88 views (last 30 days)

hello

I have 2x2 matrix

G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)] where G(1,1)=/(s+1) G(1,2)=1/(s+2) G(2,1)=1/(s+3) G(2,2)=1/(s+4)

Now because it is a 2x2 matrix it must have 2 eigen values .

so my questions are:

- How to calculate the determinant of G matrix?
- How to find the eigen values of the G matrix?
- How to get the eigen vectors of the G matrix?
- I want to perform the following operation ------- SQUAREROOT OF((G(1,1)+G(2,2))/2) but I am unable to do.

Paul
on 26 Aug 2020

Edited: Walter Roberson
on 26 Aug 2020

If you want to use the symbolic appoach, why not just create a matlab function to evaluate lambda(2) and then create the plot using an frd model:

syms s

G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)];

lambda=eig(G);

f=matlabFunction(lambda(2));

w=logspace(-1,3,500);

nyquist(frd(f(1j*w),w));

Unclear how well this symbolic approach will work for systems of even moderate complexity ....

Paul
on 26 Aug 2020

Walter,

I see that you edited my answer, I think to remove the >> from the code snippet. Can anyone edit anyone else's Answer?

Walter Roberson
on 26 Aug 2020

You are correct, I removed the >> so that the code could be copied and pasted.

People with reputation 3000 or higher can edit answers. That is about 45 people (out of over 200000 users) . We mostly reformat text into code, or adjust html links to be usable, but sometimes we remove >> so that code can be run more easily. Sometimes we fix spelling mistakes that are interfering with understanding what has been posted (a lot of the users do not have English as a first language, so incorrect spelling can make it difficult for them to understand what was said.)

Less pleasantly, from time to time we remove inappropriate wording such as personal insults.

Walter Roberson
on 23 Aug 2020

If you use the symbolic toolbox,

syms s

G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)]

then you can do all of those operations directly.

If you use

s = tf('s');

G=[1/(s+1) 1/(s+2);1/(s+3) 1/(s+4)]

then you can do det(G) and eig(G) but eig(G) will not return the eigenvectors

An example of finding eigenvectors from eigenvalues is at https://www.scss.tcd.ie/Rozenn.Dahyot/CS1BA1/SolutionEigen.pdf

SQUAREROOT OF((G(1,1)+G(2,2))/2)

The sqrt() is the problem; sqrt() is not defined for transfer functions

Maple tells me that that particular expression might have an inverse laplace,

exp(-4*t)*int(3*((4*Dirac(_U1)*sqrt(t - _U1))/3 + sqrt(t)*exp((9*_U1)/4)*(BesselI(0, (3*_U1)/4) + BesselI(1, (3*_U1)/4)))/sqrt(t - _U1), _U1 = 0 .. t)/(4*sqrt(Pi)*sqrt(t))

MANAS MISHRA
on 24 Aug 2020

Walter Roberson
on 26 Aug 2020

I traced the calls further, and found that the nyquist plot code converts the system to zpk form, and then iterates through a list of frequencies to calculate the zpk response at the frequency. Unfortunately that calculation routine is a mex file so I do not know how it calculates the response.

To calculate the zpk it finds the roots of the numerator and denominator and the ratio of the leading coefficients.

The zpk representation assumes polynomials. You can seek out the roots anyhow thinking you might get a hint about the behaviour. The roots of the numerator are -4. The roots of the denominator are -4 and -1. -4 is an overall zero in theory because of limits.

... but really you have to examine the poles of the sqrt in the numerator, which are -2 and -3, so the overall poles are -4 -3 -2 -1. And the function goes complex for part and I do not know what to do with that.

MANAS MISHRA
on 28 Aug 2020

Edited: Walter Roberson
on 28 Aug 2020

Paul
on 28 Aug 2020

Opportunities for recent engineering grads.

Apply TodayFind the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
## 1 Comment

## Direct link to this comment

https://au.mathworks.com/matlabcentral/answers/583430-eigen-value-of-the-transfer-function-2x2-matrix#comment_985517

⋮## Direct link to this comment

https://au.mathworks.com/matlabcentral/answers/583430-eigen-value-of-the-transfer-function-2x2-matrix#comment_985517

Sign in to comment.