MCQs on Control Systems

1. What is the primary goal of a control system?

A. Amplification
B. Feedback elimination
C. Control a system’s behavior
D. Noise suppression
ANSWER: C

2. Which component provides the desired output in a control system?

A. Controller
B. Process or Plant
C. Sensor
D. Feedback
ANSWER: B

3. An open-loop control system is characterized by:

A. Feedback presence
B. No feedback
C. Nonlinear control
D. Adaptive behavior
ANSWER: B

4. In a closed-loop control system, the output is compared with:

A. Disturbance
B. Setpoint or Reference input
C. Amplifier gain
D. Actuator position
ANSWER: B

5. The thermostat in a home heating system is an example of:

A. Open-loop system
B. Feedforward control system
C. Closed-loop control system
D. None of the above
ANSWER: C

6. Which of the following is an example of an open-loop control system?

A. Air conditioning system
B. Traffic light system
C. Electric iron with thermostat
D. Servo motor system
ANSWER: B
7. A control system where the output has no effect on the input signal is called:
A. Closed-loop system
B. Feedback system
C. Open-loop system
D. Adaptive system
ANSWER: C

8. Feedback in a control system improves:

A. Stability
B. Accuracy
C. Sensitivity
D. All of the above
ANSWER: D

9. Which of the following is NOT a type of control system?

A. Open-loop
B. Closed-loop
C. Proportional-only control
D. Static control
ANSWER: D

10. Which type of control system adjusts its parameters automatically?

A. Adaptive control system
B. Static control system
C. Feedforward control system
D. Integral control system
ANSWER: A

11. What is the purpose of mathematical modeling in control systems?

A. To improve design
B. To simplify analysis
C. To predict system behavior
D. All of the above
ANSWER: D

12. The equation F = ma is used in:

A. Electrical systems
B. Translational mechanical systems
C. Rotational mechanical systems
D. Hydraulic systems
ANSWER: B

13. A spring-mass-damper system is represented using:

A. First-order differential equations
B. Second-order differential equations
C. Linear equations only
D. Algebraic equations
ANSWER: B

14. In a mechanical translational system, velocity is given by:

A. dx/dt
B. d^2x/dt^2
C. ∫dx
D. kx
ANSWER: A

15. Rotational systems are modeled using which of the following laws?
A. Kirchhoff's law
B. Ohm’s law
C. Newton’s second law
D. Hooke’s law
ANSWER: C

16. What is the purpose of block diagram reduction?

A. Simplify the system representation
B. Increase complexity
C. Introduce more blocks
D. None of the above
ANSWER: A

17. A block diagram is a representation of a:

A. Physical structure
B. Mathematical model
C. Electrical circuit
D. Logical algorithm
ANSWER: B

18. In block diagram algebra, blocks in series are combined by:

A. Addition
B. Multiplication
C. Subtraction
D. Division
ANSWER: B

19. Feedback loop gain is calculated as:

A. G - H
B. G × H
C. G / (1 + GH)
D. 1 + GH
ANSWER: C
20. To reduce two parallel blocks into one, their gains are:
A. Multiplied
B. Added
C. Subtracted
D. Divided
ANSWER: B

21. A spring-mass-damper system has m = 2 kg, c = 4 Ns/m, k = 10 N/m. What is the

transfer function X(s)/F(s)?
A. 1/(2s^2 + 4s + 10)
B. 1/(4s^2 + 10s + 2)
C. 1/(10s^2 + 4s + 2)
D. None of the above
ANSWER: A

22. Find the equivalent gain of a system with G1 = 5, G2 = 3 in series.

A. 15
B. 2
C. 8
D. 1
ANSWER: A

23. In a closed-loop system, G = 10 and H = 2. What is the overall transfer function?

A. 5
B. 10/(1 + 20)
C. 10/(1 - 20)
D. 10/2
ANSWER: B

24. A rotational system has J = 5 kg·m^2, B = 3 N·s/rad. What is the transfer function
θ(s)/T(s)?
A. 1/(5s^2 + 3s)
B. 1/(3s^2 + 5s)
C. 1/(5s + 3)
D. None of the above
ANSWER: A

25. Two blocks with gains G1 = 4 and G2 = 2 are in parallel. What is the equivalent gain?
A. 8
B. 6
C. 2
D. 4
ANSWER: B
26. A mechanical system has k = 20 N/m and F = 40 N. What is the displacement x?
A. 2 m
B. 20 m
C. 0.5 m
D. 4 m
ANSWER: A

27. A block diagram has G = 5 and H = 0.2. What is the closed-loop transfer function?
A. 5/(1 + 1)
B. 5/(1 - 1)
C. 5/0.8
D. 1/5
ANSWER: A

28. A mass of 3 kg is subjected to a force F = 9 N. What is the acceleration a?

A. 1 m/s^2
B. 3 m/s^2
C. 9 m/s^2
D. 27 m/s^2
ANSWER: B

29. If two blocks have transfer functions T1(s) = 2/s and T2(s) = 3, what is the equivalent
transfer function in series?
A. 6/s
B. 5/s
C. 6
D. 1/s
ANSWER: A

30. A system has G = 8 and feedback H = 0.5. What is the closed-loop transfer function?
A. 8/(1 + 4)
B. 8/(1 - 4)
C. 8
D. 1/4
ANSWER: A

MCQs on Controllers
31. What is the primary purpose of a PD controller?
A. To improve steady-state error
B. To improve system stability and speed of response
C. To reduce the integral error
D. To provide lead compensation
ANSWER: B
32. Which of the following components does the PD controller NOT include?
A. Proportional term
B. Integral term
C. Derivative term
D. Error signal
ANSWER: B

