Use the following transfer function G(s) to evaluate the root locus conditions for each of the cases given. This system G(s) is in the feedback given in Problem 2 with a proportional controller. s+5 s? +9s+8 K(s) = K G(s) = (a) Use the root locus angle condition to show that it is possible to place a closed loop pole at -2. Find the gain K that will place a pole at this location. (b) Use the root locus angle condition to show that it is not possible to place any closed loop pole at -7. (c) Use the root locus angle condition to show that it is possible to place a closed loop pole at -15. Find the gain K that will place a pole at this location.

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Use the following transfer function G(s) to evaluate the root locus conditions for each of the cases given.
This system G(s) is in the feedback given in Problem 2 with a proportional controller.
s+5
K(s) = K
G(s) =
8+ $6 + 28
(a) Use the root locus angle condition to show that it is possible to place a closed loop pole at -2. Find
the gain K that will place a pole at this location.
(b) Use the root locus angle condition to show that it is not possible to place any closed loop pole at -7.
(c) Use the root locus angle condition to show that it is possible to place a closed loopP pole at -15. Find
the gain K that will place a pole at this location.
2. Consider the feedback loop below with plant G(s) and proportional controller K(s) = K. Use the Routh-
Hurwitz criterion to determine the full range of K that produces a stable feedback system GcL(s).
s+6
G(s) =
3 + 4s2 + 3s
R(S)
K(s)
G(s)
Transcribed Image Text:Use the following transfer function G(s) to evaluate the root locus conditions for each of the cases given. This system G(s) is in the feedback given in Problem 2 with a proportional controller. s+5 K(s) = K G(s) = 8+ $6 + 28 (a) Use the root locus angle condition to show that it is possible to place a closed loop pole at -2. Find the gain K that will place a pole at this location. (b) Use the root locus angle condition to show that it is not possible to place any closed loop pole at -7. (c) Use the root locus angle condition to show that it is possible to place a closed loopP pole at -15. Find the gain K that will place a pole at this location. 2. Consider the feedback loop below with plant G(s) and proportional controller K(s) = K. Use the Routh- Hurwitz criterion to determine the full range of K that produces a stable feedback system GcL(s). s+6 G(s) = 3 + 4s2 + 3s R(S) K(s) G(s)
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