A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. For what value of K does the closed-loop system have a minimum settling time? For this value of K a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.3P
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A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1.
For what value of K does the closed-loop system have a minimum settling time?
For this value of K
0.78
0.89
2 0.97
K=8
0.97
0.89
a. What is the natural frequency of the dominant poles of the system?
b.
List all the poles of the closed-loop system
K=6 k=3
0.78
K=1
00
K=4 X=2
0.66
K=I
0.66
43
0.52
K=4
(K=3
K=4
K=2
0.52
0.38
K=1
K=6
K=6
0.38
Figure 1
0.26
0.26
0.12
K=8
K=3
K=4
0.12
K=3
K=6
K=2
K=8T
Im s
K=1
K=4
Res
K=1
K=6
K=8₁
1
Transcribed Image Text:A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. For what value of K does the closed-loop system have a minimum settling time? For this value of K 0.78 0.89 2 0.97 K=8 0.97 0.89 a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system K=6 k=3 0.78 K=1 00 K=4 X=2 0.66 K=I 0.66 43 0.52 K=4 (K=3 K=4 K=2 0.52 0.38 K=1 K=6 K=6 0.38 Figure 1 0.26 0.26 0.12 K=8 K=3 K=4 0.12 K=3 K=6 K=2 K=8T Im s K=1 K=4 Res K=1 K=6 K=8₁ 1
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