Question

A unity-feedback control system has the open-loop transfer function $G\left(s\right)=\frac{4(1+2s)}{s^2(s+2)}$ if the input to the system is a unit ramp, the steady-state error will be

• A. $0$
• B. $0.5$
• C. $2$
• D. Infinity

Answer 1

The correct option is A $0$

$K_V=\underset{s\to 0}{lim}sG\left(s\right)H\left(s\right)=\underset{s\to 0}{lim}\frac{s4(1+2s)}{s^2(s+2)}$
$=\underset{s\to 0}{lim}\frac{4(1+2s)}{s(s+2)}=\infty$
$e_{ss}=\frac{A}{K_V}=\frac{A}{\infty }=0$