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Which has one of the following transfer functions the greatest overshoot?

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Answer (Detailed Solution Below)

Option 4 :
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Detailed Solution

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Concept:

The transfer function of the standard second-order system is:

Characteristic equation: 

ζ is the damping ratio

ωn is the undamped natural frequency

Mp is the maximum peak overshoot of the closed-loop transfer function

Calculation:

Option A:

 

On Solving we'll get:

ωn = 2

ζ = 0.33

Option B:

On Solving we'll get:

ωn = 4

ζ = 0.25

Option C:

On Solving we'll get:

ωn = 5

ζ = 0.2

Option D:

On Solving we'll get:

ωn = 6

ζ = 0.16

Thus, Option 4 has the lowest ζ, So it has maximum Overshoot.

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