Warning: The model order was increased to handle real negative poles.

Hi!

Why order of continuous transfer function increase when I apply 'zoh' to a discrete transfer function?

I know it writes that the reason is to handle the real negative poles, but that does not clarify me.

Te = 4.5e-4;
Hd_w_arx =
 
      -2.145 z + 4.224
  ------------------------
  z^2 - 0.9742 z - 0.01883
Hc_w_arx = d2c(Hd_w_arx,'zoh')
Hc_w_arx =
 
    -3.183e04 s^2 - 4.419e08 s + 5.749e11
  ------------------------------------------
  s^3 + 1.764e04 s^2 + 1.267e08 s + 1.919e09

Answer 1

[Sarvani Panguluri]

Hi,

As the documentation mentions, For discrete-time LTI models having negative real poles, ZOH d2c conversion produces a continuous system with higher order.

A negative real pole in the z domain maps to a pure imaginary value in the s domain. Such mapping results in a continuous-time model with complex data. So to avoid this issue, the interpolation algorithm maps the real negative pole in the z domain to pair of complex conjugate poles in the s domain thereby increasing the order.

For more detailed information, you can go through the References.

Hope this helps!