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25a_SEMD3_BodePlotsW12

# 25a_SEMD3_BodePlotsW12 - Fig 14 Bode Fig 14.2 Bode diagram...

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Unformatted text preview: Fig 14 Bode Fig 14.2 Bode diagram for a first-order process (no time delay) time delay) Slope = -1 All G(s) have the same plot of “normalized” ARN vs (omega*tau) ! Assymptotes at lower & higher frequencies Fig 14.3 Bode diagram for second-order processes All G(s) have the same plot of normalized ARN vs (omega*tau) ! τ second-order = 1 ω where φ = −90 degrees AR max = K 2ζ 1 − ζ 2 Bode diagram for third Bode diagram for third-order process example, corner frequencies at 0.1, 0.2 and 1 rad/min. Note phase angle approaches 3 x (-90) degrees at large frequencies. See Table 14.2 and handout for many “other examples”. Figure 14.4 14 Pure time delay e −θ s → e −θω j = eφ j So φ = (−ωθ ) radians = Phase Angle = (−ωθ ) 180 π = −57.29(ωθ ) degrees % Table14_1.m = a Bode plot for G =5(0.5s+1)e^-0.5s/((20s+1)(4s+1)) clear all, format compact 5(0.5s + 1)e −0.5 s gain=5;tdead=0.5;num=[0.5 1]; G (s) = in SEMD3 in SEMD3 den=[80 24 1]; (20 s + 1)(4 s + 1) G=tf(gain*num,den) % Define system as a transfer function w/o time delay points=500; %Define the number of points %Define the number of points ww=logspace(-2,2,points); %Frequencies to be evaluated [mag,phase,ww]=bode(G,ww); %Generate numerical values for Bode plot AR=zeros(points,1); %Preallocate vector for Amplitude Ratio PA=zeros(points,1); %Preallocate vector for Phase Angle for ii=1:points AR(ii)=mag(1,1,ii)/gain; %Normalized AR PA(ii)=phase(1,1,ii)-((180/pi)*tdead*ww(ii)); %Add effect of time delay end figure subplot(2,1,1) loglog(ww,AR) axis([0.01 100 0.001 1]) title('Frequency Response of a SOPTD with Zero') SOPTD ylabel('AR/K'),grid subplot(2,1,2) semilogx(ww,PA) axis([0.01 100 -270 0]) ylabel('Phase Angle (gegrees)') xlabel('Frequency (rad/time)'),grid 10 -1 AR/K 10 Frequency Response of a SOPTD with Zero 0 10 -2 -3 10 -2 10 10 -1 10 0 10 1 10 2 Phase Ang le (gegrees) 0 -50 -100 -150 -200 -250 10 -2 10 -1 0 10 Frequency (rad/time) 10 1 10 2 ...
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