Problems with natural frequency and damping ratio (step response)

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Gustavo Araujo
Gustavo Araujo 2020-10-20
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)

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