Question

The transfer function of the system is \( G(s) = \frac{100}{(s + 1)(s + 100)} \). For a unit step input, the approximate settling time for the 2 percent criterion is

• A. 100 sec
• B. 4 sec
• C. 1 sec
• D. 0.01 sec

Hint:

Dominant poles determine the settling time in second-order systems.

Answer 1

The Correct Option is B

- The settling time for a second-order system is approximated as \[ T_s \approx \frac{4}{\zeta \omega_n} \] - From the poles at \( s = -1 \) and \( s = -100 \), the dominant pole is at \( s = -1 \). \[ T_s \approx \frac{4}{1} = 4 \, \text{sec} \]
Conclusion: The correct settling time is given by option (b).