1 Example 2.6 OGATA 4edition( Laplace transform, partial fractions)

We will expand into partial-fractions through Scilab the transfer function:

[画像:\begin{displaymath}\frac{B(s)}{A(s)}=\frac{(2\cdot s^{3}+5\cdot s^{2}+3\cdot s+6)}{(s^{3}+6\cdot s^{2}+11\cdot s+6)} \end{displaymath}]

Program in Scilab

s=%s;
num=2*s^3+5*s^2+3*s+6;
den=s^3+6*s^2+11*s+6;
g=syslin('c',num/den);
gf=tf2ss(g);
se=pfss(gf)

Solution:

se =
 
 
 se(1)
 
 - 6 
 ----- 
 3 + s 
 
 se(2)
 
 3 
 ----- 
 1 + s 
 
 se(3)
 
 - 4 
 ----- 
 2 + s 
 
 se(4)
 
 2.

The partial-fraction expansion we would:

[画像:\begin{displaymath}\frac{B(s)}{A(s)}=-\frac{6}{s+3}+\frac{3}{s+1}-\frac{4}{s+2}+2\end{displaymath}]

If you want the equation of beginning, use these lines of code to Scilab

g2=0;
for k=1:size(se),
g2=g2+se(k),
end;