Merge pull request #2361 from SciML/baggepinnen-patch-4

Handle dummy derivatives in `linearization_function`

Author: baggepinnen

src/systems/abstractsystem.jl

@@ -1303,7 +1303,7 @@ function linearization_function(sys::AbstractSystem, inputs,
         op = merge(defs, op)
     end
     sys = ssys
-    x0 = merge(defaults(sys), op)
+    x0 = merge(defaults(sys), Dict(missing_variable_defaults(sys)), op)
     u0, p, _ = get_u0_p(sys, x0, p; use_union = false, tofloat = true)
     p, split_idxs = split_parameters_by_type(p)
     ps = parameters(sys)

test/inversemodel.jl

@@ -0,0 +1,165 @@
+using ModelingToolkit
+using ModelingToolkitStandardLibrary
+using ModelingToolkitStandardLibrary.Blocks
+using OrdinaryDiffEq
+using Test
+using ControlSystemsMTK: tf, ss, get_named_sensitivity, get_named_comp_sensitivity
+
+# ==============================================================================
+## Mixing tank
+# This tests a common workflow in control engineering, the use of an inverse-based
+# feedforward model. Such a model differentiates "inputs", exercising the dummy-derivative functionality of ModelingToolkit. We also test linearization and computation of sensitivity functions
+# for such models.
+# ==============================================================================
+
+connect = ModelingToolkit.connect;
+@parameters t;
+D = Differential(t);
+rc = 0.25 # Reference concentration 
+
+@mtkmodel MixingTank begin
+    @parameters begin
+        c0 = 0.8, [description = "Nominal concentration"]
+        T0 = 308.5, [description = "Nominal temperature"]
+        a1 = 0.2674
+        a21 = 1.815
+        a22 = 0.4682
+        b = 1.5476
+        k0 = 1.05e14
+        ϵ = 34.2894
+    end
+
+    @variables begin
+        gamma(t), [description = "Reaction speed"]
+        xc(t) = c0, [description = "Concentration"]
+        xT(t) = T0, [description = "Temperature"]
+        xT_c(t) = T0, [description = "Cooling temperature"]
+    end
+
+    @components begin
+        T_c = RealInput()
+        c = RealOutput()
+        T = RealOutput()
+    end
+
+    begin
+        τ0 = 60
+        wk0 = k0 / c0
+        wϵ = ϵ * T0
+        wa11 = a1 / τ0
+        wa12 = c0 / τ0
+        wa13 = c0 * a1 / τ0
+        wa21 = a21 / τ0
+        wa22 = a22 * T0 / τ0
+        wa23 = T0 * (a21 - b) / τ0
+        wb = b / τ0
+    end
+    @equations begin
+        gamma ~ xc * wk0 * exp(-wϵ / xT)
+        D(xc) ~ -wa11 * xc - wa12 * gamma + wa13
+        D(xT) ~ -wa21 * xT + wa22 * gamma + wa23 + wb * xT_c
+
+        xc ~ c.u
+        xT ~ T.u
+        xT_c ~ T_c.u
+    end
+end
+
+begin
+    Ftf = tf(1, [(100), 1])^3
+    Fss = ss(Ftf)
+
+    "Compute initial state that yields y0 as output"
+    function init_filter(y0)
+        (; A, B, C, D) = Fss
+        Fx0 = -A \ B * y0
+        @assert C * Fx0≈[y0] "C*Fx0*y0 ≈ y0 failed, got $(C*Fx0*y0) ≈ $(y0)]"
+        Fx0
+    end
+
+    # Create an MTK-compatible constructor 
+    RefFilter(; y0, name) = ODESystem(Fss; name, x0 = init_filter(y0))
+end
+@mtkmodel InverseControlledTank begin
+    begin
+        c0 = 0.8    #  "Nominal concentration
+        T0 = 308.5 #  "Nominal temperature
+        x10 = 0.42
+        x20 = 0.01
+        u0 = -0.0224
+
+        c_start = c0 * (1 - x10) # Initial concentration
+        T_start = T0 * (1 + x20) # Initial temperature
+        c_high_start = c0 * (1 - 0.72) # Reference concentration
+        T_c_start = T0 * (1 + u0) # Initial cooling temperature
+    end
+    @components begin
