A unity feedback control system has an open-loop transfer function Gs - Kss2-7s-12- The gain K for which s- -1-j1 will lie on the root locus of the system is

T.F. =G(s)1+G(s) As H(s) =1 For the point s= 1+j1 to lie on the root locus 1+G(s)=0 ⇒ 1+Ks(s^2+7s+12)=0 (s^2+7s+12)+K=0 Putting s= 1+j ( 1+j)(1 2j 1 7 ...

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Control Systems

Gain Calculation

A unity feedb...

Question

A unity feedback control system has an open-loop transfer function $G (s) = \frac{K}{s (s^{2} + 7 s + 12)} .$ The gain $K$ for which $s = - 1 + j 1$ will lie on the root locus of the system is

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Solution

The correct option is D $10$
$T . F . = \frac{G (s)}{1 + G (s)}$

$A s H (s) = 1$

For the point $s = - 1 + j 1$ to lie on the root locus $1 + G (s) = 0$

$\Rightarrow 1 + \frac{K}{s (s^{2} + 7 s + 12)} = 0$

$(s^{2} + 7 s + 12) + K = 0$

$P u t t i n g s = - 1 + j$

$(- 1 + j) (1 - 2 j - 1 - 7 - 7 j + 12) + K = 0$

$\Rightarrow K = + 10$

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A unity feedback control system has an open-loop transfer function G(s)=Ks(s2+7s+12). The gain K for which s=−1+j1 will lie on the root locus of the system is

The correct option is D 10T.F.=G(s)1+G(s) As H(s)=1 For the point s=−1+j1 to lie on the root locus 1+G(s)=0 ⇒1+Ks(s2+7s+12)=0 (s2+7s+12)+K=0 Putting s=−1+j (−1+j)(1−2j−1−7−7j+12)+K=0 ⇒K=+10

A unity feedback control system has an open-loop transfer function $G (s) = \frac{K}{s (s^{2} + 7 s + 12)} .$ The gain $K$ for which $s = - 1 + j 1$ will lie on the root locus of the system is