Get difference equation from continuous transfer function

2024 12 22
1 个回答
回答已采纳
更新时间：2024 12 22
6 次查看（30 天）

0 个投票

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'))

请先登录，再回答此问题。

 采纳的回答

Star Strider
Star Strider 2024-12-22
Ran in:

1 个投票

Ran in:
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.
.

2 个评论
显示 无 隐藏 无

ANDREA
ANDREA 2024-12-22
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
Star Strider 2024-12-22
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.
.

请先登录，再进行评论。

更多回答（0 个）

类别

在 帮助中心 和 File Exchange 中查找有关 Conversion Between Symbolic and Numeric 的更多信息

产品

版本

R2023b

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by