How to define dominant poles of high order system?

Hi

I create a 5th order random system using rss() command. Then i get poles using pole() command. I took two conjugate imaginery poles as dominant poles. I produce a characteristic equation with that poles. wn and zeta calculated with that equation. I put zeta value into the overshoot formulation. But it's not true value.

When I apply step input the system, overshoot becomes %142 but with this method I took % 74.

What can be faulse?

clear all;

clc;

%system=tf(rss(5));

% 0.3521 s^4 + 2.036 s^3 + 21.5 s^2 + 16.34 s + 1.281

% ---------------------------------------------------------

% s^5 + 2.696 s^4 + 11.37 s^3 + 20.04 s^2 + 11.41 s + 1.695

s=tf('s');

system = (0.3521*s^4 + 2.036*s^3 + 21.5*s^2 + 16.34*s + 1.281) / (s^5 + 2.696*s^4 + 11.37*s^3 + 20.04*s^2 + 11.41*s + 1.695)

p=pole(system);

% p =

% -0.27477 + 2.9746i

% -0.27477 - 2.9746i

% -1.2615 + 0i

% -0.65514 + 0i

% -0.22984 + 0i

s1= -0.27477 + 2.9746i

s2= -0.27477 - 2.9746i

%so we get the dominant poles

%most closed poles to origin

char_eq=(s-s1)*(s-s2);

% s^2 + 0.5495 s + 8.924

w_n=(8.924)^(1/2);

zeta = 0.5495 / (2*w_n);

overshoot = 100*exp((-zeta*pi)/((1-zeta^2)^(1/2)))