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A feedback control system is shown in the figure. What is the value of K for unit ramp input so that the system will have damping ratio of 0:5?

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  1. 50
  2. 150
  3. 125
  4. 25

Answer (Detailed Solution Below)

Option 3 : 125
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Detailed Solution

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Concept:

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

Where,

ζ is the damping ratio

ωn is the undamped natural frequency

Characteristic equation: 

Roots of the characteristic equation are: 

α is the damping factor

Calculation:

Given ζ = 0.5

G(s) = K / s(s+5)

H(s) = 0.2

Comparing with standard second-order system

2ζωn = 5 (ζ = 0.5)2

ωn = 5 

ωn2 = 0.2 K

K = 125

Additional Information

The nature of the system is described by its ‘ζ’ value

ζ

Nature

ζ = 0

Undamped

0 < ζ < 1

Underdamped

ζ = 1

Critically damped

ζ > 1

Overdamped

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