# Control systems question involving laplace transforms

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## Main Question or Discussion Point

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 cancelled 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 dont 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 im going to get the 3/4. I just should of kept going!.

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