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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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- Fall '08