Dear members, I case some of you found these discussions related to your work. I found this link to the Mathematica documentation that helped me better understand the difficulties of directly initializing dynamical systems. https://reference.wolfram.com/language/tutorial/NDSolveDAE.html Very instructive!! Cheers Jesús

Dear Sergio,

I am afraid I do not know where/how to add such modification. Looking at the element smee, I see that I can set phiMechanical or wMechanical, but not idq_dr.

can you be more explicit?

Jesus

Actually, there is technically not even a guarantee that there will be a choice at all; one can imagine using integration methods that don't perform reduction to ODE (state-space) form, or ODE forms where the equations used don't have a closed-form relation to the original equations of the model.

This is very clear thank you.

However, I still do not understand why SystemModeler cannot accept the initial values I am declaring in my example.

Thanks again.

Jesus

Is it possible at all, to always know which are the independent differential equations that systemmodeler is simulating?

Regards,

Jesus

Dear Jesus,

I'm glad to hear it's working out for you, although I must admit that I found it difficult to see through the computations in the notebook.

It is true that System Modeler doesn't include methods for finding periodic steady-state, so this is a nice examples of building functionality on top of System Modeler using Wolfram Language.

Dear Henrik and Sergio

Thank you for your generous explanations. I think the setting "fixed" as true reduces my initialization problems. Yes, I think there is a bug in the report yielded by system["StateVariables"] However, to be honest, I still have to process all the information you gave me. I let you know more about it later on.

Best regards to you two.

Jesus

Also, can someone direct me to verify the circuit system approach that WSM used in the automated generation of equations.? Is it Modified Nodal Analysis? I cannot find this kind of documentation.

There is no "circuit system approach" applied inside WSM. Instead, WSM – similar to other Modelica tools – relies on generic index reduction and state selection methods. The index reduction used in WSM is based on Pantelides' algorithm for consistent initialization, enhanced in various ways to avoid some of the pitfalls that the purely structural analysis of the basic algorithm would fall into.

Dear Jesus,

I am part of the System Modeler development team, and will try to answer even though I don't consider myself one of the real "users of System Modeler".

To make sure we're on the same page, this is what I get when building the attached example:

Building "SteadyStateComputations.MartiExample" as experiment "temporary-experiment" started at 11:35:13 
Notification: interactive The following variables are selected as states: L3.i, c2.v
Notification: interactive The initialization problem is underdetermined, the following variables were chosen to be initialized from their start values: c2.v, L3.i
Notification: interactive C/C++ compiler output:
…

For some reason, I'm getting L3.i instead of L1.i as a state, and will return to this difference below.

In Model Center, I then set fixed = true for both L3.i and c2.v, and the result is a balanced initialization problem:

Building "SteadyStateComputations.MartiExample" as experiment "temporary-experiment" started at 11:39:28 
Notification: interactive The following variables are selected as states: L3.i, c2.v
Notification: interactive C/C++ compiler output:
…

That we don't get the same selection of states is in the nature of automatic state selection, and means that one generally have to find the right balance between fiddling with stateSelect in the models (not unlikely to end up getting in the way of the automatic state selection) and finding ways to cope with uncertainty about where the states are. The latter requires good tool support, and although there are situations where System Modeler could act more intelligently, an example of it working well is that I can set the fixed = true on L1.i instead, and the selection of states changes to make it straight-forward to respect this choice of initialization constraints instead:

Building "SteadyStateComputations.MartiExample" as experiment "temporary-experiment" started at 11:46:53 
Notification: interactive The following variables are selected as states: L1.i, c2.v

Note, that the fixed attribute is a so-called structural property of a model, meaning that it must be known at the time of translating the model, so if L3.i and c2.v were reported to be selected as states when the model was built, is is precisely where you find the two degrees of freedom in the initialization when looking at the Initial Values column of the Variables tab in Simulation Center.