Question

Let c(t) be the unit step response of a system with transfer function K(s+a)/(s+K). If c(0+) = 2 and c(∞) = 10, then the values of a and K are respectively.

(a) 2 and 10

(b) -2 and 10

(c) 10 and 2

(d) 2 and -10

I got this question in an online quiz.

I'd like to ask this question from Time Response of Second Order Systems topic in division Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

Right option is (c) 10 and 2

Best explanation: Applying initial value theorem which state that the initial value of the system is at time t =0 and this is used to find the value of K and final value theorem to find the value of a.