Question

A unity feedback system has an open-loop transfer function  \(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\) If the damping ratio is 0-5, then what is the value of K?A unity feedback system has an open-loop transfer function If the damping ratio is 0-5, then what is the value of K?

1. 150
2. 100
3. 50
4. 10

Answer 1

Correct Answer - Option 2 : 100

Concept:

Open loop transfer function is given by:

G(s)H(s)

Characteristic equation is given by:

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

The characteristic equation for second order system is given by:

s² + 2ζω_ns + ω²_n = 0

TB Solution:

Given ζ = 0.5

\(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\)

Characteristic equation is given by:

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

\(1+ \frac{K}{{s\left( {s + 10} \right)}}=0\)

s² + 10s + k = 0

Comparing the above equation with  s2 + 2ζωns + ω2n = 0

2ζω_n = 10 and k = ω²_n

2(0.5)√k = 10

√k = 10

k = 10²

k = 100