Question

Consider a system with transfer function G(s) = s+6/Ks^2+s+6. Its damping ratio will be 0.5 when the values of k is:

(a) 2/6

(b) 3

(c) 1/6

(d) 6

The question was posed to me in my homework.

This interesting question is from Time Response of Second Order Systems topic in division Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

Correct option is (c) 1/6

To elaborate: s+6/K[s^2+s/K+6/K]

Comparing with s^2+2Gw+w^2

w= √6/K

2Gw=1/K

2*0.5*√6/K =1/K

K=1/6.