1
GATE EE 2012
+2
-0.6
The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

$${G_c}\left( s \right)$$ is a lead compensator if

A
$$a = 1,b = 2$$
B
$$a = 3,b = 2$$
C
$$a = -3,b = -1$$
D
$$a = 3,b = 1$$
2
GATE EE 2012
+2
-0.6
The transfer function of a compensator is given as $${G_c}\left( s \right) = {{s + a} \over {s + b}}$$

The phase of the above lead compensator is maximum at

A
$$\sqrt 2 \,rad/s$$
B
$$\sqrt 3 \,rad/s$$
C
$$\sqrt 6 \,rad/s$$
D
$$1/$$ $$\sqrt 3 \,rad/s$$
3
GATE EE 2008
+2
-0.6
The transfer function of two compensators are given below: $${C_1} = {{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}},\,{C_2} = {{s + 10} \over {10\left( {s + 1} \right)}}$$

Which one of the following statements is correct?

A
$${C_1}$$ is lead compensator and $${C_2}$$ is a lag compensator
B
$${C_1}$$ is a lag compensator and $${C_2}$$ is a lead compensator
C
Both $${C_1}$$ and $${C_2}$$ are lead compensator
D
Both $${C_1}$$ and $${C_2}$$ are lag compensator
4
GATE EE 2007
+2
-0.6
The system $$900/s(s+1)(s+9)$$ is to be such that its gain crossover frequency becomes same as its uncompensated phase crossover frequency and provides at $${45^0}$$ phase margin . To achieve this, one may use
A
a lag compensator that provides an attenuation of $$20dB$$ and a phase lag of $${45^0}$$ at the frequency of $$3\sqrt 3$$ rad/s
B
a lead compensator that provides an amplification of $$20dB$$ and a phase lead of $${45^0}$$ at the frequency of $$3$$ rad/s
C
a lag - lead compensator that provides an amplification of $$20dB$$ and a phase alg of $${45^0}$$ at the frequency of $$\sqrt 3$$ rad/s
D
a lag - lead compensator that provides an attenuation of $$20dB$$ and phase lead of $${45^0}$$ at the frequency of $$3$$ rad/s
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