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The time taken for the output to settle within ± 2% of step input for the control system represented by  is given by

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  1. 1.2 s
  2. 1.6 s
  3. 2.0 s
  4. 0.4 s

Answer (Detailed Solution Below)

Option 2 : 1.6 s
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Detailed Solution

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Concept:

The characteristic equation is given by:

1 + G(s) H(s) = 0

Also, the standard second-order characteristic equation is:

Settling Time is the time taken by the response to reach ± 2%, tolerance band.

  for a 5% tolerance band.

 for 2% tolerance band

Calculation:

Characteristic equation:

s2 + 5s + 25 = 0

By comparing this with the standard second-order equation, we get:

Settling time is, therefore:

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