MATLAB: Is damp function got any limitation

damp

Hi,
fs =
        3
  -------------
  s^2 + 3 s + 2
Continuous-time transfer function.
   Pole        Damping       Frequency      Time Constant  
                           (rad/seconds)      (seconds)    
 -1.00e+00     1.00e+00       1.00e+00         1.00e+00    
 -2.00e+00     1.00e+00       2.00e+00         5.00e-01
above are the result of my damp line, why my wn not √2 and damping not (3√2)/2 ? is there any limitation for damp function?

Best Answer

I don't understand clearly your question, but the damping ratio and natural frequency can be found mathematically as follows:
It is known that an ideal second order transfer function is as follows:
           K*Wn^2
  ------------------------
  s^2 + 2*zeta*Wn*s + Wn^2
If we extract the coefficients of both transfer functions' denominator and solve for zeta and Wn,
 2*zeta*wn=3
 Wn^2=2;
From this, Wn is found as sqrt(2) and zeta(damping ratio) is found as 3/(2*sqrt(2)). This means zeta is greater than 1, which is normal since both poles are real, which will result in an overdamped step response. Hope this helps.
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