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Control Systems

Break Points

The root locu...

Question

The root locus of the feedback control system having the characteristic equation,
$s^{2} + 6 K s + 2 s + 5 = 0$

Where K>0, enters into the real axis at

s = - 1

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s = - \sqrt{5}

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s = - 5

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s = \sqrt{5}

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Solution

The correct option is B $s = - \sqrt{5}$
$G (s) H (s) = \frac{6 K s}{s^{2} + 2 s + 5}$

The point at which root locus enters real axis (breakway point) is given by

$\frac{d K}{d s} = 0$

$K = - \frac{(s^{2} + 2 s + 5)}{6 s}$

$\frac{d K}{d s} = 0 \Rightarrow s = \pm \sqrt{5}$

$∴ s = - \sqrt{5}$

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The root locus of the feedback control system having the characteristic equation, s2+6Ks+2s+5=0 Where K>0, enters into the real axis at

The correct option is B s=−√5G(s)H(s)=6Kss2+2s+5 The point at which root locus enters real axis (breakway point) is given by dKds=0 K=−(s2+2s+5)6s dKds=0⇒s=±√5 ∴s=−√5

The root locus of the feedback control system having the characteristic equation,
$s^{2} + 6 K s + 2 s + 5 = 0$

Where K>0, enters into the real axis at

The correct option is B $s = - \sqrt{5}$
$G (s) H (s) = \frac{6 K s}{s^{2} + 2 s + 5}$

The point at which root locus enters real axis (breakway point) is given by

$\frac{d K}{d s} = 0$

$K = - \frac{(s^{2} + 2 s + 5)}{6 s}$

$\frac{d K}{d s} = 0 \Rightarrow s = \pm \sqrt{5}$

$∴ s = - \sqrt{5}$