A root locus for a unity-feedback system is shown in Fig.Q6. Find: i. G(s)H(s) ii.The minimum damping ratio iii.The gain K correspond to = 0.9 iv.The dominant poles correspond to = 1 v.The gain K so that the system is unstable. Imaginary Axis (seconds ¹) 15 12 9 6 & 6 -9 0.955 -12 -15 0.9 0.988. 30 0.988 -35 0.955 0.9. -30 25 -25 0,82- o 20 0.72 0.82- -20 0.58 10 0:4 0.2 0.72 0.58 0.4 0.2 -15 -10 Quin (reconds) -5 Fig.Q6 0 2

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A root locus for a unity-feedback system is
shown in Fig.Q6. Find:
i. G(s)H(s)
ii.The minimum damping ratio
iii.The gain K correspond to = 0.9
iv.The dominant poles correspond to } = 1
v.The gain K so that the system is unstable.
Imaginary Axis (seconds)
15
12
9
6
?
-6
-9
0.955
-12
-15
0.9
0:988.
30
0.988
-35
0.955
0.9..
-30
25
-25
0,82-
20
4.
0.72.
0.82
0.58 0:4 0:2
0.72
-20
-15
Real Axis (seconds)
0.58 0:4 0.2
-10
-5
Fig.Q6
0 2
Transcribed Image Text:A root locus for a unity-feedback system is shown in Fig.Q6. Find: i. G(s)H(s) ii.The minimum damping ratio iii.The gain K correspond to = 0.9 iv.The dominant poles correspond to } = 1 v.The gain K so that the system is unstable. Imaginary Axis (seconds) 15 12 9 6 ? -6 -9 0.955 -12 -15 0.9 0:988. 30 0.988 -35 0.955 0.9.. -30 25 -25 0,82- 20 4. 0.72. 0.82 0.58 0:4 0:2 0.72 -20 -15 Real Axis (seconds) 0.58 0:4 0.2 -10 -5 Fig.Q6 0 2
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