XML
Laplace.T Root-locus Transient response Frecuency response
       
 
 
next up previous contents
Next: 12 Problem A8.14 OGATA Up: FrequencyResponse Previous: 10 Problem A8.11 OGATA   Contents

 

11 Problem A8.13 OGATA 4ed(Nyquist plot)



    Let's draw on polar plot the points of frequency $w=0.2,0.3,0.5,1,2,6,10,20$ and calculate the phase and gain of these points by Scilab.

    \begin{displaymath}G(s)=\frac{20 \cdot (s^{2}+s+0.5)}{s\cdot(s+1) \cdot(s+10)}\end{displaymath}

    Scilab program 
    clf;

s=%s/(%pi*2);

g=20*(s^2+s+0.5)/(s*(s+1)*(s+10));

gs=syslin('c',g);

w=[0.2, 0.3, 0.5, 1, 2, 6, 10, 20];

fr=repfreq(gs,w);

nyquist(gs);

for i=1:8,

x(i)=real(fr(i));

y(i)=imag(fr(i));

t(i)=string(w(i));

plot(x(i),y(i),'o');

xstring(x(i),y(i),t(i));

end;

mtlb_axis([-0.1 2 -5 0]);

[db,phi]=dbphi(fr);

[db;phi]


    Results: 
    ans  =
 
    13.835036    10.217883    6.0097561    3.9361863    4.9485002    4.5670563    2.9671948 
 - 0.9799372  
  - 78.95713   - 72.224395  - 55.992508  - 24.145542  - 14.489763  - 31.094569  - 45.028505  
- 63.438525
    Image ProblemaA8-13Pag601