u=ao= Frequency Ratio 5=0.05 0405060810 Figure 11.5 Bode diagram of 1/(som2+(2yos+1. Example 1 A(s) s2+11005+105(s+100)(s+1000) (s/100+1)(s/1000+1) In Fig. 11.6, the individual contributions of the four factored terms of A(s) are shown as long dashed lines. The straight line approximations for gain and phase are shown with solid lines. The exact cu with short dashed lines Example 2 50(s/500+1) G(s) 1000(s+500) s2+70s+10,000(s/00)2+2(0.35)(s/100)+1 Note that the damping factor for the quadratic term in the denominator is 5=0.35. If drawing the response curves by hand, the resonance peak near the breakpoint at @= 100 would be estimated from Fig. 11 Figure 11.7 shows the exact gain and phase frequency response curves for G(s) e 2000 by CRC Press LLC© 2000 by CRC Press LLC Example 1 In Fig. 11.6, the individual contributions of the four factored terms of A(s) are shown as long dashed lines. The straight line approximations for gain and phase are shown with solid lines. The exact curves are presented with short dashed lines. Example 2 Note that the damping factor for the quadratic term in the denominator is z = 0.35. If drawing the response curves by hand, the resonance peak near the breakpoint at w = 100 would be estimated from Fig. 11.5. Figure 11.7 shows the exact gain and phase frequency response curves for G(s). Figure 11.5 Bode diagram of 1/[(s/wn)2 + (2z/wn)s + 1]. 10 20 0 -10 -20 -30 -40 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2 3 4 5 6 7 8 9 10 z = 0.05 0.10 0.15 0.20 0.25 0.3 0.4 0.5 0.6 0.8 1.0 u = w/wn = Frequency Ratio 20 log|G| Phase Angle, Degrees w/wn = Frequency Ratio (a) (b) -20 0 -40 -60 -80 -100 -120 -140 -160 -180 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2 3 4 5 6 7 8 9 10 z = 0.05 0.10 0.15 0.20 0.25 0.3 0.4 0.5 0.6 0.8 1.0 A s s s s s s s s s s ( ) = 104 2 5 4 1 1100 10 10 100 1000 10 + + 100 1 1000 1 = + + = + + - ( )( ) ( / )( / ) G s s s s s s s ( ) ( ) , ( / ) ( / ) ( . )( / ) = + + + = + + + 1000 500 70 10 000 50 500 1 100 2 0 35 100 1 2 2