The loop transfer function of a unity feedback L(s) = Gc(s)G(s) = K(s + 2) (s + 3) s²(s + 1)(s +15) (s +20) This system is called conditionally stable because it is stable only for a range of the gain K such that k1 < K < k2. Using the Routh-Hurwitz criteria and the root locus method, determine the range of the gain for which the system is stable. Sketch the root locus for 0 < K < inf.

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Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.6P
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Hi, I could use some help with the following problems for controls. I am trying to get this to work, but I keep getting stuck. I'm trying to review some problems for an upcoming test by using some online resources.

The loop transfer function of a unity feedback
L(s) = Gc(s)G(s)
=
K(s + 2) (s + 3)
s²(s + 1)(s +15) (s +20)
This system is called conditionally stable because it is stable only for a range of the gain K such that
k1 < K < k2. Using the Routh-Hurwitz criteria and the root locus method, determine the range of the
gain for which the system is stable. Sketch the root locus for 0 < K < inf.
Transcribed Image Text:The loop transfer function of a unity feedback L(s) = Gc(s)G(s) = K(s + 2) (s + 3) s²(s + 1)(s +15) (s +20) This system is called conditionally stable because it is stable only for a range of the gain K such that k1 < K < k2. Using the Routh-Hurwitz criteria and the root locus method, determine the range of the gain for which the system is stable. Sketch the root locus for 0 < K < inf.
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