Question

What is the response of the feedback function with open loop transfer function G(s) = 4/s(s+5) and input is input step?

(a) 1-1/3(4e^-t – e^-4t)

(b) 1-1/2(6e^-t – e^-4t)

(c) 1-1/3(6e^-t – e^-4t)

(d) 1-1/2(4e^-t – e^4t)

This question was posed to me in semester exam.

This intriguing question comes from Integral Square Error & its Minimization topic in chapter Error Analysis of Control Systems

Answer 1

Correct option is (a) 1-1/3(4e^-t – e^-4t)

Easiest explanation: We should first get the response in s domain which is C(s)/R(s) = G(s)/1+G(s) = R(s) 4/(s+1)(s+4) and as the input is unit step which R(s)=1/s the equation becomes 4/s(s+1)(s+4). Then we apply partial fraction to the equation and we get values of A, B, C as 1, -4/3, 1/3 and then inverse Laplace transform is applied to C(s) and we get response as  1-1/3(4e^-t – e^-4t).