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Is there a way to extract my 3 transfer function in matlab given these equations.

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Jorje German
Jorje German on 3 Sep 2020
Commented: Sam Chak on 10 Sep 2020
I have these 3 equations
X1(s)*[m1*s^2 + c1*s+(k01+k12)] = F(s) + k12*X2(s)
X2(s)*[m2*s^2 + c2*s +(k12+k23)] = k12*X1(s)+k23*X3(s)
X3(s) [m3*s^2 + c3*s +(k23+k34)] = k23*X2(s)
and I am wondering if there is a possibility to be able to extract my 3 transfer functions, X1(s)/F(s), X2(s)/F(s), and X3(s)/F(s).
Ive really havent explore this part of Matlab and am interested to know if it is possible. I ask because currently I am doing it by hand and setting the left side S polynomial to be P1, P2, and P3 respectively.
but it is alot of algabra and I fear I will make a simple arithmetic mistake and ruin the whole thing.
Can this be done.

  2 Comments

Sam Chak
Sam Chak on 3 Sep 2020
I think the equations can be expressed in this form:
where you can algebraically solve
If exists, then
, ,
Jorje German
Jorje German on 3 Sep 2020
Interesting concept. I just showed my wife and she said, this is why you are still a student. I will try this method and play around in Matlab. Thank you. You have given me a direction to go to.

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Accepted Answer

Sam Chak
Sam Chak on 3 Sep 2020
The transfer functions for your case in given in the first column of the matrix. You can use the functions in Symbolic Math toolbox to simplify the rational expressions. Hope my answer helps.

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Jorje German
Jorje German on 8 Sep 2020
Also. This methods works for Amy system correct? It's ready going through my calculator and doing rref
Sam Chak
Sam Chak on 10 Sep 2020
The method works as long as the matrix inverse exists. For more info about Symbolic Math Toolbox, please visit:
https://www.mathworks.com/products/symbolic.html

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