doc: MTK example throw error if u arg is used inside output function

Author: franckgaga

docs/src/manual/mtk.md

@@ -60,23 +60,45 @@ function generate_f_h(model, inputs, outputs)
     if any(ModelingToolkit.is_alg_equation, equations(io_sys)) 
         error("Systems with algebraic equations are not supported")
     end
-    h_ = ModelingToolkit.build_explicit_observed_function(io_sys, outputs; inputs)
-    nx = length(dvs)
+    nu, nx, ny = length(inputs), length(dvs), length(outputs)
     vx = string.(dvs)
     p = varmap_to_vars(defaults(io_sys), psym)
     function f!(ẋ, x, u, _ , p)
-        f_ip(ẋ, x, u, p, 1)
+        try
+            f_ip(ẋ, x, u, p, nothing)
+        catch err
+            if err isa MethodError
+                error("NonLinModel does not support a time argument t in the f function, "*
+                      "see the constructor docstring for a workaround.")
+            else
+                rethrow()
+            end
+        end
         return nothing
     end
+    h_ = ModelingToolkit.build_explicit_observed_function(io_sys, outputs; inputs)
+    u_nothing = fill(nothing, nu)
     function h!(y, x, _ , p)
-        y .= h_(x, 1, p, 1)
+        y .= try
+            # MTK.jl supports a `u` argument in `h_` function but not this package. We set
+            # `u` as a vector of nothing and `h_` function will presumably throw an
+            # MethodError it this argument is used inside the function
+            h_(x, u_nothing, p, nothing)
+        catch err
+            if err isa MethodError
+                error("NonLinModel only support strictly proper systems (no manipulated "*
+                      "input argument u in the output function h)")
+            else
+                rethrow()
+            end
+        end
         return nothing
     end
-    return f!, h!, p, nx, vx
+    return f!, h!, p, nu, nx, ny, vx
 end
 inputs, outputs = [mtk_model.τ], [mtk_model.y]
-f!, h!, p, nx, vx = generate_f_h(mtk_model, inputs, outputs)
-nu, ny, Ts = length(inputs), length(outputs), 0.1
+f!, h!, p, nu, nx, ny, vx = generate_f_h(mtk_model, inputs, outputs)
+Ts = 0.1
 vu, vy = ["\$τ\$ (Nm)"], ["\$θ\$ (°)"]
 nothing # hide
 ```