Gate 2021 control system practice bits

1. If the initial conditions for a system are inherently zero, what does it physically mean?
(A) The system is at rest but stores energy

(B) The system is working but does not store energy

(C) The system is at rest or no energy is stored in any of its parts

(D) The system is working with zero reference input

• View Answer
  • Answer:c

2. The closed loop transfer function of a unity negative feedback system is . Its open loop transfer function is

• View Answer
  • Answer:D

3. A forcing function (t2 - 2t) u(t-1) is applied to a linear system. The Laplace transform of the forcing function is

• View Answer
  • Answer:D

4.

3. Basically, the transfer function is derived for an isolated circuit by assuming that the output is unloaded. In other words, the load impedance is assumed to be finite, which means that no power is being withdrawn at the output.
Of these statements,
(A) Statement 1 is true and statement 3 is correct explanation for this
(B) Statement 2 is true and statement 3 is correct explanation for this
(C) Statement 2 is False and statement 3 is correct (D) All the statements are false

• View Answer
  • Answer:B

5. Closed-loop transfer function of unity feedback system is given by . Then system Kv is

• View Answer
  • Answer:A

6. A unit feedback system has open-loop transfer function  . The system has
(a) damping ratio = 1/2 and natural frequency = 9 rad/s
(b) damping ratio = 1/6 and natural frequency = 3 rad/s
(c) damping ratio = 1/6 and natural frequency = 9 rad/s
(d) damping ratio = 1/2 and natural frequency = 3 rad/s

• View Answer
  • Answer:D

7. A servomechanism is represented by the equation  where is the actuating signal. The value of damped frequency of oscillations in rad/s is ________

• View Answer
  • Answer:Ans: 11.18 range: 11.0 to 11.3

8. A unity feedback system is characterized by the open-loop transfer function
.
By considering 2% tolerance criterion, the approximate settling time is
(Note: You are suggested to use physical scientific calculator instead of virtual calculator given in this test platform)
(a) 4.05 s
(b) 2.7 s
(c) 5.4 s
(d) cannot be determined

• • Answer:C

9. The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is
(a) negative real and exponential functions of ‘s’
(b) negative real, both exponential and sinusoidal functions of ‘s’
(c) both exponential and sinusoidal functions of ‘s’
(d) complex, both exponential and sinusoidal functions of ‘s’

• View Answer
  • Answer:D

10. Which one of the following open-loop transfer function has root locus parallel to the imaginary axis?

• View Answer
  • Answer:C

11. A feedback system has open-loop transfer function where .
By using Taylor’s series approximation of transport lag, the range of K for the system to be stable is
(A) K < 7.5

(B) K < 4.1

(C) K > 4.1

(D) K > 0

• View Answer
  • Answer:B

12. A unity feedback system has an open-loop transfer function , the closed-loop poles are
(a) all real and distinct (b) one real and two complex conjugate
(c) all real and repeated (d) all are complex conjugate

• View Answer
  • Answer:A

13. Consider the following statements and select the appropriate options
(i) Given the characteristic equation s3 + 3s2 + 2s + k = 0. Increasing K will improve damping
(ii) Given the characteristic equation s2 + 2s + k(0.2s + 1) = 0. Increasing K will improve damping

(a) Both statements are false
(b) Statement (i) is true and statement (ii) is false
(c) Statement (i) is false and statement (ii) is true
(d) Both statements are true

• View Answer
  • Answer:C

14. Consider the following statements and select the appropriate options
(i) Given the characteristic equation s3 + 3s2 + 2s + k = 0 . Increasing K will improve damping
(ii) Given the characteristic equation s2 + 2s + K(0.2s + 1) = 0 . Increasing K will improve damping

(a) Both statements are false
(b) Statement (i) is true and statement (ii) is false
(c) Statement (i) is false and statement (ii) is true
(d) Both statements are true

• View Answer
  • Answer:C

15. An engineer applies the input r(t) = 2sin t to a chemical process and measures the output as y(t) = 0.4 sin(t - 1.55) . What are the gain and phase of the system?
(a) (0.2, –1.55°) (b) (0.4, –1.55°)
(c) (0.2, –89°) (d) (0.4, –89°)

• View Answer
  • Answer:C

16. The closed-loop dynamics of a system is of second-order. To improve the damping, we should
(a) decrease the phase margin (b) increase the phase margin
(c) decrease the gain margin (d) increase the gain margin

• View Answer
  • Answer:B

17. Open-loop transfer function of a unity feedback system is . The gain K that results in a phase margin of 45° is approximately
(a) 25
(b) 5

(c) 5v2

(d) 25v2

• View Answer
  • Answer:D

18. The open-loop transfer function of a unity feedback system is  .
The value of K so that the gain margin is 20 dB is _______

• View Answer
  • Answer: Ans: 5.2 range: 5.1 to 5.3

19. Time response specifications of a system are given as follows:
Damping ratio = 0.7
Settling time = 1.4 s (5% tolerance)
Equivalent frequency response specifications are
(a) Resonant peak = 1 and Bandwidth = 2.5 rad/s
(b) Resonant peak = 1.2 and Phase margin = 65°
(c) Phase margin = 65° and Bandwidth = 3.1 rad/s
(d) Phase margin = 70° and resonant peak = 0.432 rad/s

• View Answer
  • Answer:C

20 A motion control system has type -2 plant. A recommended cascade compensation scheme for this system employs
(a) a lag compensator
(b) a lead compensator
(c) either a lag or a lead compensator
(d) neither a lag nor a lead compensator

• View Answer
  • Answer:B

21. Open-loop transfer function of a unity feedback control system is .
By using asymptotic approximation in Bode plot, the gain crossover frequency is approximately
(a) 4 rad/s (b) 0.5 rad/s (c) 8 rad/s (d) 6 rad/s

• View Answer
  • Answer:A

22. The transfer function of a lag – lead compensator is given by

• View Answer
  • Answer:B

23. In a Bode magnitude plot, the initial slope is –40dB/dec. This low frequency asymptote (or its extension) intersects the 0 dB line at 10 rad/s.
Then gain K is equal to
(a) 10
(b) v10
(c) 100
(d) 1

• View Answer
  • Answer:C

24. A state variable formulation of a system is given by the equations:

• View Answer
  • Answer:D

25. State equation of a control system is given by

• View Answer
  • Answer:C

BNSS Shankar,
M.Tech (IIT K), MIE,
Expert faculty – GATE/ESE/PSUs
OHM Institute, Hyderabad
www.ohminstitue.com
Email: support@ohminstitute.com
Mobile: 9515694053