1
GATE EE 2017 Set 1
+2
-0.6
In the system whose signal flow graph is shown in the figure, $${{U_1}\left( s \right)}$$ and $${{U_2}\left( s \right)}$$ are inputs. The transfer function $${{Y\left( s \right)} \over {{U_1}\left( s \right)}}\,$$ is
A
$${{{k_1}} \over {JL{s^2} + JRs + {k_1}{k_2}}}$$
B
$${{{k_1}} \over {JL{s^2} - JRs - {k_1}{k_2}}}$$
C
$${{{k_1} - {U_2}\left( {R + sL} \right)} \over {JL{s^2} + \left( {JR - {U_2}L} \right)s + {k_1}{k_2} - {U_2}R}}$$
D
$${{{k_1} - {U_2}\left( {sL - R} \right)} \over {JL{s^2} - \left( {JR + {U_2}L} \right)s - {k_1}{k_2} + {U_2}R}}$$
2
GATE EE 2015 Set 1
+2
-0.6
Find the transfer function $${{Y\left( s \right)} \over {X\left( s \right)}}$$ of the system given below:
A
$${{{G_1}} \over {1 - H{G_1}}} + {{{G_2}} \over {1 - H{G_2}}}$$
B
$${{{G_1}} \over {1 + H{G_1}}} + {{{G_2}} \over {1 + H{G_2}}}$$
C
$${{{G_1} + {G_2}} \over {1 + H\left( {{G_1} + {G_2}} \right)}}$$
D
$${{{G_1} + {G_2}} \over {1 - H\left( {{G_1} + {G_2}} \right)}}$$
3
GATE EE 2014 Set 3
+2
-0.6
The block diagram of a system is shown in the figure

If the desired transfer function of the system is $${{C\left( s \right)} \over {R\left( s \right)}}\, = {s \over {{s^2} + s + 1}},$$ then $$G(s)$$ is

A
$$1$$
B
$$s$$
C
$$1/s$$
D
$${{ - s} \over {{s^3} + {s^2} - s - 2}}$$
4
GATE EE 2013
+2
-0.6
The signal flow graph for a system is given below. The transfer function $${{Y\left( s \right)} \over {U\left( s \right)}}$$ for this system is
A
$${{s + 1} \over {5{s^2} + 6s + 2}}$$
B
$${{s + 1} \over {{s^2} + 6s + 2}}$$
C
$${{s + 1} \over {{s^2} + 4s + 2}}$$
D
$${1 \over {5{s^2} + 6s + 2}}$$
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