The transfer function of a compensator is given as: $$G_{ ext{c}}(s) = frac{s + a}{s + b} $$ The phase of the above lead compensator is maximum at( GATE 2012 || EC || MCQ ||2 MARK)

$$ frac{1}{ sqrt{3}} ext{ rad/s} $$

GATE EC|| CONTROL SYSTEM || COMPENSATOR|| PYQS(2000-2025)

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Question 1

Which of the following statements is incorrect?
(GATE 2017 || EC || MCQ ||1 MARK)

Lead compensator is used to reduce the settling time.
Lag compensator is used to reduce the steady-state error.
Lead compensator may increase the order of a system.
Lag compensator always stabilize an unstable system.

Question 2

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?
( GATE 2017 || EC || MCQ ||1 MARK)

Question 3

For the following feedback system [Tex]G(s) = \frac{1}{(s+1)(s+2)}. [/Tex] The 2% settling time of the step response is required to be less than 2 seconds.

Which one of the following compensators C(s) achieves this?
(GATE 2014 || EC || MCQ ||2 MARK)

[Tex]3\left(\frac{1}{s+5}\right) [/Tex]
[Tex]5\left(\frac{0.03}{s}+1\right) [/Tex]
[Tex]2(s+4)[/Tex]
[Tex]4\left(\frac{s+8}{s+3}\right) [/Tex]

Question 4

The transfer function of a compensator is given as:

[Tex]G_{\text{c}}(s) = \frac{s + a}{s + b} [/Tex]

The phase of the above lead compensator is maximum at

( GATE 2012 || EC || MCQ ||2 MARK)

[Tex]\sqrt{2} \text{ rad/s} [/Tex]
[Tex]\sqrt{3} \text{ rad/s} [/Tex]
[Tex]\sqrt{6} \text{ rad/s} [/Tex]
[Tex]\frac{1}{\sqrt{3}} \text{ rad/s} [/Tex]

Question 5

The transfer function of a compensator is given as:

[Tex]G_{\text{c}}(s) = \frac{s + a}{s + b} [/Tex]

[Tex]G_{\text{c}}(s)[/Tex] is a lead compensator if

( GATE 2012 || EC || MCQ ||2 MARK)

a = 1, b = 2
a = 3, b = 2
a = –3, b = –1
a = 3, b = 1

Question 6

The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot?

( GATE 2009 || EC || MCQ ||1 MARK)

Lead compensator
Lag compensator
PID controller
Lead-Lag compensator

Question 7

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition R₂C₂ > R₁C₁. The transfer function

represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II.

(GATE 2008 || EC || MCQ ||2 MARK)

Group I

Group II

1. PID Controller

2. Lead Compensator

3. Lag Compensator

Q – 1, R – 2
Q – 1, R – 3
Q – 2, R – 3
Q – 3, R – 2

Question 8

The open-loop transfer function of a plant is given as [Tex]G(s) = \frac{1}{s^2 - 1} [/Tex] . If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control is

(GATE 2007 || EC || MCQ ||2 MARK)

[Tex]\frac{10(s-1)}{(s+2)} [/Tex]
[Tex]\frac{10(s+4)}{(s+2)} [/Tex]
[Tex]\frac{10(s+4)}{(s+1)} [/Tex]
[Tex]\frac{10(s+2)}{(s+10)} [/Tex]

Question 9

The transfer function of a phase-lead compensator is given by

[Tex]G_{\text{c}}(s) = \frac{1 + 3Ts}{1 + Ts} [/Tex] where T > 0

The maximum phase-shift provided by such a compensator is:

[Tex]\frac{\pi}{2} [/Tex]
[Tex]\frac{\pi}{3} [/Tex]
[Tex]\frac{\pi}{4} [/Tex]
[Tex]\frac{\pi}{6} [/Tex]

Question 10

Which one of the following polar diagrams corresponds to a lag network?
(GATE 2005 || EC || MCQ ||2 MARK)

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