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.p...@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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