1
GATE EE 2022
+1
-0.33

The open loop transfer function of a unity gain negative feedback system is given as

$$G(s) = {1 \over {s(s + 1)}}$$

The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point ($$-$$1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to

A
0
B
1
C
2
D
3
2
GATE EE 2017 Set 1
+1
-0.3
The transfer function of a system is given by $${{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}} = {{1 - s} \over {1 + s}}$$

Let the output of the system be $${v_0}\left( t \right) = {v_m}\sin \left( {\omega t + \phi } \right)$$ for the input $${v_i}\left( t \right) = {v_m}\sin \left( {\omega t} \right).$$ Then the minimum and maximum values of ϕ (in radians) are respectively

A
$${{ - \pi } \over 2}\,$$ and $${{ \pi } \over 2}\,$$
B
$${{ - \pi } \over 2}\,$$ and $$0$$
C
$$0$$ and $${{ \pi } \over 2}\,$$
D
$${ - \pi }$$ and $$0$$
3
GATE EE 2017 Set 1
Numerical
+1
-0
Consider the unity feedback control system shown. The value of $$K$$ that results in a phase margin of the system to be $${30^0}$$ is ____________. (Give the answer up to two decimal places).
4
GATE EE 2016 Set 1
+1
-0.3
The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\left( {2t + \phi } \right)$$ for the input $$\cos \left( {2t} \right).$$ The values of $$A$$ and $$\phi ,$$ respectively are
A
$${1 \over {\sqrt 2 }}, - {45^0}$$
B
$${1 \over {\sqrt 2 }}, + {45^0}$$
C
$$\sqrt 2 ,\, - {45^0}$$
D
$$\sqrt 2 ,\, + {45^0}$$
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