Solution 9.10.2.6 The MATLAB statements load bodeid6 topm = size(bodeid6) top = topm(1,1) w=bodeid6(1:top,1);; mag = bodeid6(1:top,2);; phase = bodeid6(1:top,3);; semilogx(w,mag);; grid on print -deps 91026mag.eps semilogx(w,phase);; grid on print -deps 91026phase.eps can be used to load the data and plot the magnitude response. You will havetoedit this data le. You only wantthe rst 138 lines. Figure 1 shows the magnitude data with the asymptotes added. The transfer function we obtain from the asymptotes is then G(s)= K s(s+ ;j! d )(s+  + j! d ) : Atlow frequency the only twoterms that contribute are K and 1=s.There- fore at s = j wehave K =10 ;18=20 =0:12589 The hump in the magnitude plot is about 18 dB, so weexpect 0:05 <<0:1: The resonantfrequency is around 9 rad/s. So our rst guess is G(s) = 0:12589 s[(s= p 82) 2 +(2=82)s+1] = 10:32 s(s+1;j9)(s+1+j9) Wecheckthe accuracy of the model bycomparing the actual magnitude and phase to the phase of the derived transfer function, as shown in Figures 2 and 3 The t is excellent, so wehavefound the transfer function. The complete MATLAB program to nd the transfer function is 1 10 -2 10 -1 10 0 10 1 10 2 10 3 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 Figure 1: ABode magnitude plot 2 10 -2 10 -1 10 0 10 1 10 2 10 3 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 Figure 2: Comparison of actual and derived Bode magnitude plots 3 10 -2 10 -1 10 0 10 1 10 2 10 3 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -80 Figure 3: Comparison of actual and derived Bode phase plots 4 load bodeid6 topm = size(bodeid6) top = topm(1,1) w=bodeid6(1:top,1);; mag = bodeid6(1:top,2);; phase = bodeid6(1:top,3);; semilogx(w,mag);; grid on print -deps 91026mag.eps semilogx(w,phase);; grid on print -deps 91026phase.eps p1 = 0 p2 = 1 - j*9 p3 = 1 + j*9 Ktc = 10^(-18/20) K=Ktc *abs( p2) * abs(p3) wp = logspace(-2,3,20);; jw = j*wp;; mag1 = 20*log10( (K)./ ( abs(jw +p1).* abs(jw + p2).*abs(jw+p3) ) );; semilogx(w,mag,'k-',wp,mag1,'kd') grid on print -deps 91026mag1.eps pause phase1 = ( -angle(jw +p1) -angle(jw + p2) - angle(jw+p3) )*180/pi;; semilogx(w,phase,'k-',wp,phase1,'kd') grid on print -deps 91026phase1.eps p1 = 0 p2 = 1 - j*9 p3 = 1 + j*9 Ktc = K=(Ktc *p1* p2 * p3) mag2 = 20*log10( (K )./ ( abs(jw +p1).* abs(jw + p2).*abs(jw+p3) ) );; semilogx(w,mag,'k-',wp,mag2,'kd') print -deps 91026mag2.eps phase2 = ( -angle(jw +p1) -angle(jw + p2) - angle(jw+p3) )*180/pi;; semilogx(w,phase,'k-',wp,phase2,'kd') grid on print -deps 91026phase2.eps p1 = 1 p2 = 3 -j*3 p3 = 3 + j*3 Ktc = 2 K=Ktc*p1*p2*p3 5 mag3 = 20*log10( K./ ( abs(jw +p1).* abs(jw + p2).*abs(jw+p3) ) );; semilogx(w,mag,'k-',wp,mag3,'kd') grid on print -deps 91026mag3.eps phase3 = ( -angle(jw +p1) -angle(jw + p2) - angle(jw+p3) )*180/pi;; semilogx(w,phase,'k-',wp,phase3,'kd') grid on print -deps 91026phase3.eps 6