Question 1

Group I lists a set of four transfer functions. Group II gives a list of possible step response y (t). Match the step responses with the corresponding transfer functions.

P - 3, Q - 1, R - 4, S - 2
P - 3, Q - 2, R - 4, S - 1
P - 2, Q - 1, R - 4, S - 2
P - 3, Q - 4, R - 1, S - 2

Answer

Correct Option: D

Question 2

The transfer function of a compensator is given as G_c(s) = (s +1)/(s +2)

The phase of the above lead compensator is maximum at

^$\sqrt2$rad/s
^$\sqrt3$rad/s
^$\sqrt6$rad/s
1/ ^$\sqrt3$rad/s

Answer

Correct Option: A

Question 3

A linear system is described by the following state equation:

X(t) = AX (t) + BU (t), A =^{$\left[
\begin{array}
\ 0 & 1 \\
-1 & 0
\end{array}
\right]$}

The state-transition matrix of the system is

$\left[ \begin{array} \ cost & sint \\ -sint & cost \end{array} \right]$
$\left[ \begin{array} \ -cost & sint \\ -sint & -cost \end{array} \right]$
$\left[ \begin{array} \ -cost & -sint \\ -sint & cost \end{array} \right]$
$\left[ \begin{array} \ cost & -sint \\ sint & cost \end{array} \right]$

Answer

Correct Option: A

Question 4

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

0
$\dfrac{1}{s+1}$
$\dfrac{2}{s+1}$
$\dfrac{2}{s+3}$

Answer

Correct Option: B

Question 5

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

G(s)H(s) = k $\dfrac{s(s+1)}{(s+2)(s+3)}$
G(s)H(s) = k$\dfrac{(s+1)}{s(s+2)(s+3)^2}$
G(s)H(s) = k$\dfrac{s(s+1)}{s(s+1)(s+2)(s+3)}$
G(s)H(s) = k $\dfrac{(s+1)}{s(s+2)(s+3)}$

Answer

Correct Option: B

Question 6

The signal flow graph of a system is shown below.

Which of the following is the state variable representation of the system?

$ x = \left[ \begin{array} \ 1 & 1 \\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\ 2 \end{array} \right] u $ y = [0 & 0.5] x
$ x = \left[ \begin{array} \ -1 & 1 \\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\ 2 \end{array} \right] u $ y = [0 & 0.5] x
$ x = \left[ \begin{array} \ 1 & -1 \\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x
$ x = \left[ \begin{array} \ -1 & 1 \\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x

Answer

Correct Option: D

Question 7

If A = $ x = \left[ \begin{array} \ -2 & 2 \\ 1 & -3 \end{array} \right] $, then sin At is

$\dfrac{1}{3}$$ x = \left[ \begin{array} \ sin(-4t) + 2sin(-t) - 2sin(-4t) + 2sin(-t) \\ -sin(-4t) + sin(-t)2sin(-4t) + sin(-t) \end{array} \right] $
$\left[ \begin{array} \ sin(-2t) sin(2t) \\ sin(t) sin(-3t) \end{array} \right]$
$\dfrac{1}{3}$$ x = \left[ \begin{array} \ sin(4t) + 2sin(t) 2sin(-4t) - 2sin(-t) \\ -sin(-4t) + sin(t)2sin(4t) + sin(t) \end{array} \right] $
$\dfrac{1}{3}$$ x = \left[ \begin{array} \ cos(-t) + 2cos(t) 2cos(-4t) + 2cos(-t) \\ -cos(-4t) + cos(-t)-2cos(-4t) + cos(-t) \end{array} \right] $

Answer

Correct Option: A

Question 8

The zero-input response of a system given by the state-space equation is

$\left[ \begin{array} \ te^t \\ t \end{array} \right]$
$\left[ \begin{array} \ e^t \\ t \end{array} \right]$
$\left[ \begin{array} \ e^t \\ te^t \end{array} \right]$
^{$\left[
\begin{array}
\ t \\
te^t
\end{array}
\right]$}* 1/2

Answer

Correct Option: C

Question 9

A linear system is equivalently represented by two sets of state equations; ^{$\bar X = AX + BU$} and W = CW + DU. The eigen values of the representations are also computed as ^$[\lambda]$ and ^$[\mu]$. Which of the following statements is true?

$[\lambda] = [\mu] \ and \ X =W $
$[\lambda] = [\mu] \ and \ X \ne W $
$[\lambda] \ne [\mu] \ and \ X = W $
$[\lambda] \ne [\mu] \ and \ X \ne W $

Answer

Correct Option: C

Question 10

The transfer function of a plant is T (s) = $ \dfrac{5}{(s+5)(s^2+s+1)} $. The second - order approximation of T(s) using dominate pole concept is

$ \dfrac{1}{(s+5)(s+1)} $
$ \dfrac{5}{(s+5)(s+1)} $
$ \dfrac{5}{(s^2+s+1)} $
$ \dfrac{1}{(s^2+s+1)} $

Answer

Correct Option: D

Question 11

The figure shows the Nyquist plot of the open-loop transfer function G(s)H(s) of a system. If G(s)H(s) has one right hand pole, the closed loop system is

always stable
unstable with one closed loop right hand pole
unstable with two closed loop right hand poles
unstable with three closed loop right hand poles

Answer

Correct Option: A

Question 12

The Nyquist plot of G (j$\omega$) H (j$\omega$) for a closed loop control system, passes through (- 1, j0) point in the GH-plane. The gain margin of the system in dB is equal to

infinite
greater than zero
less than zero
zero

Answer

Correct Option: D

Question 13

The signal flow graph of a system is shown below.

