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Test 3 - Control System | Electronics and Communication (ECE)

Topic wise test 3 for Control System (ECE) of GATE Electronics and Communication

20 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

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?

  1. Lead compensator
  2. Lag compensator
  3. PID compensator
  4. Lead-lag compensator
Question 2 Multiple Choice (Single Answer)

Which one of the following polar diagrams corresponds to a lag network?

Question 3 Multiple Choice (Single Answer)

The pole-zero given below corresponds to a

  1. Law pass filter
  2. High pass filter
  3. Band filter
  4. Notch filter
Question 4 Multiple Choice (Single Answer)

The feedback system shown below oscillates at 2 rad/s when

  1. K = 2 and a = 0.75
  2. K = 3 and a = 0.75
  3. K = 4 and a = 0.5
  4. K = 2 and a = 0.5
Question 5 Multiple Choice (Single Answer)

Given G(s) H(s) = $\dfrac{K}{s(s+1)(s+3)}$. The point of intersection of the asymptotes of the root loci with the real axis is

  1. - 4
  2. 1.33
  3. - 1.33
  4. 4
Question 6 Multiple Choice (Single Answer)

Direction: The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

Which of the following statements is true?

  1. G (s) is an all-pass filter.
  2. G (s) has a zero in the right half plane.
  3. G (s) is the impedance of a passive network.
  4. G (s) is marginally stable.
Question 7 Multiple Choice (Single Answer)

The transfer function of a phase-lead compensator is given by Gc = $\dfrac{1+3T_s}{1+T_s}$, where T > 0. What is the maximum phase shift of the compensator?

  1. $\dfrac{\pi}{2}$
  2. $\dfrac{\pi}{3}$
  3. $\dfrac{\pi}{4}$
  4. $\dfrac{\pi}{6}$
Question 8 Multiple Choice (Single Answer)

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the conditions R2C2 > R1C1. The transfer functions $\dfrac{V_0}{V_i}$represents a kind of controller.

Match the impedances in Group I with the type of controllers in Group II.

  1. Q - 1, R - 2
  2. Q - 1, R - 3
  3. Q - 2, R - 3
  4. Q - 3, R - 2
Question 9 Multiple Choice (Single Answer)

The signal flow graph of a system is shown in figure. The transfer function $\dfrac{C(s)}{R(s)}$ of the system is

  1. $\dfrac{6}{s^2+29s+6}$
  2. $\dfrac{6s}{s^2+29s+6}$
  3. $\dfrac{s(s+2)}{s^2+29s+6}$
  4. $\dfrac{s(s+27)}{s^2+29s+6}$
Question 10 Multiple Choice (Single Answer)

Consider the Bode magnitude plot shown in the fig. The transfer function H(s) is

  1. $\dfrac{s+10}{(s+1)(s+100)}$
  2. $\dfrac{10(s+1)}{(s+10)(s+100)}$
  3. $\dfrac{10^2(s+1)}{(s+10)(s+100)}$
  4. $\dfrac{10^3(s+100)}{(s+1)(s+10)}$
Question 11 Multiple Choice (Single Answer)

The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G(s) corresponding to this Bode plot is

  1. $\dfrac{1}{(s+1)(s+20)}$
  2. $\dfrac{1}{s(s+1)(s+20)}$
  3. $\dfrac{100}{s(s+1)(s+20)}$
  4. $\dfrac{100}{s(s+1)(1+0.05s)}$
Question 12 Multiple Choice (Single Answer)

A control system with a PD controller is shown in the figure. If the velocity error constant KV = 1000 and the damping ratio $\xi$= 0.5, the values of KP and KD are

  1. Kp = 100, KD = 0.09
  2. Kp = 100, KD = 0.9
  3. Kp = 10, KD = 0.09
  4. Kp = 10, KD = 0.9
Question 13 Multiple Choice (Single Answer)

Consider a linear system whose state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =$
\left[
\begin{array}
\ 1 \\
-2
\end{array}
\right]
$, the system response is x (t) = $
\left(
\begin{array}
\ e^{-2t} \\
-2 e^{-2t}
\end{array}
\right)
$. If the initial state vector of the system changes, the system response becomes x(t) = $
\left[
\begin{array}
\ e^{-t} \\

  • e^{-6}
    \end{array}
    \right]
    $.

