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Topic: [Matlab Question] Converting H(s) to H(z) using derivative approximation?
Replies: 8   Last Post: Dec 7, 2013 3:13 AM

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Nasser Abbasi

Posts: 5,706
Registered: 2/7/05
Re: [Matlab Question] Converting H(s) to H(z) using derivative approximation?
Posted: Oct 24, 2010 3:43 AM
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On 10/24/2010 12:21 AM, frodonet wrote:
> Hi All,
>
> I been having some issue with my lab work.
>
> I'm supposed to do :
>
> Transfer function H(s):
> 1
> --------------------------------------------
> s^4 + 2.613 s^3 + 3.414 s^2 + 2.613 s + 1
>
>
> Convert H(s) into a digital IIR filterH(z)using the derivative approximation method
> for the following three cases: T=0.05, T=0.25 and T=0.5.
>
> The problem is, I unable to use Matlab to convert the transfer function
> from s to z, when s = (1 - z^-1) / T.
>
> Matlab can only accept variable (z^-1)
>
> Not sure why, and when i see the calculation part, the maths is so rigorous....and
>
> I need to know whether using matlab is possible to find the coefficients of z?



You never did show what you did, so I do not understand what you mean by
"I unable to use Matlab to convert the transfer function".

It always helps to show what you actually did.

Any way, I am not sure if derivative approximation method is supported,
look at the options to c2d to make sure. the name might be called
something else. I know bilinear is there.

To do the conversion:


EDU>> s=tf('s');
EDU>> sys=1/(s^4 + 2.613*s^3 + 3.414*s^2 + 2.613*s + 1)

Transfer function:
1
-----------------------------------------
s^4 + 2.613 s^3 + 3.414 s^2 + 2.613 s + 1

EDU>> T=0.01;
EDU>> sysz=c2d(sys,T,'zoh')

Transfer function:
4.145e-010 z^3 + 4.536e-009 z^2 + 4.512e-009 z + 4.08e-010
----------------------------------------------------------
z^4 - 3.974 z^3 + 5.922 z^2 - 3.922 z + 0.9742


also
sysz=c2d(sys,T,'foh')

etc..

--Nasser



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