[Z transform] problem with MATLAB

Question

Franklin Ngo 2017-9-11

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/356019-z-transform-problem-with-matlab

编辑： Jeovane Sousa 2021-4-21

Hi experts, I have a question about Z-transform on MALTAB. When I convert a Laplace function F(s)=1/s to Z function, MATLAB says it is T/(z-1), but the Laplace-Z conversion table show that is z/(z-1). I know MATLAB cannot wrong because I drew a step graph of all these three functions. But all the books I found about Laplace and Z-transform also say the conversion table is right.

It's confusing me and I need an answer. Could anyone give me an explain for that? Thank in advanced.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Star Strider 2017-9-11

3
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/356019-z-transform-problem-with-matlab#answer_281059

在 MATLAB Online 中打开

The Symbolic Math Toolbox doesn’t know you’re trying to convert it from the Laplace domain to the ‘z’ domain. You have to play by its rules.

This works:

syms s t z 
T1(s) = 1/s
T2(t) = ilaplace(T1)
T3(z) = ztrans(T2)
T1(s) =
 1/s
T2(t) =
 1
T3(z) =
 z/(z - 1)

5 个评论
显示 3更早的评论隐藏 3更早的评论

Star Strider 2017-9-12

As always, my pleasure.

If my Answer hslped you solve your problem, please Accept it!

Jeovane Sousa 2021-4-21

编辑：Jeovane Sousa 2021-4-21

As I understand from here https://www.mathworks.com/help/control/ug/continuous-discrete-conversion-methods.html#bs78nig-12

Matlab uses the following method to calculate c2d by ZOH

The ZOH block generates the continuous-time input signal u(t) by holding each sample value u(k) constant over one sample period:

The signal u(t) is the input to the continuous system H(s). The output y[k] results from sampling y(t) every Ts seconds.

Resolving to

:

each term will look something like that

thus,

And

Or remember the z-transform of a signal tha goes through a sample and holder, tha is:

This is what I think how c2d was implemented. No garantees it is correct or valid.

I hope I have made the correct considerations. Feel free to complement or point any mistake. Sorry about the poor English, it is not my primary language.

请先登录，再进行评论。