A controlled process is described by the closed-loop transfer function G(s).
G(s) = K(s + 1)/2s^2 + (K-1)s + (K-1)
What values of K will stabilize the process?
(A) K < 1
(B) K > 1
(C) K > 0.75
(D) K > 0

Answer :

Answer:

The answer is "Option B".

Explanation:

Given equation:

[tex]G(s) =\frac{K(s + 1)}{2s^2 + (K-1)s + (K-1)}\\\\[/tex]

if

[tex]\to 2s^2 + (K-1)s + (K-1)=0[/tex]

Calculating by the Routh's Hurwitz table:

[tex]\to s^2 \ \ \ \ \ 2 \ \ \ \ \ \ K-1 \\\\\to s^2 \ \ \ \ \ K-1 \ \ \ \ \ \ \\\\\to s^0 \ \ ( \frac{(K-1)(K-1)(-2) (0)}{K-1} \\\\ \ \ \ \ = (K-1) )[/tex]

Form the above table:

[tex]\to K-1 > 0 \\\\ \to K > 1[/tex]

In the above, the value of k is greater than 1.

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