How to write equations less redundant

Specific Domains Modelling & Simulations
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1

How can this code be written less redundant?

    if lin
        @parameters a=eq.a_bar b=eq.b_bar
        eqs = [D(ω)    ~ (Pr - Pg) / (J * ω),
            D(Uest) ~ Ku * e_p,
            r_ω     ~ Uest * λnom / R,
            e_ω     ~ r_ω - ω,
            e_p     ~ Pg - Pr_est + J * D(ω) * ω,
            λest    ~ ω * R / Uest,
            Pr_est  ~ 0.5 *  ρ * A * Uest^3 * Γest * (a*λest + b),
            λ       ~ ω * R/U,
            Pr      ~ 0.5 * ρ * A * U^3 * Γ * (a*λ + b),
            Pg      ~ Pgc + Pge]
    else
        eqs = [D(ω)    ~ (Pr - Pg) / (J * ω),
            D(Uest) ~ Ku * e_p,
            r_ω     ~ Uest * λnom / R,
            e_ω     ~ r_ω - ω,
            e_p     ~ Pg - Pr_est + J * D(ω) * ω,
            λest    ~ ω * R / Uest,
            Pr_est  ~ 0.5 *  ρ * A * Uest^3 * Γest * Cp(λest),
            λ       ~ ω * R/U,
            Pr      ~ 0.5 * ρ * A * U^3 * Γ * Cp(λ),
            Pg      ~ Pgc + Pge]
    end
2 
eqs = [D(ω)    ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω     ~ Uest * λnom / R,
       e_ω     ~ r_ω - ω,
       e_p     ~ Pg - Pr_est + J * D(ω) * ω,
       λest    ~ ω * R / Uest,
       λ       ~ ω * R/U,
       Pg      ~ Pgc + Pge]
if lin
    @parameters a=eq.a_bar b=eq.b_bar
    append!(eqs,
            [Pr_est  ~ 0.5 *  ρ * A * Uest^3 * Γest * (a*λest + b),
             Pr      ~ 0.5 * ρ * A * U^3 * Γ * (a*λ + b)])
else
    append!(eqs,
            [Pr_est ~ 0.5 *  ρ * A * Uest^3 * Γest * Cp(λest),
             Pr     ~ 0.5 * ρ * A * U^3 * Γ * Cp(λ)]_
end

Or

eqs = [D(ω)    ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω     ~ Uest * λnom / R,
       e_ω     ~ r_ω - ω,
       e_p     ~ Pg - Pr_est + J * D(ω) * ω,
       λest    ~ ω * R / Uest,
       Pr_est  ~ 0.5 *  ρ * A * Uest^3 * Γest * ifelse(lin, (a*λest + b), Cp(λest)),
       λ       ~ ω * R/U,
       Pr      ~ 0.5 * ρ * A * U^3 * Γ * ifelse(lin, (a*λ + b), Cp(λ)),
       Pg      ~ Pgc + Pge]

Or even

eqs = [D(ω)    ~ (Pr - Pg) / (J * ω),
       D(Uest) ~ Ku * e_p,
       r_ω     ~ Uest * λnom / R,
       e_ω     ~ r_ω - ω,
       e_p     ~ Pg - Pr_est + J * D(ω) * ω,
       λest    ~ ω * R / Uest,
       Cp′     ~ ifelse(lin, (a*λest + b), Cp(λest))
       Pr_est  ~ 0.5 *  ρ * A * Uest^3 * Γest *  Cp′,
       λ       ~ ω * R/U,
       Pr      ~ 0.5 * ρ * A * U^3 * Γ *  Cp′,
       Pg      ~ Pgc + Pge]

if lin is a Bool, ifelse will be evaluated when the equations are constructed, if lin is a symbolic expression then it will be evaluated when the equations are evaluated which may not be what you want.

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3

lin is Bool

OK, your last version is a little bit wrong, because there is Cp(λ) and Cp(λest), but I get the idea…

4

It would make sense to have a Cp() function for both cases.
A simplified example:

using ModelingToolkit, OrdinaryDiffEq
using Plots

lin = true  # case distinction

function CpNew(λ::Float64, a::Float64, b::Float64)::Float64
    if lin
        a*λ + b
    else
        λ*λ # your function here
    end
end

@register_symbolic CpNew(λ,a,b)

@variables t x(t)
@parameters a  b
D = Differential(t)
eqs = [ D(x) ~ CpNew(x, a, b)  ]
@named sys = ODESystem(eqs)
prob = ODEProblem(sys, [0.1], (0.0,5.0), [0.01, 0.5])
sol = solve(prob, Tsit5())

display(plot(sol))
display(sol)
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