I am currently working on a project where I need to equate a transfer function with its symbolic representations using real components (some resistors and capacitors). Up to this point, I have been manually performing this task using SymPy, specifically employing the Eq function (e.g., exp1 = Eq(x, y)) and solving for variables (e.g., solve(exp1, C)).
I chose SymPy.jl due to some challenges I encountered with the current development state of Symbolics.jl (for reference, please see Feature Completeness Against SymPy · Issue #59 · JuliaSymbolics/Symbolics.jl · GitHub . However, I am finding the manual assignment of terms to be quite tedious and time-consuming.
Therefore, I am considering automating this process, but I ran into issues when trying to use the method outlined in this article Extracting All Coefficients in Sympy Using Python 3 - DNMTechs - Sharing and Storing Technology Knowledge . Unfortunately, it did not yield the expected results (see below screenshot).
Could you please advise me on what I might be doing wrong? Additionally, is there a more efficient way to achieve my goal of automating the equating of transfer functions with their symbolic representations?
Thank you for your help.
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It’s not 100% clear to me what you are trying to do when you say
are you trying to solve for the parameters, C_1, R_1,... etc., given a numeric transfer function?
There are some utilities for working with SymPy symbolic transfer functions here
C-code generation and an interface between ControlSystems.jl and SymPy.jl
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Your understanding is correct, i.e. I am trying to solve for the parameters C1, R1 given a numeric transfer function.
The below first screenshot shows the symbolic and numeric transfer functions. The symbolic transfer function being of type Sym{PyCall.PyObject}.
I then manually assign each symbolic term to its corresponding numerical term (see below), which is a bit tedious.
If you have a symbolic transfer function and have loaded SymbolicControlSystems, you should be able to call tf(symbolic_tf)
julia> symbolic_tf = w^2 / (s^2 + 2*d*w*s + w^2) # Define symbolic expression
2
w
─────────────────
2 2
2⋅d⋅s⋅w + s + w
julia> G = tf(symbolic_tf) # Convert symbolic expression to TransferFunction
TransferFunction{Continuous, SisoRational{Sym}}
w^2
---------------------
1*s^2 + 2*d*w*s + w^2
and then obtain the coefficients using ControlSystemsBase.numpoly(G) or ControlSystemsBase.numvec(G) (and denpoly, denvec for denominator).
You can see how this is done under the hood here
function ControlSystemsBase.tf(sys::Sym, h = nothing)
n, d = sp.fraction(sys)
# d = d.monic() # Don't do this here
if h === nothing || h isa Continuous
d = sp.Poly(d, s)
n = n isa Number ? 1.0*n : sp.Poly(n, s)
tf(expand_coeffs(n, s), expand_coeffs(d, s))
else
d = sp.Poly(d, z)
n = n isa Number ? 1.0*n : sp.Poly(n, z)
tf(expand_coeffs(n, z), expand_coeffs(d, z), h)
end
end
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