Question

Unit step response of a linear time invariant (LTI) system is given by y(t) = (1 − e^−2t) u(t). Assuming zero initial condition, the transfer function of the system is
1. \(\frac{1}{{s + 1}}\)
2. \(\frac{2}{{\left( {s + 1} \right)\left( {s + 2} \right)}}\)
3. \(\frac{1}{{s + 2}}\)
4. \(\frac{2}{{s + 2}}\)

Answer 1

Correct Answer - Option 4 : \(\frac{2}{{s + 2}}\)

y(t) = (1 – e^-2t) u(t)

By applying Laplace transform,

\(y\left( s \right) = \frac{1}{s} - \frac{1}{{s + 2}} = \frac{2}{{s\left( {s + 2} \right)}}\)

Transfer function \(= \frac{{Y\left( s \right)}}{{R\left( s \right)}} = \frac{{\frac{2}{{s\left( {s + 2} \right)}}}}{{\frac{1}{s}}} = \frac{2}{{s + 2}}\)