Question

A system with transfer function 1/Ts+1, subjected to a step input takes to seconds to reach 50% of step height. The value of t is :

(a) 6.9s

(b) 10s

(c) 14.4s

(d) 20s

I have been asked this question in a job interview.

Question is taken from Time Response of First Order Systems in division Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

Correct choice is (c) 14.4s

To elaborate: The response of a first order system is:

  A(t)=a[1-e^-t/T]

  ½= 1-e^-10/t

  T= 14.43 sec.