25a_SEMD3_BodePlotsW12

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.

Ask a homework question - tutors are online