Question

A ramp input applied to an unity feedback system results in $5\%$ steady state error. The type number and zero frequency gain of the system are respectively

• A. $1\text{and}20$
• B. $0\text{and}20$
• C. $1\text{and}1/20$
• D. $1\text{and}1/20$

Answer 1

The correct option is A $1\text{and}20$

$e_{ss}=\underset{s\to 0}{lim}sE\left(s\right)/R\left(s\right)=\frac{1}{s^2}$
$=\underset{s\to 0}{lim}s\frac{R\left(s\right)}{1+G\left(s\right)}$ $=\underset{s\to 0}{lim}\frac{1}{s+sG\left(s\right)}=\text{finite(given)}$
$K_v=\underset{s\to 0}{lim}sG\left(s\right)$
$e_{ss}=\underset{s\to 0}{lim}\frac{1}{sG\left(s\right)}=\text{finite}=5\%=\frac{1}{20}$
$\therefore K=20$
$K_V$ is finite for type 1 system having ramp input.