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

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

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

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

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

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;