I'm trying to convert a system from c2d and then from d2c but the results are not the same. Why? There is no delay!

My system is: s^2/s^3+1 My code is:

num=[1 0 0];
den=[1 0 0 1];
sys=tf(num,den)
sysd=c2d(sys,0.3)
sys2=d2c(sysd)

Why is the "sys" different from the "sys2"? Why a system like this 1/(s+1) gives correct results?

num=[1];
den=[1 1];
sys=tf(num,den)
sysd=c2d(sys,0.3)
sys2=d2c(sysd)

Answer 1

[zohar]

Hi sadel

I execute your code and I got :

Transfer function:
  s^2
-------
s^3 + 1

Transfer function:
 0.2997 z^2 - 0.6 z + 0.3003
-----------------------------
z^3 - 2.987 z^2 + 3.014 z - 1

Sampling time: 0.3

Transfer function:
    s^2 - 6.217e-015 s - 1.066e-014
---------------------------------------
s^3 - 6.106e-015 s^2 - 1.377e-014 s + 1

1.377e-014 is very close to zero !

Isn't it enough ?

[sadel]

yes, but how can I make it looks like the first?

[Walter Roberson]

Polynomial fitting almost always has round-off error.

[sadel]

There is no way I to fix it? Even if I take the coefficients and round them?