Assignment_4_2007_Solutions

3 we can calculate the zncontrollersettingsas k c

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Unformatted text preview: was obtained to be 51 using Routh’s criterion and Root­Locus. We now validate these results by performing the cont inuous cycling to obtain the values of the crit ical controller gain under P­controller. Figures 8 and 9 illustrate the closed­loop response for a set­point change. As the gain is increased, the system reaches the sustained oscillat ion condit ion result ing in a limit ing value for the controller gain o f 51 consistent with the results obtained before. However, in this case, we also obtain the value o f the ult imate period Pu = 0.9 . With these two values, using Table 12.3, we can calculate the ZN controller settings as: k c = 22.95 t I = 0 75 ; . Figures 10 and 11, show the closed­loop performance under a PI controller using the ZN settings for both set­point tracking and disturbance rejection. Figure 8: Closed­loop response with a P­controller using k c = 20 . Figure 9: Closed­loop response with a P­controller using k c = 51 . Figure 10: Closed­loop response with a PI...
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