Question
Download Solution PDFFor a system having transfer function \(G\left( s \right) = \frac{{ - s + 1}}{{s + 1}}\), a unit step input is applied at time t = 0. The value of the response of the system at t = 1.5 sec (rounded off to three decimal places) is __________.
Answer (Detailed Solution Below) 0.550 - 0.556
Detailed Solution
Download Solution PDF\(G\left( s \right) = \frac{{ - s + 1}}{{s + 1}}\)
r(t) = u(t)
\(\Rightarrow r\left( s \right) = \frac{1}{s}\)
Output, C(s) = R(s) G(s)
\(= \frac{1}{s}\left( {\frac{{1 - s}}{{1 + s}}} \right)\)
\(\Rightarrow c\left( s \right) = \frac{1}{s} - \frac{2}{{1 + s}}\)
By applying inverse Laplace transform,
⇒ c(t) = u(t) – 2e-t u(t)
At t = 1.5 sec,
c(t = 1.5s) = 1 – 2e-1.5 = 0.553Last updated on Feb 19, 2024
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