test: test called parameters are still differentiated

Author: AayushSabharwal

test/structural_transformation/utils.jl

@@ -311,4 +311,36 @@ end
     end
 
     @test !(D(sys.k) in vs)
+
+    @testset "Called parameter still has derivative" begin
+        @component function FilteredInput2(; name, x0 = 0, T = 0.1)
+            ts = collect(0.0:0.1:10.0)
+            spline = LinearInterpolation(ts .^ 2, ts)
+            params = @parameters begin
+                (k::LinearInterpolation)(..) = spline
+                T = T
+            end
+            vars = @variables begin
+                x(t) = k(t)
+                dx(t) = 0
+                ddx(t)
+            end
+            systems = []
+            eqs = [D(x) ~ dx
+                   D(dx) ~ ddx
+                   dx ~ (k(t) - x) / T]
+            return ODESystem(eqs, t, vars, params; systems, name)
+        end
+
+        @mtkbuild sys = FilteredInput2()
+        vs = Set()
+        for eq in equations(sys)
+            ModelingToolkit.vars!(vs, eq)
+        end
+        for eq in observed(sys)
+            ModelingToolkit.vars!(vs, eq)
+        end
+
+        @test D(sys.k(t)) in vs
+    end
 end