1
GATE EE 2003
+2
-0.6
The following equation defines a separately exited $$dc$$ motor in the form of a differential equation $${{{d^2}\omega } \over {d{t^2}}} + {{B\,d\omega } \over {j\,\,dt}} + {{{K^2}} \over {LJ}}\omega = {K \over {LJ}}{V_a}$$

The above equation may be organized in the state space form as follows
$$\left( {\matrix{ {{{{d^2}\omega } \over {d{t^2}}}} \cr {{{d\omega } \over {dt}}} \cr } } \right) = P\left( {\matrix{ {{{d\omega } \over {dt}}} \cr \omega \cr } } \right) + Q{V_a}$$

where the $$P$$ matrix is given by

A
$$\left( {\matrix{ { - {B \over J}} & { - {{{K^2}} \over {LJ}}} \cr 1 & 0 \cr } } \right)$$
B
$$\left( {\matrix{ { - {{{K^2}} \over {LJ}}} & { - {B \over J}} \cr 0 & 1 \cr } } \right)$$
C
$$\left( {\matrix{ 0 & 1 \cr { - {{{K^2}} \over {LJ}}} & { - {B \over J}} \cr } } \right)$$
D
$$\left( {\matrix{ 1 & 0 \cr { - {B \over J}} & { - {{{K^2}} \over {LJ}}} \cr } } \right)$$
2
GATE EE 2002
+2
-0.6
For the system $$X = \left[ {\matrix{ 2 & 3 \cr 0 & 5 \cr } } \right]X + \left[ {\matrix{ 1 \cr 0 \cr } } \right]u,$$ Which of the following statement is true?
A
The system is controllable but unstable
B
The system is uncontrollable and unstable
C
The system is controllable and stable
D
The system is uncontrollable and stable
3
GATE EE 2002
+2
-0.6
For the system $$\mathop X\limits^ \bullet = \left[ {\matrix{ 2 & 0 \cr 0 & 4 \cr } } \right]X + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u;\,\,\,y = \left[ {\matrix{ 4 & 0 \cr } } \right]X,\,$$ with u as unit impulse and with zero initial state, the output, $$y$$, becomes
A
$$2{e^{2t}}$$
B
$$4{e^{2t}}$$
C
$$2{e^{4t}}$$
D
$$4{e^{4t}}$$
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
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