doc: updating MTK example to v11 in manual.

[franckgaga]

Hello @baggepinnen,

I'm trying to update the MTK example to v11 but i'm stuck at the varmat_to_vars function here:

using ModelPredictiveControl, ModelingToolkit
using ModelingToolkit: D_nounits as D, t_nounits as t, varmap_to_vars
@parameters g=9.8 L=0.4 K=1.2 m=0.3
@variables θ(t)=0 ω(t)=0 τ(t)=0 y(t)
eqs = [
    D(θ) ~ ω
    D(ω) ~ -g/L*sin(θ) - K/m*ω + τ/m/L^2
    y ~ θ * 180 / π
]
@named mtk_model = System(eqs, t)
function generate_f_h(model, inputs, outputs)
    (_, f_ip), x_sym, p_sym, io_sys = ModelingToolkit.generate_control_function(
        model, inputs, split=false, simplify=true
    )
    if any(ModelingToolkit.is_alg_equation, equations(io_sys)) 
        error("Systems with algebraic equations are not supported")
    end
    nu, nx, ny = length(inputs), length(x_sym), length(outputs)
    function f!(ẋ, x, u, _ , p)
        try
            f_ip(ẋ, x, u, p, nothing)
        catch err
            if err isa MethodError
                error("NonLinModel does not support a time argument t in the f function, "*
                      "see the constructor docstring for a workaround.")
            else
                rethrow()
            end
        end
        return nothing
    end
    (_, h_ip) = ModelingToolkit.build_explicit_observed_function(
        io_sys, outputs; inputs, return_inplace = true
    )
    u_nothing = fill(nothing, nu)
    function h!(y, x, _ , p)
        try
            # MTK.jl supports a `u` argument in `h_ip` function but not this package. We set
            # `u` as a vector of nothing and `h_ip` function will presumably throw an
            # MethodError if this argument is used inside the function
            h_ip(y, x, u_nothing, p, nothing)
        catch err
            if err isa MethodError
                error("NonLinModel only support strictly proper systems (no manipulated "*
                      "input argument u in the output function h)")
            else
                rethrow()
            end
        end
        return nothing
    end
    println(bindings(io_sys))
    p = varmap_to_vars(bindings(io_sys), p_sym) # crashes here
    return f!, h!, p, x_sym, nu, nx, ny
end
inputs, outputs = [τ], [y]
f!, h!, p, x_sym, nu, nx, ny = generate_f_h(mtk_model, inputs, outputs)
x_sym

this code prints:

ReadOnlyDicts.ReadOnlyDict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}, ModelingToolkitBase.AtomicArrayDict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}, Dict{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}, SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymReal}}}}(τ(t) => missing)
ERROR: Initial condition underdefined. Some are missing from the variable map.
Please provide a default (`u0`), initialization equation, or guess
for the following variables:

L, K, m, g

Stacktrace:
 [1] varmap_to_vars(varmap::ReadOnlyDicts.ReadOnlyDict{…}, vars::Vector{…}; tofloat::Bool, use_union::Bool, container_type::Type, buffer_eltype::Type, toterm::Function, check::Bool, allow_symbolic::Bool, is_initializeprob::Bool, substitution_limit::Int64, missing_values::ModelingToolkitBase.MissingGuessValue.var"typeof(MissingGuessValue)")
   @ ModelingToolkitBase ~/.julia/packages/ModelingToolkitBase/uIKoY/src/systems/problem_utils.jl:378
 [2] varmap_to_vars
   @ ~/.julia/packages/ModelingToolkitBase/uIKoY/src/systems/problem_utils.jl:331 [inlined]
 [3] generate_f_h(model::System, inputs::Vector{Num}, outputs::Vector{Num})
   @ Main ~/.julia/dev/ModelPredictiveControl/docs/src/manual/mtk.md:89
 [4] top-level scope
   @ ~/.julia/dev/ModelPredictiveControl/docs/src/manual/mtk.md:93
Some type information was truncated. Use `show(err)` to see complete types.

Do you know why bindings(io_sys) does not contain the parameter values anymore ?

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.59%. Comparing base (20f8634) to head (b5912f7).

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##             main     #340   +/-   ##
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  Coverage   98.59%   98.59%           
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