Finding zero poles in eigenvalues

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Tobias Engelhardt
评论： Tobias Engelhardt 2017-2-3
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.

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回答（1 个）

Star Strider
Star Strider 2017-2-3
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.
  1 个评论
Tobias Engelhardt
Tobias Engelhardt 2017-2-3
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.

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