R(s)* G(3) · Y(s) Figure 1: Negative unity feedback system. 1. Consider the negative unity feedback system shown in Figure , with 1 G(s) = (s² + 4s + 8)(s – 1) (a) Find the characteristic equation of the closed-loop system. Y(s) is (b) Use a Routh table to find the values of K > 0, if any, which will ensure that R(s) asymptotically stable. (c) For values of K that result in instability in , how many poles of the closed-loop system are in the RHP?

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R(s)
K
G(s)
Y(s)
Figure 1: Negative unity feedback system.
1.
Consider the negative unity feedback system shown in Figure , with
1
G(s) =
(s2 + 48 + 8)(s – 1)
(a) Find the characteristic equation of the closed-loop system.
Y(s)
(b) Use a Routh table to find the values of K > 0, if any, which will ensure that
is
asymptotically stable.
(c) For values of K that result in instability in , how many poles of the closed-loop
R(3)
system are in the RHP?
Transcribed Image Text:R(s) K G(s) Y(s) Figure 1: Negative unity feedback system. 1. Consider the negative unity feedback system shown in Figure , with 1 G(s) = (s2 + 48 + 8)(s – 1) (a) Find the characteristic equation of the closed-loop system. Y(s) (b) Use a Routh table to find the values of K > 0, if any, which will ensure that is asymptotically stable. (c) For values of K that result in instability in , how many poles of the closed-loop R(3) system are in the RHP?
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