# Convergence Issues with Controllable Switch and Square Wave using MTK
**URL:** https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264
**Category:** Modelling & Simulations
**Tags:** modelingtoolkit
**Created:** [July 31, 2025, 11:07pm UTC](https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264 "2025-07-31T23:07:46Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@junmorenodi99](https://discourse.julialang.org/u/junmorenodi99)
#### Post date: [July 31, 2025, 11:07pm UTC](https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264/1 "2025-07-31T23:07:46Z")
Hi everyone,
I am new to the Julia community and I’m interested in the applications of the `ModelingToolkit` package.
In particular, I’m trying to simulate a _switching circuit_ using an _External Control Signal_ and a _Controllable Switch_. The Switch is designed as a non-ideal resistor where the resistance value varies from high to low in response to the Control Signal. I tried a simple test circuit as below with two approaches :
```julia-auto
+V
|
┌┴┐ Control (Square Wave)
│S│<─────●
└┬┘
|
[R] ← Load resistor R
|
GND
```
1. Using a sinusoidal wave as Control Signal. In this case the model works. Here’s the plot of the Voltage on the load and the resistance of the Cotrollable “Switch”:
1. Using a square wave as Control Signal. In this case the model has convergence problems. It don’t show any “error” but two warnings:
```julia-auto
┌ Warning: Rosenbrock methods on equations without differential states do not bound the error on interpolations.
```
and
```julia-auto
┌ Warning: At t=0.0, dt was forced below floating point epsilon 5.0e-324, and step error estimate = NaN. Aborting. There is either an error in your model specification or the true solution is unstable (or the true solution can not be represented in the precision of Float64).
```
and the resulting plot is empty :
So I’m having some questions as I’m stuck in the implementation
- Which solver and settings (tolerances, max step size) work best for fast switching circuits in ModelingToolkit.jl?
- Are there any references or examples of switching models using MTK?
- Can ModelingToolkit.jl reliably handle non-linear, hybrid systems like this?
Here’s the code of the Circuit model:
```julia-auto
@mtkmodel R_Test begin
@parameters begin
RLoad_param = 10, [description = "Output Load (Ohm)"]
Vin_param = 200, [description = "Vin Souce (Vdc)"]
f = 100, [description = "Switch input Frequency (Hz)"]
end
@components begin
switch_input = squareWave(frequency = f, amplitude = 1, offset = 0, dutyCycle = 0.3)
#switch_input = Sine(frequency = f, amplitude = 0.99, offset = 1.0)
voltage_input = Constant(k = Vin_param)
switch = IdealSwitch(Ron = 1e-3, Roff = 1)
source = Voltage()
RLoad = Resistor(R = RLoad_param)
ground = Ground()
end
@equations begin
connect(voltage_input.output, source.V)
connect(switch_input.output, switch.conduction)
connect(source.p, switch.p)
connect(switch.n,RLoad.p)
connect(source.n, RLoad.n, ground.g)
end
end
```
The Switch is defined as
```julia-auto
@mtkmodel IdealSwitch begin
@extend v, i = oneport = OnePort()
@parameters begin
Ron = 1e-3, [description = "On resistance magnitud"]
Roff = 1e6, [description = "Off resistance magnitud"]
end
@components begin
conduction = RealInput()
end
@variables begin
q(t), [description = "Control Signal "]
R(t), [description = "Resistance "]
end
@equations begin
q ~ conduction.u
R ~ Ron + q * Roff
v ~ i * R
end
end
```
The square wave is defined as
```julia-auto
@component function squareWave(;name, frequency, amplitude = 1, offset = 0, dutyCycle = 0.5)
@named output = RealOutput()
pars = @parameters amplitude=amplitude frequency=frequency dutyCycle=dutyCycle
equation = amplitude * mod1(t, 1/frequency) < dutyCycle/frequency
eqs = output.u ~ equation
compose(System(eqs, t, [], pars; name = name), [output])
end
```
and the solver configuration is
```julia-auto
@mtkcompile sys = R_Test()
prob = ODEProblem(sys, Pair[], (0.0, 100e-3); guesses = [sys.switch.i => 5.0])
sol = solve(prob, Rodas5();
reltol=1e-8,
abstol=1e-10,
dt=1e-7,
dtmax=1e-5,
saveat=1e-5)
```
Any pointers or references to prior work are greatly appreciated!
Thanks!
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 31, 2025, 11:51pm UTC](https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264/2 "2025-07-31T23:51:13Z")
> [@junmorenodi99](#):
>
> - Are there any references or examples of switching models using MTK?
> - Can [ModelingToolkit.jl](https://juliaregistries.github.io/General/packages/redirect_to_repo/ModelingToolkit) reliably handle non-linear, hybrid systems like this?
> **[Model building reference · ModelingToolkit.jl](https://docs.sciml.ai/ModelingToolkit/stable/API/model_building/#ModelingToolkit.IfLifting)**
>
> Documentation for ModelingToolkit.jl.
It’s still a bit experimental but you can try the iflifting to see if the event handling fixes it. Right now it’s opt-in.
---
### Author:  [@junmorenodi99](https://discourse.julialang.org/u/junmorenodi99)
#### Post date: [August 2, 2025, 2:41pm UTC](https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264/3 "2025-08-02T14:41:26Z")
Thanks for your help @ChrisRackauckas. I’ve integrated the `iflifting` call into my code but now I’m seeing this error for both control signals:
```julia-auto
ERROR: BoundsError: attempt to access 0-element Vector{Int64} at index [1]
```
I suspect the problem is how I added `iflifting`, rather than the feature itself… Here’s the change I made:
```julia-auto
#@mtkcompile sys = R_Test()
@named sys_dec = R_Test()
sys = structural_simplify(sys_dec,additional_passes = [IfLifting])
```
Any ideas on how I can debug this? Thanks
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [August 3, 2025, 1:13am UTC](https://discourse.julialang.org/t/convergence-issues-with-controllable-switch-and-square-wave-using-mtk/131264/4 "2025-08-03T01:13:36Z")
Open an issue, easier to track it there.