1
GATE EE 1991
Subjective
+5
-0
A unity feedback system has the forward loop transfer function $$G\left( s \right) = {{K{{\left( {s + 2} \right)}^2}} \over {{s^2}\left( {s - 1} \right)}}$$

(a) Determine the range of $$K$$ for stable operation

(b) Determine the imaginary axis crossover points

(c) Without calculating the real axis break - away points, sketch the form of root loci for the system.

2
GATE EE 1991
MCQ (More than One Correct Answer)
+1
-0.3
The system having the Bode magnitude plot shown in Fig. below has the transfer function
A
$${{60\left( {s + 0.01} \right)\left( {s + 0.1} \right)} \over {{s^2}{{\left( {s + 0.05} \right)}^2}}}$$
B
$${{10\left( {1 + 10s} \right)} \over {s\left( {1 + 20s} \right)}}$$
C
$${{3\left( {s + 0.05} \right)} \over {s\left( {s + 0.1} \right)\left( {s + 1} \right)}}$$
D
$${{5\left( {s + 0.1} \right)} \over {s\left( {s + 0.05} \right)}}$$
3
GATE EE 1991
+1
-0.3
Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below.
A
$${K \over {s{{\left( {s + 2} \right)}^2}\left( {s + 5} \right)}}$$
B
$${K \over {{s^2}\left( {s + 2} \right)\left( {s + 5} \right)}}$$
C
$${{K\left( {s + 1} \right)} \over {{s^2}\left( {s + 2} \right)\left( {s + 5} \right)}}$$
D
$${{K\left( {s + 1} \right)\left( {s + 3} \right)} \over {{s^2}\left( {s + 2} \right)\left( {s + 5} \right)}}$$
4
GATE EE 1991
Numerical
+2
-0
An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\,\,$$ has frequency response plot shown in Fig. below, then the system gain $$K$$ is __________ and the damping factor is approximately _______
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