Finding zero poles in eigenvalues

Hello Matlab Community, I have problems finding the zero pole of my eigenvalues of a matrix. I have a given 4x4 matrix A:

   A=[0 1 0 0;
      -35.7 -d/841.5 35.7 d/841.5;
       0 0 0 1;
       1200 d/25 -9200 (-100-d)/25];
lambda=eig(A);

I can imagine the code to be something like: find(min(real(lambda(1)-lambda(2)))&&min(imag(lambda(1)-lambda(2))));

I can change the value of d within a given range of 800 till 12000;

As you can see in the picture, the steps at the results get even bigger, so a loop didn't really do the trick for me, as I would need to adapt the stepsize of d when I get closer to my desired result.

Could it be possible to solve this problem with fminsearch(@d eig(A))? I have no idea how to get the matrix into my fminsearch function.

Would be nice if no optimization toolbox is needed.

Thank you for your help.

Answer 1

[Star Strider]

If I remember correctly, the eigenvalues of the ‘A’ matrix of a control system are the poles. To find the zeros of your system, you first need to convert it to a transfer function.

[Tobias Engelhardt]

That is correct sir, but I am looking for a different use:

If I find the value of d to the given poles above, I know that my system will be critically damped (D=1), which is what I am trying to accomplish here. The matrix A represents my system matrix.