Question

The transfer function of a plant is
$T\left(s\right)=\frac{5}{(s+5)(s^2+s+1)}.$ The second-order approximation of $T\left(s\right)$ using dominant pole concept is

• A. $\frac{1}{(s+5)(s+1)}$
• B. $\frac{5}{(s+5)(s+1)}$
• C. $\frac{5}{s^2+s+1}$
• D. $\frac{1}{s^2+s+1}$

Answer 1

The correct option is D $\frac{1}{s^2+s+1}$

In dominant pole concept, the factor that has to be eliminated should be in time constant form
$\frac{5}{(s+5)(s^2+s+1)}=\frac{5}{5(1+\frac{s}{5})(s^2+s+1)}$
$=\frac{1}{s^2+s+1}$