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<p>Thanks Lucien, however, to complete the task, you should first
reopen bug #15368 at
<a class="moz-txt-link-freetext" href="https://bugzilla.scilab.org/show_bug.cgi?id=15368">https://bugzilla.scilab.org/show_bug.cgi?id=15368</a></p>
<p>S.<br>
</p>
<p>Can you create a bug<br>
</p>
<div class="moz-cite-prefix">Le 25/09/2019 à 16:06, lucien.povy a
écrit :<br>
</div>
<blockquote type="cite"
cite="mid:2761d5f1-63e8-b343-baae-516f5abff7b9@free.fr">Hello all
!
<br>
I believe that there are new problems with "freson.sci" program in
CACSD module.
<br>
If you are running two programs, one for continuous system another
for sampled system,
<br>
sometimes you have a result as [ ] : you must improve the accuracy
of result ;("ffreson.sci" program is proposed).
<br>
(Bugs not bugs ???? yes bugs : see in text REMARK.
<br>
<br>
1 . Example : continuous system.
<br>
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 ;
<br>
h = syslin("c",num,den)
<br>
fr = freson(h)
<br>
fr =
<br>
[]
<br>
gainplot(h,0.01,1)
<br>
with my new function "ffreson.sci" :
<br>
ffreson(h)//La nouvelle fonction.
<br>
ans =
<br>
0.111164226146
<br>
<br>
2 . Example : sampled system.
<br>
The exercise in "help" page of "freson" with sampling period
Ts=0.01s : the program gives "fr=[]" .
<br>
With sampling period Ts=0.04s you have a good result (problem
of accuracy) : run the example in help
<br>
and change sampling period.
<br>
<br>
3 . My opinion and the proposed solutions.
<br>
<br>
- For continuous system :
<br>
If you calculated the function "h(s)*h(-s)" by convolution, the
result, as I mentioned before,
<br>
must be an even rational : with "horner" it's not, but by
convolution the result is OK. (take a look on "ffreson" program :
<br>
you find a program "hps_hms" which gives "h(s)*h(-s)" by
convolution).
<br>
- 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
<br>
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
<br>
of the result : I use this method in my program.
<br>
<br>
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").
<br>
<br>
- For sampled system :
<br>
- We calculated the function "hh=h(z)*h(1/z)", also with
convolution, the result of convolution gives for coefficients
vectors
<br>
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".
<br>
- After that we take account of
"z^(degree(h.num)-degree(h.den)) in "hh", and calculated the
numerator of derivative of new
<br>
"hh".
<br>
- Like for continuous system, you excluded "z=1" and "z=-1",
which corresponds to frequencies f0=0 and f1=1/*(2*ts) (Nyquist
frequency).
<br>
- 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".
<br>
I use those methods in the new program "ffreson.sci".
<br>
REMARK : the same.
<br>
<br>
Yours sincerely
<br>
<a class="moz-txt-link-abbreviated" href="mailto:lucien.povy@free.fr">lucien.povy@free.fr</a>
<br>
<br>
PS
<br>
I attached the new function "ffreson.sci" and a report
("Exemples freson.pdf", sorry in french language) to my email.
<br>
In "ffreson" you have two functions "hps_hms" for h(s)*h(-s)
and "hpz_hiz" for h(z)*h(1/z).
<br>
This program "ffreson" can be used for "iodelay systems", and
" hps_hms" , "hpz_hiz" used in m_margin and p_margin
<br>
to improve the accuracy of results.
<br>
<br>
<br>
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<pre class="moz-signature" cols="72">--
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
<a class="moz-txt-link-freetext" href="http://www.utc.fr/~mottelet">http://www.utc.fr/~mottelet</a>
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