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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