu)).*cos((Lambda + Mu)*pi/2) + ...
    250*K_i ...
    )./(250*(Omega.^Lambda).*cos(Lambda*pi/2));

figure; plot(K_p(:), K_i(:), '.')

It would appear that you're trying to plot the stability regions for a PID controller. I'm not sure this is the best approach...

[arich82]

Looking more closely at your (updated) problem, the plot you show (Figure 5) that indicates that mu and lambda are fixed in the plot ( 1.15 and 0.9, respectively). I assume that means the plot in the figure is essentially a parametric plot as a function of omega.

However, it doesn't seem like fixing these values in the code above reproduces the plot, though I might have made a mistake...

[arich82]

Note: I appear to have made an error in my first post: the expression for K_i has a leading negative sign which shouldn't be there.

(This also invalidates the values for K_p, and both plots, but the comments about the inf and NaN, the parametric nature of the plot, and the suggested range for omega still stand.)