A unity feedback system has an open - loop transfer function of the centroid and breakaway points are respectively. $G (s) H (s) = \frac{K}{s^{2} (s + 2)}$

- 1.24 and

- \frac{2}{3}

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- 1.24 and

- \frac{4}{3}

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- 0.667 and

- \frac{4}{3}

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-0.667 and 0

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Solution

The correct option is D -0.667 and 0
Centroid $= \frac{\sum real part of OL poles - \sum real part of OL zeros}{p - z}$
$= - \frac{2}{3} = - 0.667$
Characteristic equation $= s^{2} (s + 2) + K = 0$
$K = - s^{2} (s + 2)$
$\frac{d K}{d s} = - 3 s^{2} - 4 s = 0$
$s (3 s + 4) = 0$
$s = 0; s = - \frac{4}{3}$
$s = - \frac{4}{3}$ is not in the root locus.
Centroid = -0.667; breakaway point = 0

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A unity feedback system has an open - loop transfer function of the centroid and breakaway points are respectively. G(s)H(s)=Ks2(s+2)

The correct option is D -0.667 and 0Centroid =∑real part of OL poles −∑real part of OL zerosp−z =−23=−0.667 Characteristic equation =s2(s+2)+K=0 K=−s2(s+2) dKds=−3s2−4s=0 s(3s+4)=0 s=0;s=−43 s=−43 is not in the root locus. Centroid = -0.667; breakaway point = 0

A unity feedback system has an open - loop transfer function of the centroid and breakaway points are respectively. $G (s) H (s) = \frac{K}{s^{2} (s + 2)}$