Q. For a second-order system, what does a damping ratio of less than 1 indicate?
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A.
Underdamped response
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B.
Critically damped response
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C.
Overdamped response
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D.
Stable response
Solution
A damping ratio less than 1 indicates an underdamped response, which oscillates before settling.
Correct Answer:
A
— Underdamped response
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Q. In root locus analysis, what does the term 'breakaway point' refer to?
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A.
Point where the root locus starts
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B.
Point where the root locus ends
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C.
Point where the system becomes unstable
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D.
Point where multiple roots meet
Solution
A breakaway point is where the root locus leaves the real axis, indicating a change in the stability of the system.
Correct Answer:
A
— Point where the root locus starts
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Q. What is the phase margin if the gain crossover frequency is at 1 rad/s and the phase at that frequency is -135 degrees?
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A.
45 degrees
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B.
135 degrees
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C.
180 degrees
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D.
0 degrees
Solution
Phase margin is calculated as 180 degrees + phase at gain crossover frequency. Here, it is 180 - 135 = 45 degrees.
Correct Answer:
A
— 45 degrees
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Q. What is the stability condition for a system with the transfer function G(s) = 1/(s^2 + 4s + 5)?
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A.
All poles in the left half-plane
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B.
At least one pole in the right half-plane
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C.
Poles on the imaginary axis
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D.
All poles in the right half-plane
Solution
The system is stable if all poles of the transfer function are in the left half-plane.
Correct Answer:
A
— All poles in the left half-plane
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Q. What is the steady-state error for a type 1 system with a step input?
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A.
Zero
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B.
Finite
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C.
Infinite
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D.
Depends on gain
Solution
A type 1 system has a finite steady-state error for a step input due to the presence of an integrator.
Correct Answer:
B
— Finite
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Q. What is the steady-state error for a unit step input in a type 1 system?
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A.
Zero
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B.
Infinity
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C.
Constant
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D.
Proportional to input
Solution
A type 1 system has zero steady-state error for a unit step input.
Correct Answer:
A
— Zero
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Q. What is the time constant of a system with a transfer function G(s) = 5/(2s + 5)?
Solution
The time constant T is given by the coefficient of s in the denominator, which is 2. Therefore, T = 5/2 = 0.4.
Correct Answer:
A
— 0.4
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Q. What is the transfer function of a first-order system with a time constant of 2 seconds?
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A.
1/(2s + 1)
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B.
2/(s + 2)
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C.
1/(s + 2)
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D.
2/(2s + 1)
Solution
The standard form of a first-order transfer function is 1/(Ts + 1), where T is the time constant. Here, T = 2.
Correct Answer:
A
— 1/(2s + 1)
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Q. Which of the following is a characteristic of a second-order underdamped system?
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A.
No oscillations
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B.
Oscillations with decreasing amplitude
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C.
Oscillations with constant amplitude
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D.
Instantaneous response
Solution
A second-order underdamped system exhibits oscillations that gradually decrease in amplitude over time.
Correct Answer:
B
— Oscillations with decreasing amplitude
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Q. Which of the following represents a closed-loop system?
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A.
Open-loop control
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B.
Feedback control
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C.
Feedforward control
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D.
Open-loop feedback
Solution
A closed-loop system uses feedback to compare the actual output with the desired output.
Correct Answer:
B
— Feedback control
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