1
GATE EE 2002
Subjective
+5
-0
The open loop transfer function of a unity feedback system is given by $$G\left( s \right) = {{2\left( {s + \alpha } \right)} \over {s\left( {s + 2} \right)\left( {s + 10} \right)}}.$$ Sketch the root locus as $$\alpha $$ varies from $$0$$ to $$\infty $$. Find the angle and real axis intercept of the asymptotes, breakaway points and the imaginary axis crossing points, if any
2
GATE EE 2002
MCQ (Single Correct Answer)
+1
-0.3
The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is
A
$${\left( {s{\rm I} - A} \right)^{ - 1}}$$
B
$${e^{AT}}\,X\left( 0 \right)$$
C
Laplace inverse of $$\,\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}} \right]$$
D
Laplace inverse of $$\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}X\left( 0 \right)} \right]$$
3
GATE EE 2002
MCQ (Single Correct Answer)
+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
4
GATE EE 2002
MCQ (Single Correct Answer)
+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
$$4{e^{4t}}$$
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