Pierre,
Thanks for your answer.
However, I believe no involved computatins are required to get the
correct result. The multiplication of the two polynomials from the
denominators is straightforward, no need to solve any system, no risk of
ill-conditioned or badly-scaled matrices.
This must be another kind of problem.
Regards,
Federico Miyara
On 17/03/2020 06:48, Perrichon wrote:
Hello Federico
I have met few months or years ago this problem when i was developping
my « OPTSIM Solution » software to fix parameters of a PID for
turbines (30 mw to 2 gw) in Nyquist and Bode Plans with hydraulic
parameters site
So I’ve seen instability of the denominator, witch damage calculus.
I don ‘t remember what I’ve done to get a cool solution, but it has
been a hard and severe problem with syslin, tf2ss and ss2tf instructions
Sincerely
Pierre P.
*De :*users <[email protected]> *De la part de* Federico
Miyara
*Envoyé :* mardi 17 mars 2020 10:31
*À :* Users mailing list for Scilab <[email protected]>
*Objet :* [Scilab-users] Strange behaviour of prod on rationals
Dear all,
Look at this code (the coefficients are actually the result of pevious
calculations):
NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
8.336136 + 7.0282601*%s + %s^2]
q = NUM./DEN
Running it yields
5.858D-09 +2.011D-08s +4.884D-08s² 5.858D-09 +8.796D-10s +7.028D-10s²
---------------------------------- ----------------------------------
0.1199597 +7.2765093s +s² 8.336136 +7.0282601s +s²
This is, correctly, a two-component rational vector with the expected
numerators and denominators.
Now let's evaluate
q = prod(NUM./DEN)
The prod documantation sys that the argument may be "an array of
reals, complex, booleans, polynomials or rational fractions". It
should provide the rational obtained by multiplying the twonumrators
and the two denominators. However, we get
3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
------------------------------------------------------------
1
The numeratoris right, but the expected denominator has been just
replaced by 1
However, rewriting the command as
prod(NUM)/prod(DEN)
we get the expected result:
3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
------------------------------------------------------------
1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴
This is quite strange!
Now we repeat with simpler polynomials:
NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN
We get
1 -s 2 -s
---- ----
1 +s 2 +s
Now evaluate
prod(NUM./DEN)
The result is the expected one!
2 -3s +s²
---------
2 +3s +s²
The behavior seems to depend on the type of polynomials.
Is this a bug or there is something I'm not interpreting correctly?
Regards,
Federico Miyara
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