EXAMPLE B–5 Expand the following B(s)/A(s)into partial fractions with MATLAB.
For this function, we have
num = [1 2 3]
den = [1 3 3 1]
The command
[r,p,k] = residue(num,den)
gives the result shown next:
B(s)
A(s)
=
s^2 +2s+ 3
(s+1)^3
=
s^2 +2s+ 3
s^3 +3s^2 +3s+ 1
Appendix B / Partial-Fraction Expansion 873
It is the MATLAB representation of the following partial-fraction expansion of B(s)/A(s):
Note that the direct term kis zero.
B(s)
A(s)
=
1
s+ 1
+
0
(s+1)^2
+
2
(s+1)^3
num = [1 2 3];
den = [1 3 3 1];
[r,p,k] = residue(num,den)
r =
1.0000
0.0000
2.0000
p =
-1.0000
-1.0000
-1.0000
k =
[]
