1
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t \right) + 2u\left( t \right)$$$ $$${{d{x_2}\left( t \right)} \over {dt}} = - 2{x_2}\left( t \right) + u\left( t \right)$$$

$$y\left( t \right) = {x_1}\left( t \right)$$ when $$u(t)$$ is the input and $$y(t)$$ is the output

The state $$-$$ transition matrix of the above system is

A
$$\left( {\matrix{ {{e^{ - 3t}}} & 0 \cr {{e^{ - 2t}} + {e^{ - 3t}}} & {{e^{ - 2t}}} \cr } } \right)$$
B
$$\left( {\matrix{ {{e^{ - 3t}}} & {{e^{ - 2t}} - {e^{ - 3t}}} \cr 0 & {{e^{ - 2t}}} \cr } } \right)$$
C
$$\left( {\matrix{ {{e^{ - 3t}}} & {{e^{ - 2t}} + {e^{ - 3t}}} \cr 0 & {{e^{ - 2t}}} \cr } } \right)$$
D
$$\left( {\matrix{ {{e^{3t}}} & {{e^{ - 2t}} - {e^{ - 3t}}} \cr 0 & {{e^{ - 2t}}} \cr } } \right)$$
2
GATE EE 2009
MCQ (Single Correct Answer)
+1
-0.3
Errors associated with each respective subsystem $$\,{G_1},\,{G_2}$$ and $${G_3}$$ are $${\varepsilon _1},\,\,{\varepsilon _2}$$ and $${\varepsilon _3}$$. The error associated with the output is : GATE EE 2009 Control Systems - Basics of Control System Question 1 English
A
$${\varepsilon _1} - {\varepsilon _2} + {\varepsilon _3}$$
B
$${\varepsilon _1}{\varepsilon _2}/{\varepsilon _4}$$
C
$${\varepsilon _1} + {\varepsilon _2} - {\varepsilon _3}$$
D
$${\varepsilon _1} + {\varepsilon _2} + {\varepsilon _3}$$
3
GATE EE 2009
MCQ (Single Correct Answer)
+1
-0.3
The first two rows of Routh's tabulation of a third order equation are as follows $$$\left. {\matrix{ {{s^3}} \cr {{s^2}} \cr } } \right|\matrix{ 2 & 2 \cr 4 & 4 \cr } $$$
this means there are

A
two roots at $$s$$ $$ = \pm j$$ and one root in right half $$s$$ - plane
B
two roots at $$s$$ $$ = \pm j2$$ and one root in left half $$s$$ - plane
C
two roots at $$s$$ $$ = \pm j2$$ and one root in right half $$s$$ - plane
D
two roots at $$s$$ $$ = \pm j$$and one root in left half $$s$$ - plane
4
GATE EE 2009
MCQ (Single Correct Answer)
+2
-0.6
The unit - step response of a unity feedback system with open loop transfer function $$G\left( s \right) = {K \over {\left( {s + 1} \right)\left( {s + 2} \right)}}$$ is shown in the figure. The value of $$K$$ is GATE EE 2009 Control Systems - Time Response Analysis Question 8 English
A
$$0.5$$
B
$$2$$
C
$$4$$
D
$$6$$
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