The system matrix A is

  1. $ \left[ \begin{array} \ 0 & 1 \\\\ -1 & 1 \end{array} \right] $
  2. $ \left[ \begin{array} \ 1 & 1 \\\\ -1 & -2 \end{array} \right] $
  3. $ \left[ \begin{array} \ 2 & 1 \\\\ -1 & -1 \end{array} \right] $
  4. $ \left[ \begin{array} \ 0 & 1 \\\\ -2 & -3 \end{array} \right] $
Question 14 Multiple Choice (Single Answer)

The open loop transfer function of a unity feedback is given by
$G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

Based on the above results, the gain and phase margins of the system will be

  1. - 7.09 dB and 87.5�
  2. 7.09 dB and 87.5�
  3. 7.09 dB and - 87.5�
  4. - 7.09 dB and - 87.5�
Question 15 Multiple Choice (Single Answer)

Consider two transfer functions:

G1 (s) = $\dfrac{1}{s^2 + as +b}$ and G2 (s) = $\dfrac{1}{s^2 + as +b}$

The 3 dB bandwidths of their frequency responses respectively are

  1. $\sqrt{a^2-4b}, \sqrt{a^2+4b}$
  2. $\sqrt{a^2+4b}, \sqrt{a^2-4b}$
  3. $\sqrt{a^2-4b}, \sqrt{a^2-4b}$
  4. $\sqrt{a^2+4b}, \sqrt{a^2+4b}$
Question 16 Multiple Choice (Single Answer)

A unity negative feedback closed loop system has a plant with the transfer function G(s) = $\dfrac{1}{s^2 + 2s +2}$ and a controller Gc(S) in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is

  1. GC(s) = $\dfrac{s+1}{s+2}$
  2. GC(s) = $\dfrac{s+2}{s+1}$
  3. GC(s) = $\dfrac{(s+1)(s+4)}{(s+2)(s+3)}$
  4. GC(s) = 1 + $\dfrac{2}{s}$+ 3s
Question 17 Multiple Choice (Single Answer)

A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively

  1. 1 and 20
  2. 0 and 20
  3. 0 and $\dfrac{1}{20}$
  4. 1 and $\dfrac{1}{20}$
Question 18 Multiple Choice (Single Answer)

Consider a linear system with state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =$
\left[
\begin{array}
\ 1 \\
-2
\end{array}
\right]
$, the system response is x (t) = $
\left(
\begin{array}
\ e^{-2t} \\
-2 e^{-2t}
\end{array}
\right)
$. If the initial state vector of the system changes, the system response becomes x(t) = $
\left[
\begin{array}
\ e^{-t} \\

  • e^{-6}
    \end{array}
    \right]
    $.

The eigen value and eigen vector pairs ($\lambda_i, V_i$) for the system are

  1. $ \left( \begin{array} \ -1, & \left[ \begin{array} \ 1 \\\\ -1 \end{array} \right] \end{array} \right) $and $ \left( \begin{array} \ -2, & \left[ \begin{array} \ 1 \\\\ -2 \end{array} \right] \end{array} \right) $
  2. $ \left( \begin{array} \ -1, & \left[ \begin{array} \ 1 \\\\ -1 \end{array} \right] \end{array} \right) $and $ \left( \begin{array} \ 2, & \left[ \begin{array} \ 1 \\\\ -2 \end{array} \right] \end{array} \right) $
  3. $ \left( \begin{array} \ 1, & \left[ \begin{array} \ 1 \\\\ -1 \end{array} \right] \end{array} \right) $and $ \left( \begin{array} \ -2, & \left[ \begin{array} \ 1 \\\\ -2 \end{array} \right] \end{array} \right) $
  4. $ \left( \begin{array} \ -2, & \left[ \begin{array} \ 1 \\\\ -1 \end{array} \right] \end{array} \right) $and $ \left( \begin{array} \ -1, & \left[ \begin{array} \ 1 \\\\ -2 \end{array} \right] \end{array} \right) $
Question 19 Multiple Choice (Single Answer)

The open loop transfer function of a unity feedback is given by
$G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

The gain and phase crossover frequencies in rad/sec are respectively

  1. 0.632 and 1.26
  2. 0.632 and 0.485
  3. 0.485 and 0.632
  4. 1.26 and 0.632
Question 20 Multiple Choice (Single Answer)

Directions : The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

The gain and phase margins of G (s) for closed loop stability are

  1. 6 dB and 1800 respectively
  2. 3 dB and 1800 respectively
  3. 6 dB and 900 respectively
  4. 3 dB and 900 respectively
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