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AayushSabharwalAayushSabharwal
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test: add tests from MTKStdlib
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‎test/analysis_points.jl‎

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using ModelingToolkit, ModelingToolkitStandardLibrary
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using ModelingToolkit, ModelingToolkitStandardLibrary.Blocks
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using OrdinaryDiffEq, LinearAlgebra
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using Test
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using ModelingToolkit: t_nounits as t, D_nounits as D
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using ModelingToolkit: t_nounits as t, D_nounits as D, AnalysisPoint, get_sensitivity,
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get_comp_sensitivity, get_looptransfer
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using Symbolics: NAMESPACE_SEPARATOR
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@testset "AnalysisPoint is lowered to `connect`" begin
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@named P = FirstOrder(k = 1, T = 1)
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@named C = Gain(; k = -1)
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ap = AnalysisPoint(:plant_input)
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eqs = [connect(P.output, C.input)
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connect(C.output, ap, P.input)]
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@test isequal(sys_ap2, sys_normal2)
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end
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# also tests `connect(input, name::Symbol, outputs...)` syntax
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@testset "AnalysisPoint is accessible via `getproperty`" begin
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@named P = FirstOrder(k = 1, T = 1)
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@named C = Gain(; k = -1)
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eqs = [connect(P.output, C.input), connect(C.output, :plant_input, P.input)]
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sys_ap = ODESystem(eqs, t, systems = [P, C], name = :hej)
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ap2 = @test_nowarn sys_ap.plant_input
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@test nameof(ap2) == Symbol(join(["hej", "plant_input"], NAMESPACE_SEPARATOR))
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@named sys = ODESystem(Equation[], t; systems = [sys_ap])
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ap3 = @test_nowarn sys.hej.plant_input
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@test nameof(ap3) == Symbol(join(["sys", "hej", "plant_input"], NAMESPACE_SEPARATOR))
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sys = complete(sys)
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ap4 = sys.hej.plant_input
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@test nameof(ap4) == Symbol(join(["hej", "plant_input"], NAMESPACE_SEPARATOR))
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end
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### Ported from MTKStdlib
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@named P = FirstOrder(k = 1, T = 1)
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@named C = Gain(; k = -1)
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ap = AnalysisPoint(:plant_input)
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eqs = [connect(P.output, C.input), connect(C.output, ap, P.input)]
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sys = ODESystem(eqs, t, systems = [P, C], name = :hej)
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@named nested_sys = ODESystem(Equation[], t; systems = [sys])
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@testset "simplifies and solves" begin
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ssys = structural_simplify(sys)
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prob = ODEProblem(ssys, [P.x => 1], (0, 10))
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sol = solve(prob, Rodas5())
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@test norm(sol.u[1]) >= 1
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@test norm(sol.u[end]) < 1e-6 # This fails without the feedback through C
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end
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@testset "get_sensitivity - $name" for (name, sys, ap) in [
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("inner", sys, sys.plant_input),
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("nested", nested_sys, nested_sys.hej.plant_input),
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("inner - nonamespace", sys, :plant_input),
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("inner - Symbol", sys, nameof(sys.plant_input)),
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("nested - Symbol", nested_sys, nameof(nested_sys.hej.plant_input))
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]
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matrices, _ = get_sensitivity(sys, ap)
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@test matrices.A[] == -2
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@test matrices.B[] * matrices.C[] == -1 # either one negative
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@test matrices.D[] == 1
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end
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@testset "get_comp_sensitivity - $name" for (name, sys, ap) in [
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("inner", sys, sys.plant_input),
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("nested", nested_sys, nested_sys.hej.plant_input),
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("inner - nonamespace", sys, :plant_input),
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("inner - Symbol", sys, nameof(sys.plant_input)),
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("nested - Symbol", nested_sys, nameof(nested_sys.hej.plant_input))
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]
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matrices, _ = get_comp_sensitivity(sys, ap)
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@test matrices.A[] == -2
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@test matrices.B[] * matrices.C[] == 1 # both positive or negative
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@test matrices.D[] == 0
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end
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#=
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# Equivalent code using ControlSystems. This can be used to verify the expected results tested for above.
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using ControlSystemsBase
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P = tf(1.0, [1, 1])
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C = 1 # Negative feedback assumed in ControlSystems
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S = sensitivity(P, C) # or feedback(1, P*C)
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T = comp_sensitivity(P, C) # or feedback(P*C)
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=#
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@testset "get_looptransfer - $name" for (name, sys, ap) in [
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("inner", sys, sys.plant_input),
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("nested", nested_sys, nested_sys.hej.plant_input),
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("inner - nonamespace", sys, :plant_input),
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("inner - Symbol", sys, nameof(sys.plant_input)),
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("nested - Symbol", nested_sys, nameof(nested_sys.hej.plant_input))
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]
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matrices, _ = get_looptransfer(sys, ap)
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@test matrices.A[] == -1
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@test matrices.B[] * matrices.C[] == -1 # either one negative
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@test matrices.D[] == 0
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end
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#=
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# Equivalent code using ControlSystems. This can be used to verify the expected results tested for above.
