In a control system with unity gain feedback- the plant has the transfer fucntion Ps-3s- Assuming that a controller of the form Cs-Ks-p is used- where K is positive constant- the value of p for which the root-locus of the closed-loop system passes through the points -3- j3-3 where j-1- is

OLTF=3ks(s+p) Given root locus passes through the point nbsp; 3± j3√(3) ∴∠ G(s)H(s)_s= 3+j3√(3)=± 180^o ∴ P=6 ...

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Control Systems

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In a control system with unity gain feedback, the plant has the transfer fucntion $P (s) = \frac{3}{s} .$ Assuming that a controller of the form $C (s) = \frac{K}{(s + p)}$ is used, where K is positive constant, the value of p for which the root-locus of the closed-loop system passes through the points $- 3 \pm j 3 \sqrt{(} 3)$ where $j = \sqrt{(} - 1), i s$

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3 \sqrt{3}

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Solution

The correct option is C 6
$O L T F = \frac{3 k}{s (s + p)}$
Given root locus passes through the point
$- 3 \pm j 3 \sqrt{3}$
$∴ ∠ G (s) H (s)_{s = - 3 + j 3 \sqrt{3}} = \pm 180^{o}$
$∴ P = 6$

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The correct option is C 6OLTF=3ks(s+p) Given root locus passes through the point −3±j3√3 ∴∠G(s)H(s)s=−3+j3√3=±180o ∴P=6

The correct option is C 6
$O L T F = \frac{3 k}{s (s + p)}$
Given root locus passes through the point
$- 3 \pm j 3 \sqrt{3}$
$∴ ∠ G (s) H (s)_{s = - 3 + j 3 \sqrt{3}} = \pm 180^{o}$
$∴ P = 6$