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# Stability Theory – 1 – 1

1. The loop transfer function of a feedback control system is given by

$\dpi{100} G(s) H(s) = k/{s (s + 2) (s^2 + 2s + 2)}$

Number of asymptotes of its root loci is :

(a) 1
(b) 2
(c) 3
(d) 4

Explanation
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2. A unity feedback system has

$\dpi{100} G(s) = k/{s (s + 1) (s + 2)}$

In the root-locus, the break-away point occurs between :

(a) s = 0 and -1
(b) s = -1 and -∞
(c) s = -1 and -2
(d) s = -2 and -∞

Explanation
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3. If the characteristic equation of a closed-loop system is

$\dpi{100} 1+{k/s(s + l)(s + 2)} = 0$

the centroid of the asymptotes in root-locus will be :

(a) zero
(b) 2
(c) – 1
(d) – 2

Explanation
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4. The intersection of root locus branches with the imaginary axis can be determined by the use of :

(a) nyquist criterion
(b) polar plot
(c) routh’s criterion
(d) none of the above

Explanation
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5. The characteristic equation of a feedback control system is

$2s^4 + s^3 + 3s^2 + 5s + 10 = 0$

The number of roots in the right half of s-plane are :

(a) zero
(b) 1
(c) 2
(d) 3