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Next: 20 Problem A9.8 OGATA Up: FrequencyResponse Previous: 18 Problem A9.5 OGATA   Contents

 

19 Problem A9.7 OGATA 4ed(Lead compensator, Nyquist plot)



    Let's draw the Nyquist plot of G(jw),$G_{1}(jw)$ and $G{c}(jw)\cdot G_{1}(jw)$ by Scilab:

    \begin{displaymath}G(jw)=\frac{4}{jw\cdot (jw+2)}\end{displaymath}


    \begin{displaymath}G(jw)=\frac{40}{jw\cdot (jw+2)}\end{displaymath}


    \begin{displaymath}G_{c}(jw)G(jw)=41.7\cdot \frac{jw+4.41}{jw+18.4}\frac{4}{jw\cdot (jw+2)}\end{displaymath}

    Scilab program: 
    s=%s;

g=4/(s*(s+2));

gc=41.7*(s+4.41)/(s+18.4)

w=0.01:0.01:1000;

gs=syslin('c',g);

gs1=syslin('c',10*g);

gs2=syslin('c',gc*g);

gr=horner(gs,%i*w);

gr1=horner(gs1,%i*w);

gr2=horner(gs2,%i*w);

theta=atan(imag(gr),real(gr));

theta1=atan(imag(gr1),real(gr1));

theta2=atan(imag(gr2),real(gr2));

ro=abs(gr);

ro1=abs(gr1);

ro2=abs(gr2);

clf;

k=0:0.01:2*%pi;

nr=10*cos(k)+10*%i*sin(k);

theta3=atan(sin(k),cos(k));

ro3=abs(nr);

polarplot(theta3,ro3);

plot(real(gr),imag(gr),'k');

plot(real(gr1),imag(gr1),'b');

plot(real(gr2),imag(gr2),'g');

mtlb_axis([-10 10 -10 10]);

legends(['G(jw)';'G1(jw)'
;'Gc(jw)*G(jw)'],[1;2;3],opt=1);

     

     

     

     


    Image ProblemaA9_7