+        ref = Constant(k = 0.25) # Concentration reference
+        ff_gain = Gain(k = 1) # To allow turning ff off
+        controller = PI(gainPI.k = 10, T = 500)
+        tank = MixingTank(xc = c_start, xT = T_start, c0 = c0, T0 = T0)
+        inverse_tank = MixingTank(xc = c_start, xT = T_start, c0 = c0, T0 = T0)
+        feedback = Feedback()
+        add = Add()
+        filter = RefFilter(y0 = c_start) # Initialize filter states to the initial concentration
+        noise_filter = FirstOrder(k = 1, T = 1, x = T_start)
+        # limiter = Gain(k=1)
+        limiter = Limiter(y_max = 370, y_min = 250) # Saturate the control input 
+    end
+    @equations begin
+        connect(ref.output, :r, filter.input)
+        connect(filter.output, inverse_tank.c)
+
+        connect(inverse_tank.T_c, ff_gain.input)
+        connect(ff_gain.output, :uff, limiter.input)
+        connect(limiter.output, add.input1)
+
+        connect(controller.ctr_output, :u, add.input2)
+
+        #connect(add.output, :u_tot, limiter.input)
+        #connect(limiter.output, :v, tank.T_c)
+
+        connect(add.output, :u_tot, tank.T_c)
+
+        connect(inverse_tank.T, feedback.input1)
+
+        connect(tank.T, :y, noise_filter.input)
+
+        connect(noise_filter.output, feedback.input2)
+        connect(feedback.output, :e, controller.err_input)
+    end
+end;
+@named model = InverseControlledTank()
+ssys = structural_simplify(model)
+cm = complete(model)
+
+op = Dict(D(cm.inverse_tank.xT) => 1,
+    cm.tank.xc => 0.65)
+tspan = (0.0, 1000.0)
+prob = ODEProblem(ssys, op, tspan)
+sol = solve(prob, Rodas5P())
+
+@test SciMLBase.successful_retcode(sol)
+
+# plot(sol, idxs=[model.tank.xc, model.tank.xT, model.controller.ctr_output.u], layout=3, sp=[1 2 3])
+# hline!([prob[cm.ref.k]], label="ref", sp=1)
+
+@test sol(tspan[2], idxs = cm.tank.xc)≈prob[cm.ref.k] atol=1e-2 # Test that the inverse model led to the correct reference
+
+Sf, simplified_sys = Blocks.get_sensitivity_function(model, :y) # This should work without providing an operating opint containing a dummy derivative
+x, p = ModelingToolkit.get_u0_p(simplified_sys, op)
+matrices1 = Sf(x, p, 0)
+matrices2, _ = Blocks.get_sensitivity(model, :y; op) # Test that we get the same result when calling the higher-level API
+@test matrices1.f_x ≈ matrices2.A[1:7, 1:7]
+nsys = get_named_sensitivity(model, :y; op) # Test that we get the same result when calling an even higher-level API
+@test matrices2.A ≈ nsys.A
+
+# Test the same thing for comp sensitivities
+
+Sf, simplified_sys = Blocks.get_comp_sensitivity_function(model, :y) # This should work without providing an operating opint containing a dummy derivative
+x, p = ModelingToolkit.get_u0_p(simplified_sys, op)
+matrices1 = Sf(x, p, 0)
+matrices2, _ = Blocks.get_comp_sensitivity(model, :y; op) # Test that we get the same result when calling the higher-level API
+@test matrices1.f_x ≈ matrices2.A[1:7, 1:7]
+nsys = get_named_comp_sensitivity(model, :y; op) # Test that we get the same result when calling an even higher-level API
+@test matrices2.A ≈ nsys.A

test/runtests.jl

@@ -55,6 +55,7 @@ end
 @safetestset "OptimizationSystem Test" include("optimizationsystem.jl")
 @safetestset "FuncAffect Test" include("funcaffect.jl")
 @safetestset "Constants Test" include("constants.jl")
+@safetestset "Inverse Models Test" include("inversemodel.jl")
 # Reference tests go Last
 if VERSION >= v"1.9"
     @safetestset "Latexify recipes Test" include("latexify.jl")