Problems with natural frequency and damping ratio (step response)

Hey everyone!

I'm having an issue with natural frequency, amplitude and damping ratio of a system. I have a transfer function (discrete time) as follows:

num = [G 2*G G] (where G = 1/50)

den = [c b a]

where:

a = (wn)^2 + 4/(T^2) - (4*ksi*wn)/T

b = 2* ((wn)^2 - 4/(T^2))

c = (wn)^2 + 4/(T^2) + (4*ksi*wn)/T

where ksi is the damping ratio and wn the natural frequency. I need to apply this TF to another system, but when I change the natural frequency, the amplitude based on step response changes too.

Somebody could help what am I getting wrong or how to solve this problem?

Thanks in advance.

Here's the full code:

G = 1.0/150;

T = 10e-6

% r = a + (b-a).*rand(N,1) no intervalo de (a,b)

%ksi = 0.35 + (0.9-0.35).*rand(10,1);

ksi = 0.35;

wn = 230;

A = 4/(T^2)

B = (4*ksi*wn)/T

C = (wn)^2

a = C + A - B

b = 2*C - 2*A

c = A + B + C

num = [G 2*G G]

den = [c b a]

sys = tf (num,den,T)

step(sys, T)