Question

The unit step response of a system with the transfer function $G\left(s\right)=\frac{1-2s}{1+s}$ is given by which one of the following waveforms?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$T.F.=\frac{1-2s}{1+s}$

$C\left(s\right)=\frac{1-2s}{1+s}.\frac{1}{s}=\frac{A}{1+s}+\frac{B}{s}$

For A,

$A={lim}_{s\to -1}(s+1).\frac{1-2s}{s(1+s)}$

$=\frac{(1-2(-1)}{(-1)}=\frac{1+2}{-1}=-3$

For B,

$B={lim}_{s\to 0}s.\frac{1-2s}{(1+s)s}=1$

$C\left(s\right)=\frac{1}{s}-\frac{3}{1+s}$

$C\left(t\right)=(1-3e^{-t})u\left(t\right)$