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The block diagram of a control system is shown in Figure 4. The gain K is to be tuned to optimize the response of the system. To do so, the range of value for Kneed to be evaluated to make sure that the tuning will not go into instability. Root locus is the tool that can help in predicting the response of the system by plotting all the possible positions of poles as K is modified.   (a) Develop the root locus sketch for the system. (b) Find the exact point and gain where the locus crosses the 0.45 damping ratio line. Conclude therefore the range of K within which the system is stable

The block diagram of a control system is shown in Figure 4. The gain K is to be tuned to optimize the response of the system. To do so, the range of value for Kneed to be evaluated to make sure that the tuning will not go into instability. Root locus is the tool that can help in predicting the response of the system by plotting all the possible positions of poles as K is modified.   (a) Develop the root locus sketch for the system. (b) Find the exact point and gain where the locus crosses the 0.45 damping ratio line. Conclude therefore the range of K within which the system is stable

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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The block diagram of a control system is shown in Figure 4. The gain K is to be tuned to

optimize the response of the system. To do so, the range of value for Kneed to be evaluated to

make sure that the tuning will not go into instability. Root locus is the tool that can help in

predicting the response of the system by plotting all the possible positions of poles as K is

modified.

 

(a) Develop the root locus sketch for the system.

(b) Find the exact point and gain where the locus crosses the 0.45 damping ratio line.

Conclude therefore the range of K within which the system is stable.

R(s) K N s² 4s 20 Figure 4 + + 1 (s+2)(s+4) C(s)
Transcribed Image Text:R(s) K N s² 4s 20 Figure 4 + + 1 (s+2)(s+4) C(s)
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