1
GATE EE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{
{ - 1} & 1 \cr
0 & { - 3} \cr
} } \right]\,\,Q = \left[ {\matrix{
0 \cr
1 \cr
} } \right]$$
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:
2
GATE EE 2013
MCQ (Single Correct Answer)
+2
-0.6
The state variable formulation of a system is given as
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$
The system is
3
GATE EE 2013
MCQ (Single Correct Answer)
+2
-0.6
The state variable formulation of a system is given as
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$
The response $$y(t)$$ to a unit step input is
4
GATE EE 2012
MCQ (Single Correct Answer)
+2
-0.6
The state variable description of an $$LTI$$ system is given by
$$$\left( {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\limits^ \bullet } \cr
{\mathop {{x_3}}\limits^ \bullet } \cr
} } \right) = \left( {\matrix{
0 & {{a_1}} & 0 \cr
0 & 0 & {{a_2}} \cr
{{a_3}} & 0 & 0 \cr
} } \right)\left( {\matrix{
{{x_1}} \cr
{{x_2}} \cr
{{x_3}} \cr
} } \right) + \left( {\matrix{
0 \cr
0 \cr
1 \cr
} } \right)u,$$$
$$$y = \left( {\matrix{
1 & 0 & 0 \cr
} } \right)\left( {\matrix{
{{x_1}} \cr
{{x_2}} \cr
{{x_3}} \cr
} } \right)$$$
where $$y$$ is the output and $$u$$ is the input. The system is controllable for
Questions Asked from State Variable Analysis (Marks 2)
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GATE EE 2023 (1)
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GATE EE Subjects
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics