Polynomials with very small coefficients gets rounded to 0

[baggepinnen]

Background: https://discourse.julialang.org/t/trouble-with-controlsystems-jl/8783/7
Constructor of Poly checks absolute magnitude of coeffs and rounds down if < 2eps(). This threshold should be a variable such that tf constructor can set it in relation to magnitude of coeffs in denominator/numerator

Test case:

using ControlSystems
rl           = 0.2
L            = 150.0e-9
dcr          = 2.0e-3 
nbulk        = 12
cbulk        = 470.0e-6
esr_bulk     = 4.5e-3
ncer         = 96
ccer         = 14.0e-6
esr_cer      = 2.0e-3
nph          = 1
s            = tf("s")
l_imp        = dcr + L*s
bulk_imp     = (esr_bulk/nbulk) + 1.0/(cbulk*nbulk*s)
cer_imp      = (esr_cer/ncer) + 1.0/(ccer*ncer*s)
cer_load_imp = cer_imp*rl/(cer_imp + rl)
den          = (bulk_imp + cer_load_imp)
num          = (bulk_imp * cer_load_imp)
tot_load_imp = num/den # Throws ERROR: Zero denominator
tot_load_imp = tf(num.matrix[1].num.a, den.matrix[1].num.a) # Workaround

[freemin7]

I just ran your code but did not get an error.

tot_load_imp = num/den
TransferFunction{ControlSystems.SisoRational{Float64}}
3.243773646808546e-26*s^6 + 1.1739482429175884e-18*s^5 + 5.521161503047678e-13*s^4 + 2.0375470079999997e-9*s^3
--------------------------------------------------------------------------------------------------------------
   1.6436741697320034e-21*s^6 + 3.837467174734453e-15*s^5 + 1.6990809055395836e-11*s^4 + 1.018773504e-8*s^3

Continuous-time transfer function model

Is the solution correct and if so can this issue be closed?
I also used a higher precision type, Double64 from DoubleFloats and the solution looked similar:

tot_load_imp = num/den
TransferFunction{ControlSystems.SisoRational{DoubleFloat{Float64}}}
3.243773646808546e-26*s^6 + 1.1739482429175888e-18*s^5 + 5.52116150304768e-13*s^4 + 2.037547008e-9*s^3
------------------------------------------------------------------------------------------------------
1.643674169732004e-21*s^6 + 3.837467174734454e-15*s^5 + 1.699080905539584e-11*s^4 + 1.018773504e-8*s^3

Continuous-time transfer function model