1
GATE ECE 2010
+2
-0.6
A unity negative feedback closed loop system has a plant with the transfer function $$G(s) = {1 \over {{s^2} + 2s + 2}}$$ and a controller $${G_c}(s)$$ in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady sate error is
A
$${G_C}\left( s \right) = {{s + 1} \over {s + 2}}$$
B
$${G_C}\left( s \right) = {{s + 2} \over {s + 1}}$$
C
$${G_C}\left( s \right) = {{\left( {s + 1} \right)\left( {s + 4} \right)} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$
D
$${G_C}\left( s \right) = 1 + {2 \over s} + {3_s}$$
2
GATE ECE 2010
+2
-0.6
The signal flow graph of a system is shown below.

The state variable representation of the system can be

A

$$\mathop x\limits^ \bullet = \left[ {\matrix{ 1 & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u$$
$$y = \left[ {\matrix{ 0 & {0.5} \cr } } \right]x$$
B
\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ { - 1} & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ 0 & {0.5} \cr } } \right]x \cr}
C
\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 1 & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ {0.5} & {0.5} \cr } } \right]x \cr}
D
\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ { - 1} & 1 \cr { - 1} & 0 \cr } } \right]x + \left[ {\matrix{ 0 \cr 2 \cr } } \right]u \cr & y = \left[ {\matrix{ {0.5} & {0.5} \cr } } \right]x \cr}
3
GATE ECE 2010
+2
-0.6
The signal flow graph of a system is shown below.

The transfer function of the system is

A
$${{s + 1} \over {{s^2} + 1}}$$
B
$${{s - 1} \over {{s^2} + 1}}$$
C
$${{s + 1} \over {{s^2} + s + 1}}$$
D
$${{s - 1} \over {{s^2} + s + 1}}$$
4
GATE ECE 2010
+1
-0.3
For the output F to be 1 in the logic circuit shown, the input combination should be
A
A = 1, B= 1. C = 0
B
A = 1, B= 0,C = 0
C
A = 0, B= 1. C = 0
D
A = 0, B= 0, C = 1
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