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

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

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
     [hidden email]

     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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Exemples freson.pdf (61K) Download Attachment
ffreson.sci (9K) Download Attachment
mottelet mottelet
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Re: New problems with "freson" in CACSD module

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
    [hidden email]

    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.


_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
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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