Question

A unity feedback control system has an open loop transfer function \(G\left( s \right) = \frac{25}{{s\left( {s + 8} \right)}}\). Its damping ratio is
1. 0.2
2. 0.5
3. 0.8
4. 0.99

Answer 1

Correct Answer - Option 3 : 0.8

Closed loop transfer function,

\(T\left( s \right) = \frac{{G\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)

\(= \frac{25}{{{s^2} + 8s + 25}}\)

Standard transfer function of second order system

\(T\left( s \right) = \frac{{{\rm{\omega }}_n^2}}{{{s^2} + 2\xi {{\rm{\omega }}_n}s + {\rm{\omega }}_n^2}}\)

By comparing both,

ω2n = 25 ⇒ ωn = 5

⇒ 2ξ ωn = 8 ⇒ ξ = 0.8