System with only discrete-time variables being treated as continuous time

[baggepinnen]

The following model contains only discrete-time variables. It simplifies and solves, but the solution is completely incorrect, possibly because it is being incorrectly treated as a continuous-time system

using ModelingToolkit
using ModelingToolkitStandardLibrary.Blocks
using ModelingToolkit: t_nounits as t
k = ShiftIndex()
@mtkmodel Del begin
    @extend u, y = siso = SISO()
    @structural_parameters begin
        n = 1
    end
    @equations begin
        y ~ u(k-n)
    end
end

@mtkmodel DelayModel begin
    @components begin
        delay = Del(n = 3)
        input = Constant(k = 1)
    end
    @equations begin
        connect(input.output, delay.input)
    end
end

@mtkbuild m = DelayModel()
prob = ODEProblem(m, [m.delay.u(k-3)=>0, m.delay.u(k-2)=>0, m.delay.u(k-1)=>0], (0.0, 10.0))

sol = solve(prob, Tsit5())

The solution should have only 1 and 0 elements

julia> sol.u
7-element Vector{Vector{Float64}}:
 [0.0, 0.0, 0.0]
 [9.999999999999996e-5, 4.9999999999999695e-9, 1.6666666666666627e-13]
 [0.0010999999999999996, 6.049999999999966e-7, 2.2183333333333146e-10]
 [0.011099999999999994, 6.160499999999969e-5, 2.2793849999999778e-7]
 [0.11109999999999993, 0.00617160499999997, 0.0002285551051666657]
 [1.1110999999999993, 0.6172716049999964, 0.22861682677183132]
 [9.999999999999996, 49.99999999999975, 166.6666666666658]

The solution here is $t, \frac{t^2}{2}, \frac{t^3}{6}$, which happens to be correct for a continuous-time triple-integrator system.

Also:

using Plots
plot(sol) # errors