Question

Using MATLAB

Use MATLAB to find the partial fraction expansions of the following: Hs(s +3)(s +4) tb) HG) (s17s2+79s +63) 3s +1 (a) G(S)-s +3s +2

Answer 1

This can be solve using the residue() function in MATLAB.

Here's how to use it

b[3 1]; a - [1 3 2]; [r,p,k] - residue(b,a) 1 2 r2x1 2 P2x1 2 -1 1l

In the above Image I've solved for Q(a)

You need to create two variables b and a and store the Coefficients of Numerator in b and Coefficients of Denominator in a. After this you just need to call the residue function passing b and a as parameters. This will return three variables r,p and k. Here r the size of r is 2x1 that means there are at least 2 terms in the expansion. Now the numerator of each term of expansion is given by r and denominator is given by p and the denominator is written as (s-p). So here in the first term is 5/(s-(-2)) = 5/(s+2). Now the second term is -2/(s+1). Now after this you have to see the value of k. Here k is empty so the expansion ends here. So the final Expansion is 5/(s+2) - 2/(s+1). Had there been some k value, say, 5. The final Expansion would have become 5/(s+2) - 2/(s+1) + 5.

The similar procedure can be done for Q(b) as well.

Here's the solution.

a [1 17 79 63]; [r,p,k] - residue(b,a) 2 r3x1 1.8750 -1.0000 0.1250 P3x1 -9.0000 -7.0000 -1.0000 1l

Here first you have to solve the Numerator which is (s+3)(s+4) which results in s² + 7s + 12. Hence b is [1 7 12].

Similarly a is [1 17 79 63]. Call the residue and results are out.

Thank you. Any doubt please comment. Thank you.