Question

If the closed-loop transfer function $T\left(s\right)$of a unity negative feedback system is given by
$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1{s}^{n-1}+...+a_{n-1}s+a_n}$ then the steady state error for a unit ramp input is

• A. $\frac{a_n}{a_{n-1}}$
• B. $\frac{a_n}{a_{n-2}}$
• C. $\frac{a_{n-2}}{a_{n-1}}$
• D. zero

Answer 1

The correct option is D zero

$T\left(s\right)=\frac{\frac{a_{n-1}s+a_n}{s^n+a_1{s}^{n-1}+...a_{n-2}{s}^2}}{1+\frac{a_{n-1}s+a_n}{s^n+a_1{s}^{n-1}+...a_{n-2}{s}^2}}$
$G\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1{s}^{n-1}+...+a_{n-2}{s}^2}$
For type 2, Ramp input
$K_v=\underset{s\to 0}{lim}sG\left(s\right)$
$K_v=\infty$
$e_{ss}=\frac{1}{K_v}=0$