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Next: 16 Example 9.2 OGATA Up: FrequencyResponse Previous: 14 Problem A8.18 OGATA   Contents

 

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