How to plot this while loop?

Hello. I’m trying to plot this while loop with no success. Each time it gives me a blank plot. Tried using hold on at the end of the loop, before the loop, or just using plot but without results. The codes work perfectly fine without plotting as it displays all the results that I want. Here I wish to plot both sigma and u in one same plot (but even tried only sigma, still nothing). Here it is:

      t=0;
      x=[1,1,1];
      v=x(1);
      vc=sin(t+1)-cos(0.5*t-2);
      sigma=v-vc;
      alpha=30;
      tau=0.0001;
      while t<=10
          f=-sin(t+5)-0.5*cos(t)-x(2);
          v=x(1);
          vc=sin(t+1)-cos(0.5*t-2);
          vcc=cos(t+1)+0.5*sin(0.5*t-2);
          sigma=v-vc;
          sigmadot=f-vcc;
          u=alpha*((abs(sigmadot)).^2*sign(sigmadot)+sigma)/((sigmadot).^2+abs(sigma));
          dx=[f,cos(1+x(1)+x(3))+(2-cos(x(1)+x(3)+1))*u,cos(x(1)+0.5*x(3)-t)-x(3)+u];
              x=x+dx*tau;
              t=t+tau;
      end

Please if someone can tell me how to plot this properly or if maybe there is a way to rewrite the code without the while loop so I can plot it without a problem hopefully, It will be appreciated.

Answer 1

[Star Strider]

Try this:

t=0;
x=[1,1,1];
v=x(1);
vc=sin(t+1)-cos(0.5*t-2);
sigma=v-vc;
alpha=30;
tau=0.0001;
k = 1;                                              % Counter
while t<=10
    f=-sin(t+5)-0.5*cos(t)-x(2);
    v=x(1);
    vc=sin(t+1)-cos(0.5*t-2);
    vcc=cos(t+1)+0.5*sin(0.5*t-2);
    sigma=v-vc;
    sigmadot=f-vcc;
    u=alpha*((abs(sigmadot)).^2*sign(sigmadot)+sigma)/((sigmadot).^2+abs(sigma));
    dx=[f,cos(1+x(1)+x(3))+(2-cos(x(1)+x(3)+1))*u,cos(x(1)+0.5*x(3)-t)-x(3)+u];
    x=x+dx*tau;
    t=t+tau;
    sigmav(k) = sigma;                              % Vector
    uv(k) = u;                                      % Vector
    tv(k) = t;                                      % Vector
    k = k + 1;                                      % Increment Countr
end

figure
plot(tv, uv)
grid

figure
plot(tv, sigmav)
grid

[Desiree]

Thanks, but I got such a strange plot for u... like an area, why is that?

[Star Strider]

As always, my pleasure.

The ‘u’ (actually ‘uv’) value for most of its range (where ) appears to rapidly oscillate between two narrow ranges of values, one near -30 and one near +30. This is easier to see when plotted with a marker (eliminating the lines connecting the values):

plot(tv, uv, '.')

I suspect that¹s because of the sign call and abs calls, although I’m not certain what this calculation is.

The ‘sigma’ value does something similar, although it takes a bit of effort to see it:

figure
plot(tv, sigmav, '.')
grid
ylim([-1  1]*1E-6)

[Desiree]

Thanks a lot!

[Star Strider]

As always, my pleasure!