1
GATE EE 2024
Numerical
+2
-1.33

Consider the closed-loop system shown in the figure with $$G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}.$$ The root locus for the closed-loop system is to be drawn for $0 \leq K < \infty$. The angle of departure (between $0^{o}$ and $360^{o})$ of the root locus branch drawn from the pole $(−1 + j2)$, in degrees, is _________________ (rounded off to the nearest integer).

GATE EE 2024 Control Systems - Root Locus Techniques Question 1 English
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2
GATE EE 2017 Set 2
MCQ (Single Correct Answer)
+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
$$s = \sqrt 5 $$
3
GATE EE 2015 Set 2
MCQ (Single Correct Answer)
+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.
4
GATE EE 2011
MCQ (Single Correct Answer)
+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
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