By performing cascading and/or summing differencing operations using transfer function block $$G_1(s)$$ and $$G_2(s)$$, one CANNOT realize a transfer function of the form(GATE 2015 || EC || MCQ ||2 MARK)

$$G_1(s) left( frac{1}{G_1(s)} + G_2(s) ight)$$

$$G_1(s) left( frac{1}{G_1(s)} - G_2(s) ight)$$

GATE || Control Systems || PYQs (2010 to 2025)

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Question 1

The equivalent of the block diagram in the figure is given as

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

Question 2

Despite the presence of negative feedback, control systems still have problems of instability because the

(GATE 2005 || EC || MCQ ||1 MARK)

Components used have nonlinearities
Dynamic equations of the systems are not known exactly
Mathematical analysis involves approximations
System has large negative phase angle at high frequencies

Question 3

Negative feedback in a closed-loop control system does not
( GATE 2015 || EC || MCQ ||1 MARK)

reduce the overall gain
reduce bandwidth
improve disturbance rejection
reduce sensitivity to parameter variation

Question 4

The transfer function Y(s)/R(s) of the system shown is

(GATE 2010 || EC || MCQ ||1 MARK)

0
[Tex]\frac{1}{s + 1}[/Tex]
[Tex]\frac{2}{s + 1}[/Tex]
[Tex]\frac{2}{s + 3}[/Tex]

Question 5

For the following system,

When X₁(s) = 0, the transfer function is: Y(s) / X₂(s)

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

(s + 1) / s²
1 / (s + 1)
(s + 2) / [s(s + 1)]
(s + 1) / [s(s + 2)]

Question 6

By performing cascading and/or summing differencing operations using transfer function block [Tex]G_1(s)[/Tex] and [Tex]G_2(s)[/Tex], one CANNOT realize a transfer function of the form

(GATE 2015 || EC || MCQ ||2 MARK)

[Tex]G_1(s)G_2(s)[/Tex]
[Tex]\frac{G_1(s)}{G_2(s)}[/Tex]
[Tex]G_1(s) \left( \frac{1}{G_1(s)} + G_2(s) \right)[/Tex]
[Tex]G_1(s) \left( \frac{1}{G_1(s)} - G_2(s) \right)[/Tex]

Question 7

The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

(GATE 2016 || EC || MCQ ||1 MARK)

G = G₁G₂ / (1 + G₁H₁)
G = G₁G₂ / (1 + G₁G₂ + G₁H₁)
G = G1G₂ / (1 + G₁G₂H₁)
G = G₁G₂ / (1 + G₁G₂ + G₁G₂H₁)

Question 8

(| GATE 2019 || EC || MCQ ||2 MARK)

[Tex]H(s) = \frac{s^2 + 1}{2s^2 + 1}[/Tex]
[Tex]H(s) = \frac{s^2 + 1}{s^3 + 2s^2 + s + 1}[/Tex]
[Tex]H(s) = \frac{s + 1}{s^2 + s + 1}[/Tex]
[Tex]\frac{Y(s)}{X_2(s)} = \frac{\frac{1}{s}}{1 + \frac{1}{s} \cdot \frac{s}{s+1}} = \frac{s+1}{s(s+2)}[/Tex]

Question 9

The block diagram of a feedback control system is shown in the figure.

The transfer function Y(x)/ X(s) of the system is

(G₁ + G₂) / (1 + G₁H)
(G₁ + G₂ + G₁G₂H) / (1 + G₁H)
G₁(s)[1 / G₁(s) + G₂(s)]
G₁(s)[1 / G₁(s) + G₂(s)]

Question 10

(GATE 2003 || EC || MCQ ||2 MARK)

[Tex]\frac{6}{s^2 + 29s + 6}[/Tex]
[Tex]\frac{6s}{s^2 + 29s + 6}[/Tex]
[Tex]\frac{s(s+2)}{s^{2} + 29s + 6}[/Tex]
[Tex]\frac{s(s+27)}{s^{2} + 29s + 6}[/Tex]

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