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Control Systems
Signal Flow Graph and Block Diagram
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Time Response Analysis
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Compensators
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Basic of Control Systems
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Frequency Response Analysis
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Stability
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Root Locus Diagram
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State Space Analysis
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1
GATE ECE 2007
MCQ (Single Correct Answer)
+2
-0.6
The state space representation of a separately excited DC servo motor dynamics is given as $$$\left[ {\matrix{ {{{d\omega } \over {dt}}} \cr {{{d{i_a}} \over {dt}}} \cr } } \right] = \left[ {\matrix{ { - 1} & 1 \cr { - 1} & { - 10} \cr } } \right]\left[ {\matrix{ \omega \cr {{i_a}} \cr } } \right] + \left[ {\matrix{ 0 \cr {10} \cr } } \right]u.$$$

Where 'ω' is the speed of the motor, 'ia' is the armature current and u is the armature voltage. The transfer function $${{\omega \left( s \right)} \over {U\left( s \right)}}$$ of the motor is

A
$${{10} \over {{s^2} + 11s + 11}}$$
B
$${1 \over {{s^2} + 11s + 11}}$$
C
$${{10s + 10} \over {{s^2} + 11s + 11}}$$
D
$${1 \over {{s^2} + s + 11}}$$
2
GATE ECE 2006
MCQ (Single Correct Answer)
+2
-0.6
A linear system is described by the following state equation $$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),A = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right].$$$
The state-transition matrix of the system is
A
$$\left[ {\matrix{ {\cos t} & {\sin t} \cr { - \sin t} & {\cos t} \cr } } \right]$$
B
$$\left[ {\matrix{ { - \cos t} & {\sin t} \cr { - \sin t} & { - \cos t} \cr } } \right]$$
C
$$\left[ {\matrix{ { - \cos t} & { - \sin t} \cr { - \sin t} & {\cos t} \cr } } \right]$$
D
$$\left[ {\matrix{ {\cos t} & { - \sin t} \cr {\cos t} & {\sin t} \cr } } \right]$$
3
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
Given A $$ = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the state transition matrix eAt is given by
A
$$\left[ {\matrix{ 0 & {{e^{ - t}}} \cr {{0^{ - t}}} & 0 \cr } } \right]$$
B
$$\left[ {\matrix{ {{e^t}} & 0 \cr 0 & {{e^t}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{e^{ - t}}} & 0 \cr 0 & {{e^{ - t}}} \cr } } \right]$$
D
$$\left[ {\matrix{ 0 & {{e^t}} \cr {{e^t}} & 0 \cr } } \right]$$
4
GATE ECE 2004
MCQ (Single Correct Answer)
+2
-0.6
If A = $$\left[ {\matrix{ { - 2} & 2 \cr 1 & { - 3} \cr } } \right],$$ then sin At is
A
$${1 \over 3}\left[ {\matrix{ {\sin \left( { - 4t} \right) + 2\sin \left( { - t} \right)} & { - 2\sin \left( { - 4t} \right) + 2\sin \left( { - t} \right)} \cr { - \sin \left( { - 4t} \right) + \sin \left( { - t} \right)} & {2\sin \left( { - 4t} \right) + \sin \left( { - t} \right)} \cr } } \right]$$
B
$$\left[ {\matrix{ {\sin \left( { - 2t} \right)} & {\sin \left( {2t} \right)} \cr {\sin \left( t \right)} & {\sin \left( { - 3t} \right)} \cr } } \right]$$
C
$${1 \over 3}\left[ {\matrix{ {\sin \left( {4t} \right) + 2\sin \left( t \right)} & {2\sin \left( { - 4t} \right) - 2\sin \left( { - t} \right)} \cr { - \sin \left( { - 4t} \right) + \sin \left( t \right)} & {2\sin \left( {4t} \right) + \sin \left( t \right)} \cr } } \right]$$
D
$${1 \over 3}\left[ {\matrix{ {\cos \left( { - t} \right) + 2\cos \left( t \right)} & {2\cos \left( { - 4t} \right) + 2\sin \left( { - t} \right)} \cr { - \cos \left( { - 4t} \right) + \sin \left( { - t} \right)} & { - 2\cos \left( { - 4t} \right) + \cos \left( { - t} \right)} \cr } } \right]$$
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GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics