A linear time invariant (LTI) system with the transfer function
$G (s) = \frac{K (s^{2} + 2 s + 2)}{(s^{2} - 3 s + 2)}$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for $0 < K < \infty$ intersects the imaginary axis for $K = 1.5$ . the closed loop system is stable for

K > 1.5

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1 < K < 1.5

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0 < K < 1.5

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no positive value of

K

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Solution

The correct option is A $K > 1.5$
Given that
$G (s) = \frac{K (s^{2} + 2 s + 2)}{s^{2} - 3 s + 2}$
The root locus plot of the given system is as follows:

$∴$ System is stable for $K > 1.5$

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A linear time invariant (LTI) system with the transfer function G(s)=K(s2+2s+2)(s2−3s+2) is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for 0<K<∞ intersects the imaginary axis for K=1.5 . the closed loop system is stable for

The correct option is A K>1.5Given that G(s)=K(s2+2s+2)s2−3s+2 The root locus plot of the given system is as follows: ∴ System is stable for K>1.5

The correct option is A $K > 1.5$
Given that
$G (s) = \frac{K (s^{2} + 2 s + 2)}{s^{2} - 3 s + 2}$
The root locus plot of the given system is as follows:

$∴$ System is stable for $K > 1.5$