The feedback configuration and the pole-zero location of $$G(s) = frac{s^2 - 2s + 2}{s^2 + 2s + 2}$$ are shown below. The root locus for Negative values of K, i.e., for –∞ < K < 0, has breakaway/break-in points and angle of departure at pole P (with respect to the positive real axis) equal to (GATE 2009 || EC || MCQ||2 MARK)

$$ pm sqrt{2} ext{ and } 45^ circ$$

$$ pm sqrt{2} ext{ and } 0^ circ$$

$$ pm sqrt{3} ext{ and } 0^ circ$$

$$ pm sqrt{3} ext{ and } 45^ circ$$

GATE EC|| CONTROL SYSTEM || ROOT LOCUS|| PYQS(2000-2025)

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Question 1

The root-locus diagram for a closed-loop feedback system is shown in the figure. The system is overdamped.

( GATE 2020 || EC || MCQ||1 MARK)

only if 0 ≤ K ≤ 1
only if 1 < K < 5
only if K > 5
if 0 ≤ K < 1 or K > 5

Question 2

Which of the following points is NOT on the root locus of a system with the open-loop transfer function

[Tex]G(s)H(s) = \frac{K}{s(s + 1)(s + 3)}[/Tex]
( GATE 2020 || EC || MCQ||1 MARK)

[Tex]s = -j\sqrt{3}[/Tex]
[Tex]s = -1.5[/Tex]
[Tex]s = -3[/Tex]
[Tex]s = -\infty[/Tex]

Question 3

Given [Tex]G(s)H(s) = \frac{K}{s(s + 1)(s + 3)}[/Tex], the point of intersection

of the asymptotes of the root loci with the real axis
( GATE 2004 || EC || MCQ||1 MARK)

-4
1.33
-1.33
4

Question 4

A unity feedback system is given as.

[Tex]G(s) = \frac{K(1 - s)}{s(s + 3)}[/Tex]

Indicate the correct root locus diagram

( GATE 2004 || EC || MCQ||2 MARK)

Question 5

The feedback configuration and the pole-zero location of [Tex]G(s) = \frac{s^2 - 2s + 2}{s^2 + 2s + 2}[/Tex]

are shown below. The root locus for Negative values of K, i.e., for –∞ < K < 0, has breakaway/break-in points and angle of departure at pole P (with respect to the positive real axis) equal to

(GATE 2009 || EC || MCQ||2 MARK)

[Tex]\pm \sqrt{2} \text{ and } 0^\circ[/Tex]
[Tex]\pm \sqrt{2} \text{ and } 45^\circ[/Tex]
[Tex]\pm \sqrt{3} \text{ and } 0^\circ[/Tex]
[Tex]\pm \sqrt{3} \text{ and } 45^\circ[/Tex]

Question 6

A unity feedback control system has an open-loop transfer function

[Tex]G(s) = \frac{K}{s(s^2 + 7s + 12)}[/Tex]

The gain K for which [Tex]s = -1 + j1[/Tex] will lie on the root locus

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

Question 7

The root locus plot for a system is given below. The open-loop transfer function corresponding to this plot is
given by

(GATE 2011 || EC || MCQ||1 MARK)

[Tex]G(s)H(s) = K \frac{s(s + 1)}{(s + 2)(s + 3)}[/Tex]
[Tex]G(s)H(s) = K \frac{(s + 1)}{s(s + 2)(s + 3)^2}[/Tex]
[Tex]G(s)H(s) = K \frac{1}{s(s - 1)(s + 2)(s + 3)}[/Tex]
[Tex]G(s)H(s) = K \frac{(s + 1)}{s(s + 2)(s + 3)}[/Tex]

Question 8

In the root locus plot shown in the figure, the pole/ zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?

( GATE 2014 || EC || MCQ||1 MARK)

[Tex]\frac{s + 1}{(s + 2)(s + 4)(s + 7)}[/Tex]
[Tex]\frac{s + 4}{(s + 1)(s + 2)(s + 7)}[/Tex]
[Tex]\frac{s + 7}{(s + 1)(s + 2)(s + 4)}[/Tex]
[Tex]\frac{(s + 1)(s + 2)}{(s + 7)(s + 4)}[/Tex]

Question 9

A unity negative feedback system has the open-loop transfer function [Tex]G(s) = \frac{K}{s(s + 1)(s + 3)}[/Tex] The value of the gain K(>0 ) at which the root locus crosses the imaginary axis is ______.

( GATE 2015 || EC || NAT||1 MARK)

Question 10

The open-loop transfer function of a unity-feedback control system is

[Tex]G(s) = \frac{K}{s^2 + 5s + 5}[/Tex]

The value of K at the breakaway point of the feedback control system's root-locus plot is

( GATE 2016 || EC || NAT||2 MARK)

1.25

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