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A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? Explain. (c) For what range of values of the gain K is the closed-loop system stable? (d) For K = 4: a. What are the closed-loop poles? b. What are the dominant poles of the closed-loop system (if exist)? c. What is the settling time of the closed-loop system? d. What is the peak time of the closed-loop system? e. What is the max. overshoot of the closed-loop system? (e) What is the maximum damping of the dominant closed-loop poles (f) For what value of K does the closed-loop system have a minimum settling time? (g) For the value of K in (f): a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system (h) For what value(s) of the gain K does the closed-loop system have two real repeated poles? (i) For the value(s) of K in (h) list the other poles 6 2 0.97 0 0.78 T K=8 -2 0.89 6 K=6 0.97 0.89 0.78 -8 K=4 k=3 K=1 -7 0.66 X=2 6 0.66 -6 5 -5 0.52 K=4 (K=3 K=4 K=2 0.52 0.38 K=1 K=6 -3 K=6 0.38 Figure 1 0.26 0.26 -2 0.12 K=8 -1 K=3 0.12 K=4 K=6 K=3 Im s K=2 K=2 K=8 K=1 K=4 0 K=1 Res K=6

A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? Explain. (c) For what range of values of the gain K is the closed-loop system stable? (d) For K = 4: a. What are the closed-loop poles? b. What are the dominant poles of the closed-loop system (if exist)? c. What is the settling time of the closed-loop system? d. What is the peak time of the closed-loop system? e. What is the max. overshoot of the closed-loop system? (e) What is the maximum damping of the dominant closed-loop poles (f) For what value of K does the closed-loop system have a minimum settling time? (g) For the value of K in (f): a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system (h) For what value(s) of the gain K does the closed-loop system have two real repeated poles? (i) For the value(s) of K in (h) list the other poles 6 2 0.97 0 0.78 T K=8 -2 0.89 6 K=6 0.97 0.89 0.78 -8 K=4 k=3 K=1 -7 0.66 X=2 6 0.66 -6 5 -5 0.52 K=4 (K=3 K=4 K=2 0.52 0.38 K=1 K=6 -3 K=6 0.38 Figure 1 0.26 0.26 -2 0.12 K=8 -1 K=3 0.12 K=4 K=6 K=3 Im s K=2 K=2 K=8 K=1 K=4 0 K=1 Res K=6

Power System Analysis and Design (MindTap Course List)
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. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? Explain. (c) For what range of values of the gain K is the closed-loop system stable? (d) For K = 4: a. What are the closed-loop poles? b. What are the dominant poles of the closed-loop system (if exist)? c. What is the settling time of the closed-loop system? d. What is the peak time of the closed-loop system? e. What is the max. overshoot of the closed-loop system? (e) What is the maximum damping of the dominant closed-loop poles (f) For what value of K does the closed-loop system have a minimum settling time? (g) For the value of K in (f): a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system (h) For what value(s) of the gain K does the closed-loop system have two real repeated poles? (i) For the value(s) of K in (h) list the other poles 2 -2 ip 0.78 0.89 0.97 K=8 K=6 0.97 0.89 0.78 K=1 0.66 K=4 X=2 k=3 K=I 0.66 LD ch 0.52 K=4 (K=3 K=4 K=2 0.52 0.38 K=I K=6 K=6 0.38 Figure 1 0.26 WEL 0.26 0.12 K=8 K=3 0.12 K=8 K=6 K=3 K=2 K=2 Im s K=1 Res K=1 K=4 K=6
Transcribed Image Text:A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? Explain. (c) For what range of values of the gain K is the closed-loop system stable? (d) For K = 4: a. What are the closed-loop poles? b. What are the dominant poles of the closed-loop system (if exist)? c. What is the settling time of the closed-loop system? d. What is the peak time of the closed-loop system? e. What is the max. overshoot of the closed-loop system? (e) What is the maximum damping of the dominant closed-loop poles (f) For what value of K does the closed-loop system have a minimum settling time? (g) For the value of K in (f): a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system (h) For what value(s) of the gain K does the closed-loop system have two real repeated poles? (i) For the value(s) of K in (h) list the other poles 2 -2 ip 0.78 0.89 0.97 K=8 K=6 0.97 0.89 0.78 K=1 0.66 K=4 X=2 k=3 K=I 0.66 LD ch 0.52 K=4 (K=3 K=4 K=2 0.52 0.38 K=I K=6 K=6 0.38 Figure 1 0.26 WEL 0.26 0.12 K=8 K=3 0.12 K=8 K=6 K=3 K=2 K=2 Im s K=1 Res K=1 K=4 K=6
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