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7 Program 6.8 OGATA 4edition (root locus, damping ratio)




Let us calculate the root-locus with indication of damping ratio $\zeta$=0.5 and asked to mark a point in the place and get the gain K and the poles of close-loop by Scilab of a system with closed loop with feedback unit whose transfer function in open loop is:

\begin{displaymath}G(s)=\frac{K}{(s^{3}+4\cdot s^{2}+5\cdot s)}\end{displaymath}


Program in Scilab 
num=poly([1 0 0 0],'s','coeff');
den=poly([0 5 4 1],'s','coeff');
g=syslin('c',num/den);
clf;
evans(g);
v=[-3 1 -2 2];
mtlb_axis(v)
sgrid([0.5],[0],32);
//mark a point with the mouse in 
the root-locus of the graph

p=locate(1)
 k=-1/real(horner(g,[1,%i]*p));
 gl=1+k*g;
numgl=numer(gl);
roots(numgl)
k

Results: 

-->p=locate(1)
 p  =
 
  - 0.6502732  
    1.0550725 
    
-->roots(numgl)
 ans  =
 
  - 0.6412384 + 1.0505487i  
  - 0.6412384 - 1.0505487i  
  - 2.7175231               
 
-->k
 k  =
 
    4.1166111