Control Systems MCQs

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1. Which of the following statements about control systems is true?
A) Open-loop systems do not use feedback
B) Closed-loop systems do not have any sensors
C) Feedback systems are always unstable
D) None of the above
Answer: A) Open-loop systems do not use feedback

2. The transfer function of a system is:
A) Ratio of output to input in the time domain
B) Ratio of output to input in the frequency domain
C) The Laplace transform of the impulse response
D) None of the above
Answer: B) Ratio of output to input in the frequency domain

3. The steady-state error of a system depends on:
A) Input signal
B) System type
C) Both A and B
D) None of the above
Answer: C) Both A and B

4. A system with high gain and positive feedback tends to:
A) Be more stable
B) Be less stable
C) Not affect stability
D) None of the above
Answer: B) Be less stable

5. The root locus method is used to:
A) Find the transfer function of a system
B) Design compensators for stability
C) Analyze steady-state error
D) None of the above
Answer: B) Design compensators for stability

6. A stable system has poles:
A) In the left half of the s-plane
B) In the right half of the s-plane
C) On the imaginary axis
D) Both A and C
Answer: A) In the left half of the s-plane

7. The phase margin of a system indicates:
A) The amount of overshoot in the step response
B) The amount of gain required for stability
C) The amount of phase lag at gain crossover frequency
D) None of the above
Answer: C) The amount of phase lag at gain crossover frequency

8. Which control system compensator improves transient response without affecting steady-state error?
A) Lead compensator
B) Lag compensator
C) Proportional controller
D) Integral controller
Answer: A) Lead compensator

9. The Bode plot consists of:
A) Magnitude plot only
B) Phase plot only
C) Both magnitude and phase plots
D) None of the above
Answer: C) Both magnitude and phase plots

10. A second-order system has:
A) One pole and one zero
B) Two poles and one zero
C) Two poles and two zeros
D) None of the above
Answer: A) One pole and one zero

11. The transfer function
𝐺(𝑠) = 𝐾/𝑠(𝑠 + 2)
represents a:
A) First-order system
B) Second-order system
C) Third-order system
D) Fourth-order system
Answer: B) Second-order system

12. A system is critically damped when:
A) All poles are real and distinct
B) All poles are real and equal
C) Poles are complex conjugates
D) None of the above
Answer: B) All poles are real and equal

13. Nyquist criterion is used to analyze:
A) Stability
B) Steady-state error
C) Transient response
D) None of the above
Answer: A) Stability

14. Which of the following controllers reduces steady-state error?
A) Proportional (P)
B) Integral (I)
C) Derivative (D)
D) All of the above
Answer: B) Integral (I)

15. The damping ratio
𝜁
of a second-order system affects:
A) Natural frequency
B) Rise time
C) Both A and B
D) None of the above
Answer: C) Both A and B

16. A lead compensator adds phase:
A) At low frequencies
B) At high frequencies
C) At all frequencies equally
D) None of the above
Answer: A) At low frequencies

17. The steady-state error of a type-1 system to a ramp input is:
A) Zero
B) Non-zero, finite
C) Non-zero, infinite
D) None of the above
Answer: C) Non-zero, infinite

18. The rise time of a system is the time taken for the response to rise from:
A) 0% to 10% of its final value
B) 10% to 90% of its final value
C) 0% to 100% of its final value
D) None of the above
Answer: B) 10% to 90% of its final value

19. In a phase-lead compensator, the zero is placed:
A) Before the pole
B) After the pole
C) At the same location as the pole
D) None of the above
Answer: A) Before the pole

20. The steady-state error of a type-0 system to a step input is:
A) Zero
B) Non-zero, finite
C) Non-zero, infinite
D) None of the above
Answer: A) Zero

21. The concept of pole-zero cancellation is related to:
A) Steady-state error reduction
B) Increasing system bandwidth
C) Improving transient response
D) None of the above
Answer: A) Steady-state error reduction

22. A system with a dominant pole:
A) Has a slower response
B) Has a faster response
C) Is more stable
D) None of the above
Answer: B) Has a faster response

23. The steady-state error of a type-2 system to a parabolic input is:
A) Zero
B) Non-zero, finite
C) Non-zero, infinite
D) None of the above
Answer: A) Zero

24. The characteristic equation of a closed-loop system is:
A) 𝐺(𝑠)𝐻(𝑠) = 0
B) 𝐺(𝑠)𝐻(𝑠) = 1
C) 1 + 𝐺(𝑠)𝐻(𝑠) = 0
D) None of the above
Answer: C) 1 + 𝐺(𝑠)𝐻(𝑠) = 0

25. A system is marginally stable if:
A) It is unstable
B) It is stable with no oscillations
C) It is stable with oscillations
D) None of the above
Answer: C) It is stable with oscillations

26. The root locus crosses the imaginary axis at points where:
A) The phase margin is zero
B) The phase is 180 degrees
C) The gain margin is zero
D) None of the above
Answer: A) The phase margin is zero

27. A lead compensator is used to:
A) Increase system bandwidth
B) Reduce overshoot
C) Reduce steady-state error
D) None of the above
Answer: A) Increase system bandwidth

28. The Laplace transform of
𝑒^𝑎𝑡
is:
A) 1/(𝑠 − 𝑎)
B) 1/(𝑠 + 𝑎)
C) 1/(𝑠^2 − 𝑎^2)
D) None of the above
Answer: A) 1/(𝑠 − 𝑎)

29. The settling time of a system is the time required for the response to:
A) Reach within a specified tolerance band and stay there
B) Settle to zero
C) Reach its peak value
D) None of the above
Answer: A) Reach within a specified tolerance band and stay there

30. The frequency at which the Nyquist plot encircles the critical point (-1, j0) once in the clockwise direction is:
A) Gain crossover frequency
B) Phase crossover frequency
C) Gain margin
D) None of the above
Answer: B) Phase crossover frequency

31. A phase-lag compensator is used to:
A) Increase system bandwidth
B) Reduce overshoot
C) Improve steady-state accuracy
D) None of the above
Answer: C) Improve steady-state accuracy

32. The damping ratio
𝜁
is defined as:
A) 1/(2π) ln(ω_n t_p)
B) 2𝜁/ω_n
C) ω_n / (2𝜁)
D) None of the above
Answer: C) ω_n / (2𝜁)

33. A system with a higher bandwidth tends to have:
A) Slower response
B) Faster response
C) Unstable response
D) None of the above
Answer: B) Faster response

34. The unit step response of a second-order system can be characterized by:
A) Overshoot and settling time
B) Damping ratio and natural frequency
C) Both A and B
D) None of the above
Answer: C) Both A and B

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