Control systems question involving laplace transforms

AI Thread Summary
The discussion revolves around a control systems question involving Laplace transforms, specifically a function with a numerator of (5s+1) and a denominator of (s+3)(3s+2)(s^2). The user initially struggles with the partial fraction expansion, particularly with the coefficient B, which they calculate as -2.25, while MATLAB and Maple provide -3/4. After further investigation, the user realizes that the discrepancy arises from misunderstanding the MATLAB residue function, which provides coefficients for time domain analysis rather than direct partial fraction results. Ultimately, the user corrects their approach and confirms that multiplying their initial result by 1/3 yields the expected value for B. The conversation highlights the importance of understanding software outputs in control systems analysis.
FOIWATER
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I have narrowed down a control systems question I am doing to the following function in the S-domain.. numerator = (5s+1) denominator = (s+3)(3s+2)(s^2)

Using partial fraction expansion - I compute A = 14/63... D = 1/6... B = -2.25 And I can go no further - because both MATLAB and MAPLE disagree with me on B. They say I have the correct A and C, but they have B listed as -3/4. I have NO idea how they are achieving this result... any ideas?

When I expanded I got this, A/(S+3) B(3S+2) C/S D/S^2 all added... and when i cross multiply and try to solve for B... I get all terms except for B having the (3S+2) (It got canceled out of the num and den in B when I cross multiplied). Can anyone agree with me so far?...

Now, I proceed to make S = -2/3, since this will drive A, C, and D to zero, leaving me with:
5S+1 = B(S+3)S^2 right?

and when I put in -2/3 no matter what I do I get -2.25 I have even tried to expand and use systems of equations, in which case I still get the -2.25... not sure why

The MATLAB function I used with this equation was the [r,p,k]= function to get the residue and poles. in maple i used invlaplace and they both give -3/4 for B, and 19/36 for C, of which I get neither.. However we both agree on A and B what am I doing wrong, anyone?
 
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Every system I compute this with gives me 3/4 for B, it must have to do with the way I am dividing B by 3s+2, although I don't see where it is incorrect..

I am so sorry for asking a question that I immediately found the answer to.

The problem was - the residue function of MATLAB apparently - the r in rpk the residue itself is not the answers to the partial fraction analysis, it is the answers to the time domain coefficients of each term? because when I now multiply -2.25 by 1/3 I am going to get the 3/4. I just should of kept going!.
 
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