Question

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 1

The answer is "Option B".

Step-by-step explanation:

Given equation:

`G(s) =(K(s + 1))/(2s^2 + (K-1)s + (K-1))\\\\`

if

`\to 2s^2 + (K-1)s + (K-1)=0`

Calculating by the Routh's Hurwitz table:

`\to s^2 \ \ \ \ \ 2 \ \ \ \ \ \ K-1 \\\\\to s^2 \ \ \ \ \ K-1 \ \ \ \ \ \ \\\\\to s^0 \ \ ( ((K-1)(K-1)(-2) (0))/(K-1) \\\\ \ \ \ \ = (K-1) )`

Form the above table:

`\to K-1 > 0 \\\\ \to K > 1`

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