1
GATE EE 2002
MCQ (Single Correct Answer)
+2
-0.6
The transfer function of the system described by $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} = {{du} \over {dt}} + 2u$$ with $$u$$ as input and $$y$$ as output is
A
$${{\left( {s + 2} \right)} \over {\left( {{s^2} + s} \right)}}$$
B
$${{\left( {s + 1} \right)} \over {\left( {{s^2} + s} \right)}}$$
C
$${2 \over {\left( {{s^2} + s} \right)}}$$
D
$${{2s} \over {\left( {{s^2} + s} \right)}}$$
2
GATE EE 2002
MCQ (Single Correct Answer)
+2
-0.6
A unity feedback system has an open loop transfer function, $$G\left( s \right) = {K \over {{s^2}}}.$$ The root locus plot is
A
GATE EE 2002 Control Systems - Root Locus Techniques Question 12 English Option 1
B
GATE EE 2002 Control Systems - Root Locus Techniques Question 12 English Option 2
C
GATE EE 2002 Control Systems - Root Locus Techniques Question 12 English Option 3
D
GATE EE 2002 Control Systems - Root Locus Techniques Question 12 English Option 4
3
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
4
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 $$\left[ {{{\left( {s{\rm I} - A} \right)}^{ - 1}}X\left( 0 \right)} \right]$$
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