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15 Example 9.1 OGATA 4ed(Lead compensator, Bode and Nyquist plot)



    Let's draw the Bode plot, polar plot and output by Scilab.

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


    \begin{displaymath}G_{c}(s)=\frac{41.7\cdot (s+4.41)}{(s+18.4)}\end{displaymath}


    Scilab program(Bode plot)
    clf;
    s=%s/(%pi*2);
    g=4/(s*(s+2));
    gc=41.7*(s+4.41)/(s+18.4);
    gt=g*gc;
    gs=syslin('c',10*g);
    gts=syslin('c',gt);
    clf;
    bode([gs;gts]);
    legend(['no compensated(10*G)';'compensated (G*Gc)'])
    
    Image Ejemplo9_1
    Scilab program (polar plot)
    
    clf;
    s=%s/(2*%pi);
    g=4/(s*(s+2));
    gc=41.7*(s+4.41)/(s+18.4);
    gt=g*gc;
    gs=syslin('c',10*g);
    gts=syslin('c',gt);
    clf;
    nyquist([gs;gts],['no compensated(10*G)';'compensated (G*Gc)']);
    m_circle([1.9;10]);
    mtlb_axis([-5 0 -2 2]);
    xgrid;
    
    Image Ejemplo9_1b
    Scilab program (unit-step response) by Scilab
    clf;
    s=%s;
    g=4/(s*(s+2));
    gc=41.7*(s+4.41)/(s+18.4);
    gt=g*gc;
    gc=g /. 1;
    gtc=gt /. 1;
    gs=syslin('c',gc);
    gts=syslin('c',gtc);
    t=0:0.02:6;
    y=csim('step',t,gs);
    yt=csim('step',t,gts);
    plot(t,y);
    plot(t,yt,'g')
    xgrid;
    legend(['no compensated';'compensated'])
    xtitle('Unit-Step response','t(seg)','y(t)')
    
    Image Ejemplo9_1c
    Scilab program (Ramp response)
    clf; 
    s=%s;
    g=4/(s*(s+2));
    gc=41.7*(s+4.41)/(s+18.4);
    gt=g*gc;
    gc=g /. 1;
    gtc=gt /. 1;
    gs=syslin('c',gc);
    gts=syslin('c',gtc);
    t=0:0.02:6;
    y=csim(t,t,gs);
    yt=csim(t,t,gts);
    plot(t,y);
    plot(t,yt,'g');
    plot(t,t,'r');
    xgrid;
    legend(['no compensated';'compensated';'ramp'])
    xtitle('Ramp response','t(seg)','y(t)')
    
    Image Ejemplo9_1d