1
GATE EE 2017 Set 2
+2
-0.6
The root locus of the feedback control system having the characteristic equation $${s^2} + 6Ks + 2s + 5 = 0$$ where $$K>0,$$ enters into the real axis at
A
$$s=-1$$
B
$$s = - \sqrt 5$$
C
$$s=-5$$
D
$$s = \sqrt 5$$
2
GATE EE 2015 Set 2
+2
-0.6
An open loop transfer function $$G(s)$$ of system is $$G\left( s \right) = {k \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

A
$$-0.42$$
B
$$-1.58$$
C
$$0.42$$ and $$-1.58$$
D
none of the above.
3
GATE EE 2011
+2
-0.6
The open loop transfer function $$G(s)$$ of a unity feedback control system is given as, $$G\left( s \right) = {{k\left( {s + {2 \over 3}} \right)} \over {{s^2}\left( {s + 2} \right)}}.\,\,$$ From the root locus, it can be inferred that when $$k$$ tends to positive infinity
A
three roots with nearly equal real parts exist on the left half of the $$s$$-plane
B
one real root is found on the right half of the $$s$$-plane
C
the root loci cross the $$j\omega$$ axis for a finite value of $$k;k \ne 0$$
D
three real roots are found on the right half of the $$s$$-plane
4
GATE EE 2010
+2
-0.6
The characteristic equation of a closed-loop system is $$s\left( {s + 1} \right)\left( {s + 3} \right) + \,\,k\left( {s + 2} \right) = 0,\,\,k > 0.$$

Which of the following statements is true?

A
Its roots are always real
B
It cannot have a breakaway point in the range $$- 1 < {\mathop{\rm Re}\nolimits} \left[ s \right] < 0$$
C
Two of its roots tend to infinity along the asymptotes $${\mathop{\rm Re}\nolimits} \left[ s \right] = - 1$$
D
It may have complex roots in the right half plane
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