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Which of the following transfer function will have the greatest maximum overshoot?
- a)9/(s2+2s+9)
- b)16/(s2+2s+16)
- c)25/(s2+2s+25)
- d)36/(s2+2s+36)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following transfer function will have the greatest maximu...
Answer: d
Explanation: Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .
Explanation: Comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .
Most Upvoted Answer
Which of the following transfer function will have the greatest maximu...
Explanation:
Maximum overshoot is defined as the maximum value reached by the response curve from steady-state value. The transfer function that exhibits the highest maximum overshoot will have a higher value of the damping ratio (ζ).
The standard form of a second-order transfer function is given as:
G(s) = K/((s^2) +2ζωns +ωn^2)
where,
K = system gain
ζ = damping ratio
ωn = natural frequency
To determine which transfer function will have the highest maximum overshoot, we need to calculate the damping ratio (ζ) for each transfer function.
a) 9/(s^2 +2s+9)
ζ = 2/2√(9*1) = 0.44
b) 16/(s^2 +2s+16)
ζ = 2/2√(16*1) = 0.5
c) 25/(s^2 +2s+25)
ζ = 2/2√(25*1) = 0.4
d) 36/(s^2 +2s+36)
ζ = 2/2√(36*1) = 0.33
From the above calculations, we can see that option D has the lowest damping ratio and hence will exhibit the highest maximum overshoot.
Therefore, the correct answer is option D (36/(s^2 +2s+36)).
Maximum overshoot is defined as the maximum value reached by the response curve from steady-state value. The transfer function that exhibits the highest maximum overshoot will have a higher value of the damping ratio (ζ).
The standard form of a second-order transfer function is given as:
G(s) = K/((s^2) +2ζωns +ωn^2)
where,
K = system gain
ζ = damping ratio
ωn = natural frequency
To determine which transfer function will have the highest maximum overshoot, we need to calculate the damping ratio (ζ) for each transfer function.
a) 9/(s^2 +2s+9)
ζ = 2/2√(9*1) = 0.44
b) 16/(s^2 +2s+16)
ζ = 2/2√(16*1) = 0.5
c) 25/(s^2 +2s+25)
ζ = 2/2√(25*1) = 0.4
d) 36/(s^2 +2s+36)
ζ = 2/2√(36*1) = 0.33
From the above calculations, we can see that option D has the lowest damping ratio and hence will exhibit the highest maximum overshoot.
Therefore, the correct answer is option D (36/(s^2 +2s+36)).
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