1
GATE EE 2009
+1
-0.3
The polar plot of an open loop stable system is shown below. The closed loop systems is
A
always stable
B
marginally stable
C
unstable with one pole on the $$RH$$ $$s-$$plane
D
unstable with two poles on the $$RH$$ $$s-$$ plane
2
GATE EE 2009
+2
-0.6
The asymptotic approximation of the log magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function is
A
$${{10\left( {s + 5} \right)} \over {s\left( {s + 2} \right)\left( {s + 25} \right)}}$$
B
$${{1000\left( {s + 5} \right)} \over {{s^2}\left( {s + 2} \right)\left( {s + 25} \right)}}$$
C
$${{100\left( {s + 5} \right)} \over {s\left( {s + 2} \right)\left( {s + 25} \right)}}$$
D
$${{80\left( {s + 5} \right)} \over {{s^2}\left( {s + 2} \right)\left( {s + 25} \right)}}$$
3
GATE EE 2009
+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 system transfer function is

A
$${{s + 2} \over {{s^2} + 5s - 6}}$$
B
$${{s + 3} \over {{s^2} + 5s + 6}}$$
C
$${{2s + 5} \over {{s^2} + 5s + 6}}$$
D
$${{2s - 5} \over {{s^2} + 5s + 6}}$$
4
GATE EE 2009
+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
$$\left( {\matrix{ {{e^{3t}}} & {{e^{ - 2t}} - {e^{ - 3t}}} \cr 0 & {{e^{ - 2t}}} \cr } } \right)$$
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