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using ControlSystemsBase
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P = tf(1.0, [1, 1])
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C = -1
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L = P*C
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=#
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@testset "open_loop - $name" for (name, sys, ap) in [
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("inner", sys, sys.plant_input),
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("nested", nested_sys, nested_sys.hej.plant_input),
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("inner - nonamespace", sys, :plant_input),
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("inner - Symbol", sys, nameof(sys.plant_input)),
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("nested - Symbol", nested_sys, nameof(nested_sys.hej.plant_input))
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]
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open_sys, (du, u) = open_loop(sys, ap)
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matrices, _ = linearize(open_sys, [du], [u])
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@test matrices.A[] == -1
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@test matrices.B[] * matrices.C[] == -1 # either one negative
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@test matrices.D[] == 0
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end
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# Multiple analysis points
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eqs = [connect(P.output, :plant_output, C.input)
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connect(C.output, :plant_input, P.input)]
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sys = ODESystem(eqs, t, systems = [P, C], name = :hej)
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@named nested_sys = ODESystem(Equation[], t; systems = [sys])
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@testset "get_sensitivity - $name" for (name, sys, ap) in [
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("inner", sys, sys.plant_input),
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("nested", nested_sys, nested_sys.hej.plant_input),
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("inner - nonamespace", sys, :plant_input),
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("inner - Symbol", sys, nameof(sys.plant_input)),
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("nested - Symbol", nested_sys, nameof(nested_sys.hej.plant_input))
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]
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matrices, _ = get_sensitivity(sys, ap)
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@test matrices.A[] == -2
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@test matrices.B[] * matrices.C[] == -1 # either one negative
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@test matrices.D[] == 1
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end
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@testset "linearize - $name" for (name, sys, inputap, outputap) in [
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("inner", sys, sys.plant_input, sys.plant_output),
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("nested", nested_sys, nested_sys.hej.plant_input, nested_sys.hej.plant_output)
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]
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@testset "input - $(typeof(input)), output - $(typeof(output))" for (input, output) in [
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(inputap, outputap),
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(nameof(inputap), outputap),
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(inputap, nameof(outputap)),
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(nameof(inputap), nameof(outputap)),
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(inputap, [outputap]),
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(nameof(inputap), [outputap]),
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(inputap, [nameof(outputap)]),
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(nameof(inputap), [nameof(outputap)])
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]
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if input isa Symbol
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# broken because MTKStdlib defines the method for
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# `input::Union{Symbol, Vector{Symbol}}` which we can't directly call
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@test_broken linearize(sys, input, output)
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linfun, ssys = @invoke linearization_function(sys::AbstractSystem,
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input::Union{Symbol, Vector{Symbol}, AnalysisPoint, Vector{AnalysisPoint}},
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output::Any)
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matrices = linearize(ssys, linfun)
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else
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matrices, _ = linearize(sys, input, output)
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end
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# Result should be the same as feedpack(P, 1), i.e., the closed-loop transfer function from plant input to plant output
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@test matrices.A[] == -2
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@test matrices.B[] * matrices.C[] == 1 # both positive
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@test matrices.D[] == 0
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end
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end
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@testset "linearize - variable output - $name" for (name, sys, input, output) in [
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("inner", sys, sys.plant_input, P.output.u),
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("nested", nested_sys, nested_sys.hej.plant_input, sys.P.output.u)
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]
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matrices, _ = linearize(sys, input, [output])
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@test matrices.A[] == -2
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@test matrices.B[] * matrices.C[] == 1 # both positive
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@test matrices.D[] == 0
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end
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using ModelingToolkit, OrdinaryDiffEq, LinearAlgebra
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using ModelingToolkitStandardLibrary.Mechanical.Rotational
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using ModelingToolkitStandardLibrary.Blocks: Sine, PID, SecondOrder, Step, RealOutput
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using ModelingToolkit: connect
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@testset "Complicated model" begin
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# Parameters
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m1 = 1
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m2 = 1
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k = 1000 # Spring stiffness
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c = 10 # Damping coefficient
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@named inertia1 = Inertia(; J = m1)
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@named inertia2 = Inertia(; J = m2)
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@named spring = Spring(; c = k)
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@named damper = Damper(; d = c)
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@named torque = Torque()
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function SystemModel(u = nothing; name = :model)
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eqs = [connect(torque.flange, inertia1.flange_a)
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connect(inertia1.flange_b, spring.flange_a, damper.flange_a)
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connect(inertia2.flange_a, spring.flange_b, damper.flange_b)]
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if u !== nothing
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push!(eqs, connect(torque.tau, u.output))
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return ODESystem(eqs, t;
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systems = [
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torque,
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inertia1,
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inertia2,
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spring,
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damper,
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u
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],
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name)
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end
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ODESystem(eqs, t; systems = [torque, inertia1, inertia2, spring, damper], name)
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end
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@named r = Step(start_time = 0)
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model = SystemModel()
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@named pid = PID(k = 100, Ti = 0.5, Td = 1)
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@named filt = SecondOrder(d = 0.9, w = 10)
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@named sensor = AngleSensor()
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@named er = Add(k2 = -1)
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connections = [connect(r.output, :r, filt.input)
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connect(filt.output, er.input1)
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connect(pid.ctr_output, :u, model.torque.tau)
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connect(model.inertia2.flange_b, sensor.flange)
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connect(sensor.phi, :y, er.input2)
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connect(er.output, :e, pid.err_input)]
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closed_loop = ODESystem(connections, t, systems = [model, pid, filt, sensor, r, er],
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name = :closed_loop, defaults = [
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model.inertia1.phi => 0.0,
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model.inertia2.phi => 0.0,
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model.inertia1.w => 0.0,
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model.inertia2.w => 0.0,
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filt.x => 0.0,
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filt.xd => 0.0
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])
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sys = structural_simplify(closed_loop)
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prob = ODEProblem(sys, unknowns(sys) .=> 0.0, (0.0, 4.0))
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sol = solve(prob, Rodas5P(), reltol = 1e-6, abstol = 1e-9)
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end

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