Q. For a second-order system, what does a damping ratio of 0.5 indicate?
A.
Underdamped response
B.
Critically damped response
C.
Overdamped response
D.
Stable response
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Solution
A damping ratio of less than 1 (0.5 in this case) indicates an underdamped response, characterized by oscillations.
Correct Answer:
A
— Underdamped response
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Q. For a second-order system, what is the damping ratio if the poles are located at -2 ± j2?
A.
0.5
B.
1
C.
0.707
D.
0
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Solution
The damping ratio (ζ) can be calculated as ζ = -σ/√(σ² + ω²), where σ = 2 and ω = 2, giving ζ = 0.707.
Correct Answer:
C
— 0.707
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Q. In a PID controller, what does the integral term do?
A.
Reduces steady-state error
B.
Increases response time
C.
Decreases overshoot
D.
Eliminates the need for a proportional term
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Solution
The integral term in a PID controller accumulates the error over time, which helps to eliminate steady-state error.
Correct Answer:
A
— Reduces steady-state error
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Q. In a PID controller, what does the proportional gain affect?
A.
Steady-state error
B.
Transient response
C.
System stability
D.
All of the above
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Solution
The proportional gain affects all aspects of system performance, including steady-state error, transient response, and stability.
Correct Answer:
D
— All of the above
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Q. What is the effect of increasing the gain in a closed-loop system?
A.
Increases stability
B.
Decreases stability
C.
No effect on stability
D.
Increases steady-state error
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Solution
Increasing the gain in a closed-loop system can lead to decreased stability, potentially causing oscillations or instability.
Correct Answer:
B
— Decreases stability
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Q. What is the integral action in a PID controller responsible for?
A.
Eliminating steady-state error
B.
Improving transient response
C.
Increasing system stability
D.
Decreasing overshoot
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Solution
The integral action in a PID controller accumulates the error over time, which helps eliminate steady-state error.
Correct Answer:
A
— Eliminating steady-state error
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Q. What is the phase margin if the gain crossover frequency is at 45 degrees?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
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Solution
The phase margin is calculated as 180 degrees minus the phase at the gain crossover frequency. If the phase is -135 degrees, the phase margin is 45 degrees.
Correct Answer:
C
— 90 degrees
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Q. What is the root locus of a system used for?
A.
To determine the frequency response
B.
To analyze the stability of the system as gain varies
C.
To find the transfer function
D.
To design the controller
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Solution
The root locus is a graphical method used to analyze how the roots of a system change with varying gain, which helps in stability analysis.
Correct Answer:
B
— To analyze the stability of the system as gain varies
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Q. What is the stability condition for a system with the characteristic equation s^2 + 3s + 2 = 0?
A.
Stable
B.
Unstable
C.
Marginally stable
D.
Cannot be determined
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Solution
The roots of the characteristic equation are s = -1 and s = -2, both of which are in the left half of the s-plane, indicating stability.
Correct Answer:
A
— Stable
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Q. What is the time constant of a system with a transfer function of 1/(2s + 1)?
A.
0.5 seconds
B.
2 seconds
C.
1 second
D.
4 seconds
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Solution
The time constant (T) is the coefficient of s in the denominator, which is 1/2, thus T = 2 seconds.
Correct Answer:
B
— 2 seconds
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Q. Which of the following describes a closed-loop control system?
A.
Output is independent of input.
B.
Feedback is used to compare output with input.
C.
No feedback is used.
D.
Only feedforward control is applied.
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Solution
A closed-loop control system uses feedback to compare the output with the desired input, allowing for adjustments.
Correct Answer:
B
— Feedback is used to compare output with input.
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