1
GATE EE 2000
MCQ (Single Correct Answer)
+1
-0.3
A linear time-invariant system initially at rest, when subjected to a unit-step input, gives a response $$y\left( t \right) = t{e^{ - t}},\,\,t > 0.$$ The transfer function of the system is:
A
$${1 \over {{{\left( {s + 1} \right)}^2}}}$$
B
$${1 \over {s{{\left( {s + 1} \right)}^2}}}$$
C
$${s \over {{{\left( {s + 1} \right)}^2}}}$$
D
$${1 \over {s\left( {s + 1} \right)}}$$
2
GATE EE 2000
MCQ (Single Correct Answer)
+1
-0.3
A unity feedback system has open loop transfer function $$G(s).$$ The steady-state error is zero for
A
step input and type $$–1$$ $$G(s)$$
B
ramp input and type $$–1$$ $$G(s)$$
C
step input and type $$-$$ $$G(s)$$
D
ramp input and type $$-$$ $$0$$ $$G(s)$$
3
GATE EE 2000
MCQ (Single Correct Answer)
+2
-0.6
A unity feedback system has open-loop transfer function $$G\left( s \right) = {{25} \over {s\left( {s + 6} \right)}}.$$ The peak overshoot in the step-input response of the system is approximately equal to
A
$$5\%$$
B
$$10\%$$
C
$$15\%$$
D
$$20\%$$
4
GATE EE 2000
Subjective
+5
-0
A unity feedback system has open loop transfer function $$G\left( s \right) = {{K\left( {s + 5} \right)} \over {s\left( {s + 2} \right)}};K \ge 0$$
(a) Draw a rough sketch of the root locus plot; given that the complex roots ofthe characteristic equation move along a circle.
(b) As K increases, does the system become less stable? Justify your answer.
(c) Find the value of $$K$$ (if it exists) so that the damping $$\xi$$ of the complex closed loop poles is $$0.3.$$
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