33. The addition of a derivative term in a PD controller primarily affects:

A. Steady-state performance
B. System stability
C. Transient response
D. Gain margin
ANSWER: C

34. What is the primary purpose of a PI controller?

A. To improve transient response
B. To eliminate steady-state error
C. To reduce overshoot
D. To stabilize the system
ANSWER: B

35. The integral term in a PI controller accumulates:

A. The current error
B. The rate of change of error
C. The sum of past errors
D. The predicted future error
ANSWER: C

36. Which of the following is NOT a property of a PID controller?

A. Can improve transient response
B. Can eliminate steady-state error
C. Can predict future errors
D. Can damp oscillations
ANSWER: C

37. The derivative term in a PID controller is used to:

A. Reduce the steady-state error
B. Reduce the rate of change of error
C. Predict the future behavior of the system
D. Increase system damping
ANSWER: B

38. A phase-lead controller is primarily used to:

A. Improve transient response
B. Reduce steady-state error
C. Stabilize unstable systems
D. Increase integral action
ANSWER: A

39. In a phase-lead controller, the zero is located:

A. Closer to the origin than the pole
B. At the same location as the pole
C. Further from the origin than the pole
D. Independent of the pole's position
ANSWER: C

40. What is the main purpose of a phase-lag controller?

A. To improve transient response
B. To improve steady-state accuracy
C. To increase system damping
D. To reduce overshoot
ANSWER: B

41. In a phase-lag controller, the pole is located:

A. Closer to the origin than the zero
B. At the same location as the zero
C. Further from the origin than the zero
D. Independent of the zero's position
ANSWER: A

42. The phase-lead controller improves:

A. Steady-state error
B. Transient response
C. System robustness
D. None of the above
ANSWER: B

43. The phase-lag controller improves:

A. Stability margins
B. Steady-state error
C. Overshoot
D. Speed of response
ANSWER: B

44. What is the main advantage of a lead-lag controller?

A. Combines the benefits of phase-lead and phase-lag controllers
B. Eliminates both transient and steady-state errors
C. Provides maximum damping ratio
D. Reduces system bandwidth
ANSWER: A
45. The lead-lag controller is typically used to:
A. Reduce overshoot
B. Improve transient response and steady-state error simultaneously
C. Stabilize highly unstable systems
D. Predict future errors
ANSWER: B

46. Which controller introduces a zero at a specific location to improve system response?
A. PID Controller
B. Phase-lead Controller
C. Phase-lag Controller
D. Lead-lag Controller
ANSWER: B

47. A phase-lag controller is most effective in:

A. Improving stability
B. Improving transient performance
C. Enhancing steady-state performance
D. Reducing gain margin
ANSWER: C

48. The addition of a phase-lead controller shifts the root locus:

A. Towards the left in the s-plane
B. Towards the right in the s-plane
C. Away from the origin
D. Along the imaginary axis
ANSWER: A

49. A lead-lag controller combines:

A. A low-pass and a high-pass filter
B. A proportional and derivative control action
C. A phase-lead and phase-lag controller
D. An integrator and differentiator
ANSWER: C

50. The main difference between a PD and a PID controller is:

A. PID includes an integral term to eliminate steady-state error
B. PD includes a derivative term to reduce overshoot
C. PID improves transient response only
D. PD improves steady-state accuracy
ANSWER: A

Signal Flow Graphs (SFG) and Mason’s Gain Formula

51. A Signal Flow Graph (SFG) represents a system using:

A. Block diagrams
B. Nodes and branches
C. Transfer functions
D. Polynomials
ANSWER: B

52. In a Signal Flow Graph, the nodes represent:

A. Signals or variables
B. Gain of the system
C. Poles of the system
D. System stability
ANSWER: A

53. What does a branch in a Signal Flow Graph indicate?

A. Input to the system
B. Feedback in the system
C. The relationship between two nodes
D. The output of the system
ANSWER: C

54. Which of the following statements is true about Mason’s Gain Formula?
A. It can only be applied to closed-loop systems.
B. It calculates the gain of the system by evaluating paths and loops in the SFG.
C. It is based on differential equations.
D. It cannot be used for feedback systems.
ANSWER: B

55. The forward path gain in Mason’s Gain Formula is defined as:
A. The product of gains along a path from input to output
B. The sum of gains in all loops
C. The ratio of output to input
D. The reciprocal of the determinant
ANSWER: A

56. In Mason’s Gain Formula, what is Δ (delta)?

A. The sum of forward path gains
B. The determinant of the system, accounting for all loops
C. The overall gain of the system
D. The feedback factor
ANSWER: B

57. Which of the following terms is included in the calculation of Δ (delta) in Mason’s Gain
Formula?
A. The sum of all individual loop gains
B. The product of all forward path gains
C. The reciprocal of all loop gains
D. The difference between input and output signals
ANSWER: A

58. In Mason’s Gain Formula, two loops are considered non-touching if:
A. They share at least one common node
B. They do not share any common nodes
C. They have the same gain value
D. They are in the forward path
ANSWER: B

59. The transfer function of a system using Mason’s Gain Formula is given by:
A. The product of forward path gains
B. The ratio of output to input
C. The sum of all loop gains
D. The sum of gains of forward paths divided by Δ
ANSWER: D

60. Which of the following is NOT a step in using Mason’s Gain Formula?
A. Identify all forward paths
B. Calculate individual loop gains
C. Derive the governing differential equations
D. Determine non-touching loops and their products
ANSWER: C