Get difference equation from continuous transfer function

Hello,

I have a continuous transfer function such as:

0.002174 s + 0.0001581

----------------------------------------------------------

6.267 s^4 + 3.378 s^3 + 0.6042 s^2 + 0.04081 s + 0.0007907

I'm trying to convert it to a difference equation with negative exponents(z^(-n)).

I've already tried to calculate it manually with syms but, i found it quite impossible to work with.

tustin =(2/Ts)*(1-z^(-1))/(1+z^(-1))

modello_disc = subs(modello, s, tustin)%this is just an example. i gotta split num and den before cause it gives me an error if i try it with the tf above.

i've also tried to use the common c2d command but it doesn't give me the result i hope for.

z = tf('z', 'Variable','z^-1')

modello = tf(c2d(modello, Ts, 'tustin'))

Answer 1

[Star Strider]

One approach —

0.002174 s + 0.0001581

----------------------------------------------------------

6.267 s^4 + 3.378 s^3 + 0.6042 s^2 + 0.04081 s + 0.0007907

s = tf('s');
Hs = (0.002174*s + 0.0001581) / (6.267*s^4 + 3.378*s^3 + 0.6042*s^2 + 0.04081*s + 0.0007907)

Hs =
 
                    0.002174 s + 0.0001581
  ----------------------------------------------------------
  6.267 s^4 + 3.378 s^3 + 0.6042 s^2 + 0.04081 s + 0.0007907
 
Continuous-time transfer function.

Ts = 1;
Hz = c2d(Hs, Ts, 'tustin')

Hz =
 
  3.472e-05 z^4 + 7.187e-05 z^3 + 7.308e-06 z^2 - 6.213e-05 z - 3.228e-05
  -----------------------------------------------------------------------
              z^4 - 3.505 z^3 + 4.598 z^2 - 2.675 z + 0.5823
 
Sample time: 1 seconds
Discrete-time transfer function.

Hz.Variable = 'z^-1'

Hz =
 
  3.472e-05 + 7.187e-05 z^-1 + 7.308e-06 z^-2 - 6.213e-05 z^-3 - 3.228e-05 z^-4
  -----------------------------------------------------------------------------
             1 - 3.505 z^-1 + 4.598 z^-2 - 2.675 z^-3 + 0.5823 z^-4
 
Sample time: 1 seconds
Discrete-time transfer function.

Other options are available. See c2dOptions for details.

.

[ANDREA Marini]

Thank you really much! You just saved me hours of wasting time with the syms library.

Just a quick question, why wouldn't my script before with

z = tf('z', 'Variable','z^-1')

Am i not doing the same thing but in a general way?

[Star Strider]

My pleasure!

That would work if you defined your transfer function in the ‘z’ domain. (See Discrete-Time Transfer Function Model Using Rational Expression for those details.) It will not automatically convert a continuous to a discrete transfer function. You need to do that similarly to the way I did here.

.