Add urethan example

test/references/urethan.jl

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+using ModelingToolkit
+using LinearAlgebra
+using DynamicOED
+
+# Define the system
+T_min, T_max = 293.16, 473.16
+
+const M = [0.11911, 0.07412, 0.19323, 0.31234, 0.35733, 0.07806]
+const rho = [1095.0, 809.0, 1415.0, 1528.0, 1451.0, 1101.0]
+
+K_REF1 = 5.0E-4
+E_A1 = 35240.0
+K_REF2 = 8.0E-8
+E_A2 = 85000.0
+K_REF4 = 1.0E-8
+E_A4 = 35000.0
+DH_2 = -17031.0
+K_C2 = 0.17
+
+R = 8.314;
+T1 = 363.16;
+
+@variables t
+@variables V(t)=0.5 [description = "Reaction volume"]
+@variables r1(t)=0.0 [description = "Reaction rate 1"]
+@variables r2(t)=0.0 [description = "Reaction rate 2"]
+@variables r3(t)=0.0 [description = "Reaction rate 3"]
+@variables r4(t)=0.0 [description = "Reaction rate 4"]
+@variables feed1(t)=0 [description = "State for feed 1"]
+@variables feed2(t)=0 [description = "State for feed 2"]
+@variables temperature(t)=293.15 [
+    bounds = [293.16, 473.16],
+    description = "State for temperature",
+]
+@variables n(t)[1:6]=[0.0; 0.0; 0.0; 0.0; 0.0; 0.0] [description = "States"]
+@parameters u1 [
+    description = "Control feed 1",
+    bounds = [0, Inf],
+    input = true,
+    measurement_rate = 10,
+]
+@parameters u2 [
+    description = "Control feed 2",
+    bounds = [0, Inf],
+    input = true,
+    measurement_rate = 10,
+]
+@parameters u3 [
+    description = "Control temperature",
+    bounds = [-40, 40],
+    input = true,
+    measurement_rate = 10,
+]
+@variables h₁(t) [description = "Observed", measurement_rate = 20]
+@variables h₂(t) [description = "Observed", measurement_rate = 20]
+h = vcat(h₁, h₂)
+@parameters p[1:6]=[1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0] [
+    description = "Scaling parameters",
+    tunable = true,
+]
+@parameters n0[1:3]=[0.12; 0.0; 0.0] [description = "Initial mole numbers", tunable = false]
+D = Differential(t)
+
+## Define the control function, returns feed1, feed2, T
+eqs_ = [V * (r1 - r2 + r3);
+    V * (r2 - r3);
+    V * r4]
+
+subs_ = Dict(r1 => p[1] * K_REF1 * exp(-p[2] * E_A1 / R * (1 / temperature - 1 / T1)) *
+                   n[1] * n[2] / (V * V),
+    r2 => p[3] * K_REF2 * exp(-p[4] * E_A2 / R * (1 / temperature - 1 / T1)) * n[1] * n[3] /
+          (V * V),
+    r3 => p[3] * K_REF2 * exp(-p[4] * E_A2 / R * (1 / temperature - 1 / T1)) *
+          inv(K_C2 * exp(-(-DH_2 / R) * (1 / temperature - 1 / T1))) * n[4] / V,
+    r4 => p[5] * K_REF4 * exp(-p[6] * E_A4 / R * (1 / temperature - 1 / T1)) * (n[1] / V)^2)
+
+eqs = map(Base.Fix2(substitute, subs_), eqs_)
+
+# Define the eqs
+@named urethan = ODESystem([D(feed1) ~ u1;
+        D(feed2) ~ u2;
+        D(temperature) ~ u3;
+        D(n[3]) ~ eqs[1];                                  #n_C
+        D(n[4]) ~ eqs[2];                                  #n_D
+        D(n[5]) ~ eqs[3];                                  #n_E
+        n[1] ~ n0[1] + feed1 - n[3] - 2 * n[4] - 3 * n[5];    #n_A
+        n[2] ~ n0[2] + feed2 - n[3] - n[4];                #n_B
+        n[6] ~ n0[3] + feed1 + u2;                         #n_L
+        V ~ sum(n .* M ./ rho)], tspan = (0.0, 80.0),
+    observed = h .~ [100 * n[1] * M[1] / sum([ni .* M[i] for (i, ni) in enumerate(n)]);
+    #100 * n[3]*M[3]/sum([ni .* M[i] for (i,ni) in enumerate(n)]);
+    #100 * n[4]*M[4]/sum([ni .* M[i] for (i,ni) in enumerate(n)]);
+        100 * n[5] * M[5] / sum([ni .* M[i] for (i, ni) in enumerate(n)])])
+
+## Build the OED System
+
+@named urethan_oed = OEDSystem(structural_simplify(urethan))
+
+oed_problem = DynamicOED.OEDProblem(urethan_oed, DCriterion())
+
+optimization_variables = states(oed_problem)
+timegrids = DynamicOED.get_timegrids(oed_problem)