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

What is the response of the feedback function with open loop transfer

1.	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» 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 as1-1/3(4e^-t – e^-4t).

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