Question

The response of a servomechanism is 1+0.2e^-60t-1.2e^-10t when subjected to a unit step input. What is the damping ratio?

(a) 1.21

(b) 1.43

(c) 1.59

(d) 1.74

The question was posed to me in an interview for job.

My question is from Integral Square Error & its Minimization in section Error Analysis of Control Systems

Answer 1

The correct choice is (b) 1.43

The best I can explain: First we apply Laplace Transform to the system and as R(s) = 1/s we get closed loop transfer function as C(s)/R(s) = 600/s^2+70s+600. Then we compare it with the standard equation for second order transfer function we got damping ratio = 70/2wn = 1.43.