GATE EE 2015 Set 2 — Question 63
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Control Systems → Time-Domain Analysis → First & Second-Order Response
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Question
The unit step response of a system with the transfer function is given by which one of the following waveforms?
Correct answer
(A) [figure]
Solution
The transfer function is . The unit step response is given by:
Using partial fraction expansion:
So, . Taking the inverse Laplace transform:
Evaluating at specific points:
At , .
At , .
The derivative is , which is always positive for , meaning the response is monotonically increasing.
Waveform (A) starts at -2 and asymptotes to 1, which matches our result.
Using partial fraction expansion:
So, . Taking the inverse Laplace transform:
Evaluating at specific points:
At , .
At , .
The derivative is , which is always positive for , meaning the response is monotonically increasing.
Waveform (A) starts at -2 and asymptotes to 1, which matches our result.
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