Deploying a Double Pendulum Model with Output Transform

This tutorial will demonstrate how to deploy a double pendulum model with a transformation of the outputs. The system evolves with states as polar coordinates of the position, but we will add a transformation such that the FMU outputs are Cartesian coordinates.

We start with importing FMUGeneration and OrdinaryDiffEq into our environment.

using FMUGeneration
using OrdinaryDiffEq

Let us clear our deployment workspace before we begin with the tutorial.

clear_deployment_workspace()

[ Info: Cleared Deployment Workspace!

We first define the system and the transforming function using @define. The function double_pendulum is our system. The function polar2cart is the transforming function that converts the polar coordinates into cartesian. This example is taken from the DifferentialEquations.jl docs

@define begin
    function double_pendulum(u, x, p, t)
        m₁, m₂, L₁, L₂, g = p
        du1 = u[2]
        du2 = -((g * (2 * m₁ + m₂) * sin(u[1]) +
                     m₂ * (g * sin(u[1] - 2 * u[3]) +
                      2 * (L₂ * u[4]^2 + L₁ * u[2]^2 * cos(u[1] - u[3])) * sin(u[1] - u[3]))) /
                    (2 * L₁ * (m₁ + m₂ - m₂ * cos(u[1] - u[3])^2)))
        du3 = u[4]
        du4 = (((m₁ + m₂) * (L₁ * u[2]^2 + g * cos(u[1])) +
                    L₂ * m₂ * u[4]^2 * cos(u[1] - u[3])) * sin(u[1] - u[3])) /
                  (L₂ * (m₁ + m₂ - m₂ * cos(u[1] - u[3])^2))
        [du1, du2, du3, du4]
    end

    function polar2cart(u, x, p, t)
        l1 = p[3]
        l2 = p[4]
        vars = (2, 4)
        p1 = l1 * u[vars[1]]
        p2 = l2 * u[vars[2]]
        x1 = l1 * sin(p1)
        y1 = l1 * -cos(p1)
        [x1 + l2 * sin.(p2), y1 - l2 * cos.(p2)]
    end
end

Now that we have defined our system and transformation into the FMU Package, let us define the initial states, default parameters, and timespan for the system.

initial_states = [0, π / 3, 0, 3pi / 5]
m₁, m₂, L₁, L₂, g = 1, 2, 1, 2, 9.8
default_parameters = [m₁, m₂, L₁, L₂, g]
tspan = (0.0, 50.0)
tend = tspan[end]

param_names = ["m1", "m2", "L1", "L2", "g"]
state_names = ["alpha", "Lalpha", "beta", "Lbeta"]
output_names = ["x", "y"]

2-element Vector{String}:
 "x"
 "y"

We call set_default and pass the keyword arguments necessary.

set_default(; initial_states = initial_states, default_parameters = default_parameters, tspan = tspan)

Now we define our continuous model, in this case, it is the double_pendulum function we have defined before.

@continuous_model double_pendulum(u, x, p, t)

And then, we define the output transform that would convert the polar coordinates to cartesian coordinates.

@output_transform polar2cart(u, x, p, t)

We will add OrdinaryDiffEq package to the FMU package using @add_packages

@add_packages(["OrdinaryDiffEq", "SciMLBase"])

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We then generate the FMU Package code using generate_fmu_code

generate_fmu_code()

We will import the package and get the package name using @import_fmu_pkg

pkg_name, FMI2Binary = @import_fmu_pkg FMUGeneration.lib_path

Now lets define the XML metadeta for the FMU with generateXML

Note

We donot have inputs for this system and hence we define an empty vector for inputs.

inputs = NamedTuple[]

params = [(name = "$(param_names[i])", description = "desc p$i", start = default_parameters[i]) for i in 1:length(default_parameters)]
conts = [(name = "$(state_names[i])", unit = "unit c$i", description = "desc c$i", start = initial_states[i])
            for i in 1:length(initial_states)]

outputs = [(name = "$o", unit = "unit c$i", description = "desc c$i")
            for (i, o) in enumerate(["x", "y"])]

generateXML(inputs, params, conts, outputs, tend; sysname = "double_pendulum")

Now that we have defined our model, generated the FMU package, and generated the metadata, we are ready to compile a FMU. We call compile_fmu

fmu_dir_path, fmu_path, fmu_so_file_path = compile_fmu()

Pkg.rm(String(pkg_name)) # hide
nothing # hide