Given is the system in a unity closed-loop (K>0): Controller Plant R(s) K P(s) Y(s) where the plant transfer function is given by: (s + 2) s(s +1) P(s) a) Prove that the point so = -1+j is on the root locus for this transfer function (Hint: Use ZL(s). No need to draw the entire root-locus) b) For which K is the point so = -1 +j on the root locus?

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Given is the system in a unity closed-loop (K>0):
Controller
Plant
R(s)
K
P(s)
Y(s)
where the plant transfer function is given by:
(s + 2)
P(s)
s(s + 1)
a) Prove that the point so = -1+j is on the root locus for this transfer function
(Hint: Use ZL(s). No need to draw the entire root-locus)
b) For which K is the point so = -1+j on the root locus?
Transcribed Image Text:Given is the system in a unity closed-loop (K>0): Controller Plant R(s) K P(s) Y(s) where the plant transfer function is given by: (s + 2) P(s) s(s + 1) a) Prove that the point so = -1+j is on the root locus for this transfer function (Hint: Use ZL(s). No need to draw the entire root-locus) b) For which K is the point so = -1+j on the root locus?
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