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

Topic wise test for Control System (ECE) of GATE Electronics and Communication

20 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

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.

  1. P - 3, Q - 1, R - 4, S - 2
  2. P - 3, Q - 2, R - 4, S - 1
  3. P - 2, Q - 1, R - 4, S - 2
  4. P - 3, Q - 4, R - 1, S - 2
Question 2 Multiple Choice (Single Answer)

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

The phase of the above lead compensator is maximum at

  1. $\sqrt2$rad/s
  2. $\sqrt3$rad/s
  3. $\sqrt6$rad/s
  4. 1/ $\sqrt3$rad/s
Question 3 Multiple Choice (Single Answer)

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

  1. $\left[ \begin{array} \ cost & sint \\\\ -sint & cost \end{array} \right]$
  2. $\left[ \begin{array} \ -cost & sint \\\\ -sint & -cost \end{array} \right]$
  3. $\left[ \begin{array} \ -cost & -sint \\\\ -sint & cost \end{array} \right]$
  4. $\left[ \begin{array} \ cost & -sint \\\\ sint & cost \end{array} \right]$
Question 4 Multiple Choice (Single Answer)

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

  1. 0
  2. $\dfrac{1}{s+1}$
  3. $\dfrac{2}{s+1}$
  4. $\dfrac{2}{s+3}$
Question 5 Multiple Choice (Single Answer)

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

  1. G(s)H(s) = k $\dfrac{s(s+1)}{(s+2)(s+3)}$
  2. G(s)H(s) = k$\dfrac{(s+1)}{s(s+2)(s+3)^2}$
  3. G(s)H(s) = k$\dfrac{s(s+1)}{s(s+1)(s+2)(s+3)}$
  4. G(s)H(s) = k $\dfrac{(s+1)}{s(s+2)(s+3)}$
Question 6 Multiple Choice (Single Answer)

The signal flow graph of a system is shown below.

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

  1. $ 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
  2. $ 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
  3. $ 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
  4. $ 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
Question 7 Multiple Choice (Single Answer)

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

  1. $\dfrac{1}{3}$$ x = \left[ \begin{array} \ sin(-4t) + 2sin(-t) - 2sin(-4t) + 2sin(-t) \\\\ -sin(-4t) + sin(-t)2sin(-4t) + sin(-t) \end{array} \right] $
  2. $\left[ \begin{array} \ sin(-2t) sin(2t) \\\\ sin(t) sin(-3t) \end{array} \right]$
  3. $\dfrac{1}{3}$$ x = \left[ \begin{array} \ sin(4t) + 2sin(t) 2sin(-4t) - 2sin(-t) \\\\ -sin(-4t) + sin(t)2sin(4t) + sin(t) \end{array} \right] $
  4. $\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] $
Question 8 Multiple Choice (Single Answer)

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

  1. $\left[ \begin{array} \ te^t \\\\ t \end{array} \right]$
  2. $\left[ \begin{array} \ e^t \\\\ t \end{array} \right]$
  3. $\left[ \begin{array} \ e^t \\\\ te^t \end{array} \right]$
  4. $\left[ \begin{array} \ t \\\\ te^t \end{array} \right]$* 1/2
Question 9 Multiple Choice (Single Answer)

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?

  1. $[\lambda] = [\mu] \ and \ X =W $
  2. $[\lambda] = [\mu] \ and \ X \ne W $
  3. $[\lambda] \ne [\mu] \ and \ X = W $
  4. $[\lambda] \ne [\mu] \ and \ X \ne W $
Question 10 Multiple Choice (Single Answer)

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

  1. $ \dfrac{1}{(s+5)(s+1)} $
  2. $ \dfrac{5}{(s+5)(s+1)} $
  3. $ \dfrac{5}{(s^2+s+1)} $
  4. $ \dfrac{1}{(s^2+s+1)} $
Question 11 Multiple Choice (Single Answer)

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

  1. always stable
  2. unstable with one closed loop right hand pole
  3. unstable with two closed loop right hand poles
  4. unstable with three closed loop right hand poles
Question 12 Multiple Choice (Single Answer)

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

  1. infinite
  2. greater than zero
  3. less than zero
  4. zero
Question 13 Multiple Choice (Single Answer)

The signal flow graph of a system is shown below.

The transfer function of the system is

  1. $ \dfrac{s+1}{(s^2+1)} $
  2. $ \dfrac{s-1}{(s^2+1)} $
  3. $ \dfrac{s+1}{(s^2+s+1)} $
  4. $ \dfrac{s-1}{(s^2+s+1)} $
Question 14 Multiple Choice (Single Answer)

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?

  1. $ \dfrac{-2.24}{(s^2+2.59s+1.12)} $
  2. $ \dfrac{-3.82}{(s^2+1.91s+1.91)} $
  3. $ \dfrac{-2.24}{(s^2-2.59s+1.12)} $
  4. $ \dfrac{-3.82}{(s^2-1.91s+1.91)} $
Question 15 Multiple Choice (Single Answer)

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

  1. $ \dfrac{500}{(s^2+10s+100)} $
  2. $ \dfrac{375}{(s^2+5s+75)} $
  3. $ \dfrac{720}{(s^2+12s+144)} $
  4. $ \dfrac{1125}{(s^2+25s+225)} $
Question 16 Multiple Choice (Single Answer)

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

  1. $ \dfrac{1 - (be+cf+dg)}{abcd} $
  2. $ \dfrac{bedg}{1 - (be+cf+dg)} $
  3. $ \dfrac{bedg}{1 - (be+cf+dg) + bedg} $
  4. $ \dfrac{1 - (be+cf+dg) + bedg}{abcd} $
Question 17 Multiple Choice (Single Answer)

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

  1. $k<5\ and \ \dfrac{1}{2} < k < \dfrac{1}{8}$
  2. $k<\dfrac{1}{8}\ and \ \dfrac{1}{2} < k < 5$
  3. $k<\dfrac{1}{8}\ and \ 5 < k$
  4. $k>\dfrac{1}{8}\ and \ k < 5$
Question 18 Multiple Choice (Single Answer)

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

Question 19 Multiple Choice (Single Answer)

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

  1. $\bar x$ = [2]x + [1]u; y = [1 2]x
  2. $\bar x$ = [- 2]x + [1]u; y = $ \left[ \begin{array} \ 1 \\\\ 2 \end{array} \right] $x
  3. $\bar x$ = $ \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
  4. $\bar x$ = $ \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
Question 20 Multiple Choice (Single Answer)

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

  1. $\sqrt3$
  2. $\dfrac{2}{\sqrt3}$
  3. 1
  4. $\dfrac{\sqrt3}{2}$
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