1
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
$$\left( {\matrix{ {{e^{3t}}} & {{e^{ - 2t}} - {e^{ - 3t}}} \cr 0 & {{e^{ - 2t}}} \cr } } \right)$$
2
GATE EE 2008
+2
-0.6
The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input, $$Y$$ is output and $$A = \left( {\matrix{ 0 & 1 \cr 0 & { - 2} \cr } } \right)\,\,B = \left( {\matrix{ 0 \cr 1 \cr } } \right)\,\,C = \left[ {\matrix{ 1 & 0 \cr } } \right]$$$The transfer function $$G(s)$$ of this system will be A $${s \over {\left( {s + 2} \right)}}$$ B $${{s + 1} \over {s\left( {s - 2} \right)}}$$ C $${s \over {\left( {s - 2} \right)}}$$ D $${1 \over {s\left( {s + 2} \right)}}$$ 3 GATE EE 2008 MCQ (Single Correct Answer) +2 -0.6 The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input, $$Y$$ is output and $$A = \left( {\matrix{ 0 & 1 \cr 0 & { - 2} \cr } } \right)\,\,B = \left( {\matrix{ 0 \cr 1 \cr } } \right)\,\,C = \left[ {\matrix{ 1 & 0 \cr } } \right]$$$

A unity feedback is provided to the above system $$G(s)$$ to make it a closed loop system as shown in figure.

For a unit step input $$r(t),$$ the steady state error in the input will be

A
$$0$$
B
$$1$$
C
$$2$$
D
$$\infty$$
4
GATE EE 2005
+2
-0.6
A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \right)u\left( t \right)$$ with the initial condition $$X\left( 0 \right) = {\left[ { - 1\,\,3} \right]^T}$$ and the unit step input $$u(t)$$ has

The state transition matrix

A
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {1 - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
B
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {{e^{ - t}} - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - t}}} \cr } } \right)$$
C
$$\left( {\matrix{ 1 & {{1 \over 3}\left( {{e^{ - t}} - {e^{ - 3t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
D
$$\left( {\matrix{ 1 & {\left( {1 - {e^{ - t}}} \right)} \cr 0 & {{e^{ - 3t}}} \cr } } \right)$$
GATE EE Subjects
Electromagnetic Fields
Signals and Systems
Engineering Mathematics
General Aptitude
Power Electronics
Power System Analysis
Analog Electronics
Control Systems
Digital Electronics
Electrical Machines
Electric Circuits
Electrical and Electronics Measurement
EXAM MAP
Joint Entrance Examination