HardAssistant Engineer (Electrical), Class-2, Road and Building Department2025✓ Editorially verified

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

⚑ Report issue

Found a wrong answer, translation, image or source problem? Send it to editorial review.

Answer & Explanation

Correct AnswerA. 1 − 1/3(4e^(−t) − e^(−4t))

Quick Explanation

For unity feedback, first form T(s)=G(s)/(1+G(s)), then multiply by the step input 1/s and perform partial fractions. For G(s)=4/[s(s+5)], the closed-loop denominator is s²+5s+4=(s+1)(s+4), giving the response 1−(1/3)(4e⁻ᵗ−e⁻⁴ᵗ).

Formula / Key Relation

T(s)=4/[s²+5s+4]

=4/[(s+1)(s+4)]

C(s)=T(s)/s

=4/[s(s+1)(s+4)]

c(t)=1−(4/3)e⁻ᵗ+(1/3)e⁻⁴ᵗ

=1−(1/3)(4e⁻ᵗ−e⁻⁴ᵗ)

Detailed Explanation

Concept & Reasoning

The closed-loop transfer function is 4/[s(s+5)+4]=4/[(s+1)(s+4)]. For a unit step, C(s)=4/[s(s+1)(s+4)]. Partial-fraction expansion gives 1/s−(4/3)/(s+1)+(1/3)/(s+4). Taking the inverse Laplace transform produces the keyed result.

How to Solve It in the Exam

Unity feedback: close the loop before applying the input.

Important Exam Point

Check c(0⁺)=0 and c(∞)=1 as quick validation.

Related Revision Path

This question sits in the revision path Control Systems → Time Response → Closed-Loop Step Response .

Unity-Feedback Step Response explanatory diagram

Quick Trick

Unity feedback: close the loop before applying the input.

Common Mistake

Using open-loop G(s) directly as the step-response transfer function.

Exam Tip

Check c(0⁺)=0 and c(∞)=1 as quick validation.

SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.

Exam Path

Knowledge Path

Study concept · Unity-Feedback Step Response →Practice concept Practice topic

11Previous Exam Appearances

6All Related Questions

87Content Quality

Previous Exam Appearances

Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 211