[Scilab-users] New problems with "freson" in CACSD module

[Stéphane Mottelet]

Thanks Lucien, however, to complete the task, you should first reopen 
bug #15368 at https://bugzilla.scilab.org/show_bug.cgi?id=15368

S.

Can you create a bug

Le 25/09/2019 à 16:06, lucien.povy a écrit :
> Hello all !
> I believe that there are new problems with "freson.sci" program in 
> CACSD module.
> If you are running two programs, one for continuous system another for 
> sampled system,
> sometimes you have a result as [ ] : you must improve the accuracy of 
> result ;("ffreson.sci" program is proposed).
> (Bugs not bugs ???? yes bugs : see in text REMARK.
>
> 1 . Example : continuous system.
>    s=%s ; num = s+1.4*s^2+1.4*s^3+0.4*s^4 ; den = 
> 0.5+0.8*s+1.4*s^2+1.4*s^3+0.4*s^4 ;
>    h = syslin("c",num,den)
>    fr = freson(h)
>    fr =
>         []
>    gainplot(h,0.01,1)
>    with my new function "ffreson.sci" :
>    ffreson(h)//La nouvelle fonction.
>    ans  =
>             0.111164226146
>
> 2 . Example : sampled system.
>    The exercise in "help" page of "freson" with sampling period 
> Ts=0.01s : the program gives "fr=[]" .
>    With sampling period Ts=0.04s you have a good result (problem of 
> accuracy) : run the example in help
>    and change sampling period.
>
> 3 . My opinion and the proposed solutions.
>
>    - For continuous system :
>    If you calculated the function "h(s)*h(-s)" by convolution, the 
> result, as I mentioned before,
>    must be an even rational : with "horner" it's not, but by 
> convolution the result is OK. (take a look on "ffreson" program :
>    you find a program "hps_hms" which gives "h(s)*h(-s)" by convolution).
>    - After that, the numerator of "h(s)*h(-s)"derivative is 
> calculated, this polynomial "der" must be odd (s=0 is a particular 
> root of "der" which   corresponds to zero frequency). If you excluded 
> this root from "der", the new polynomial is even, and you can solve
>     the finding roots problem with a new polynomial in u=s*s as 
> variable.If "rac" is the vector of square roots of this new 
> polynomial, the vector "r", roots of "der", is r=[rac;-rac;0]. You 
> divide by two the degree of "der" and increase the accuracy
>     of the result : I use this method in my program.
>
>     REMARK : If you run "freson" and "ffreson", step by step, when you 
> calculated the roots of derivatives, the number of roots are not the 
> same !!!  (see "Exemple freson.pdf").
>
>     - For sampled system :
>     - We calculated the function "hh=h(z)*h(1/z)", also with 
> convolution, the result of convolution gives for coefficients vectors
>     of "hh" a symmetric vector [c1,c2, ....cn], (for numerator and 
> denominator), c1=cn, c2=c(n-1) etc ....see "hpz_hiz" at the end of 
> function "ffreson.sci".
>     - After that we take account of "z^(degree(h.num)-degree(h.den)) 
> in "hh", and calculated the numerator of derivative of new
>     "hh".
>     - Like for continuous system, you excluded "z=1" and "z=-1", which 
> corresponds to frequencies f0=0 and f1=1/*(2*ts) (Nyquist frequency).
>     - At the end you calculated the roots "r" of new polynomial (the 
> degree of polynomial decreases by two) . A "good" solution must 
> respect "rp=exp(%i*%pi*fp*ts)"; so |rp|=1 and fp>0. The end of my new 
> program is the same as "freson.sci".
>     I use those methods in the new program "ffreson.sci".
>     REMARK : the same.
>
>     Yours sincerely
>     lucien.povy at free.fr
>
>     PS
>     I attached the new function "ffreson.sci" and a report ("Exemples 
> freson.pdf", sorry in french language) to my email.
>     In "ffreson" you have two functions "hps_hms" for h(s)*h(-s) and  
> "hpz_hiz" for h(z)*h(1/z).
>     This program "ffreson" can be used for "iodelay systems", and " 
> hps_hms" , "hpz_hiz" used in m_margin and p_margin
>     to improve the accuracy of results.
>
>
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-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

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