An unity feedback system is given as-Gs - K1-sss-3Indicate the correct root locus diagram

1+G(s)H(s)=0 K=s^2+3s1 s For break away and break in point dKds= (1 s)(2s+3)+s^2+3s=0 = s^2+2s+3=0 ⇒ s^2 2s 3=0 ⇒ (s 3)(s+1)=0 s=3, 1 1 is the breakaway point ...

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Question

An unity feedback system is given as,
$G (s) = \frac{K (1 - s)}{s (s + 3)}$
Indicate the correct root locus diagram

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Solution

The correct option is C
$1 + G (s) H (s) = 0$
$K = \frac{s^{2} + 3 s}{1 - s}$
For break away and break in point
$\frac{d K}{d s} = (1 - s) (2 s + 3) + s^{2} + 3 s = 0$
$= - s^{2} + 2 s + 3 = 0$
$\Rightarrow s^{2} - 2 s - 3 = 0$
$\Rightarrow (s - 3) (s + 1) = 0$
$s = 3, - 1$
$- 1$ is the breakaway point and $3$ is the breakaway point

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An unity feedback system is given as, G(s)=K(1−s)s(s+3) Indicate the correct root locus diagram

The correct option is C 1+G(s)H(s)=0 K=s2+3s1−s For break away and break in point dKds=(1−s)(2s+3)+s2+3s=0 =−s2+2s+3=0 ⇒s2−2s−3=0 ⇒(s−3)(s+1)=0 s=3,−1 −1 is the breakaway point and 3 is the breakaway point

An unity feedback system is given as,
$G (s) = \frac{K (1 - s)}{s (s + 3)}$
Indicate the correct root locus diagram