Theory:
The forward path transfer function of general second order system is given by,

$$ {FPTF ~ G(s) ~ = \frac{w_n^2}{s(s+2ζw_n)}} $$

Addition of pole to forward path transfer function :

When we add a pole, transfer function becomes,

$$ {G'(s) = \frac{w_n^2}{s(s+2ζw_n)(T_ps+1)}} $$

$$ {~~~~~~~ = \frac{w_n^2}{s(s+2ζw_n)(s+P)}} $$

$$ {\frac{C(s)}{R(s)} = \frac{G'(s)}{1+G'(s)H(s)} = \frac{G'(s)}{1+G'(s)}} $$

$$ {\frac{C(s)}{R(s)} = \frac{w_n^2P}{s^3+(P+2ζw_n)s^2 + 2ζw_nPs+w_n^2P}} $$