The transfer function of the system is

$ \dfrac{s+1}{(s^2+1)} $
$ \dfrac{s-1}{(s^2+1)} $
$ \dfrac{s+1}{(s^2+s+1)} $
$ \dfrac{s-1}{(s^2+s+1)} $

Answer

Correct Option: C

Question 14

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has theses properties?

$ \dfrac{-2.24}{(s^2+2.59s+1.12)} $
$ \dfrac{-3.82}{(s^2+1.91s+1.91)} $
$ \dfrac{-2.24}{(s^2-2.59s+1.12)} $
$ \dfrac{-3.82}{(s^2-1.91s+1.91)} $

Answer

Correct Option: B

Question 15

The magnitude of frequency responses of an underdamped second order system is 5 at 0 rad/sec and peaks to $\dfrac{10}{\sqrt3}$ at 5 $\sqrt2$ rad/sec. The transfer function of the system is

$ \dfrac{500}{(s^2+10s+100)} $
$ \dfrac{375}{(s^2+5s+75)} $
$ \dfrac{720}{(s^2+12s+144)} $
$ \dfrac{1125}{(s^2+25s+225)} $

Answer

Correct Option: A

Question 16

Consider the signal flow graph shown in figure. The gain $ \dfrac{x_5}{x_1} $ is

$ \dfrac{1 - (be+cf+dg)}{abcd} $
$ \dfrac{bedg}{1 - (be+cf+dg)} $
$ \dfrac{bedg}{1 - (be+cf+dg) + bedg} $
$ \dfrac{1 - (be+cf+dg) + bedg}{abcd} $

Answer

Correct Option: C

Question 17

The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

$k<5\ and \ \dfrac{1}{2} < k < \dfrac{1}{8}$
$k<\dfrac{1}{8}\ and \ \dfrac{1}{2} < k < 5$
$k<\dfrac{1}{8}\ and \ 5 < k$
$k>\dfrac{1}{8}\ and \ k < 5$

Answer

Correct Option: B

Question 18

A second-order system has the transfer function ^{$\dfrac{C(s)}{R(s)}$} = ^{$\dfrac{4}{s^2+4s+4}$} with r(t) as the unit-step function, the response c(t) of the system is represented by

Answer

Correct Option: D

Question 19

The block diagram of a system with one input it and two outputs y₁ and y₂ is given below:

A state space model of the above system in terms of the state vector x and the output vector y = [y₁ y₂]^T is

^{$\bar x$} = [2]x + [1]u; y = [1 2]x
^{$\bar x$} = [- 2]x + [1]u; y = ^{$
\left[
\begin{array}
\ 1 \\
2
\end{array}
\right]
$}x
^{$\bar x$} = ^{$
\left[
\begin{array}
\ -2 & 0 \\
0 & -2
\end{array}
\right]
$}x + ^{$
\left[
\begin{array}
\ 1 \\
1
\end{array}
\right]
$}u; y = ^{_{$
\left[
\begin{array}
\ 1 & 2
\end{array}
\right]
$}}x
^{$\bar x$} = ^{$
\left[
\begin{array}
\ 2 & 0 \\
0 & 2
\end{array}
\right]
$}x + ^{$
\left[
\begin{array}
\ 1 \\
2
\end{array}
\right]
$}u; y = ^{$
\left[
\begin{array}
\ 1 \\
2
\end{array}
\right]
$}x

Answer

Correct Option: B

Question 20

A system with transfer function ^{$
\left[
\begin{array}
\ Y(s) \\
X(s)
\end{array}
\right]
$} = ^{$\dfrac{s}{s+p}$}has an output y(t) = cos ^{$
\left(
\begin{array}
\ 2t - \dfrac{\pi}{3}
\end{array}
\right)
$}for the input signal x(t) = p cos ^{$
\left(
\begin{array}
\ 2t - \dfrac{\pi}{2}
\end{array}
\right)
$}. Then, the system parameter ‘p’ is

$\sqrt3$
$\dfrac{2}{\sqrt3}$
1
$\dfrac{\sqrt3}{2}$

Answer

Correct Option: B

Description: Topic wise test for Control System (ECE) of GATE Electronics and Communication
Number of Questions: 20
Created by: Yashbeer Singh
Tags: ECE Control System

Test 2 - Control System | Electronics and Communication (ECE)

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