Fabian,

I do not think that this statement is true

As far as I understand, in order to generate a state space model in Mathematica (via WSMLinearize) with such variable as an input, in the Modelica model the position of the suspension point must be declared as an input variable within the connector representing the physical attachment point to the ground, making the connector causal.

I am not certain what you want but I think you can do the following.

Take your multibody system and hook up an input to drive the model. Here is an example. I hooked an input, u, to the "y" direction of the force and 0 to the x and z directions (since the bodies were constrained to move only in "y".

I obtained the transfer function, tf, from the following and I verified the vibration frequency of 0.528 hz against a simulation in WSM.

model = SystemModel["Model1"]
eigensys = SystemModelSimulate[model,All,0.01];
nlsm =WSM`LocalizedSystemModel[eigensys,"StopTime"];
nsimp = nlsm["SelectOutputs",{"body1.r_0[2]"}];
nsimp2 = nsimp["Simplify"];
nssmodel = nsimp2["Linearization"];
tf =TransferFunctionModel[nssmodel];
poles = Flatten[TransferFunctionPoles[tf]];
freq = Abs[poles[[1]]]/2/Pi

You can also leave in some variables in the linearization with something like this:

lsm =WSM`LocalizedSystemModel[eigensys,"StopTime",<|"SymbolicParameters"->{"springDamper1.c"}|>];

and get the transfer function (and the corresponding eigenvalues) as a function of the damper (after completing the other steps above obtaining tf). You can get the eigenvalues by doing:

Eigenvalues[First[Normal[StateSpaceModel[tf]]]]

I hope this helps.

Regards

Neil

Edit: fixed the image

Dear Neil,

Thank you very much for your suggestion again.

I did try but unfortunately Mathematica is not able to linearize the system (vibratingSystem1 in the diagram you posted previously) when the boolean "exact" variable is set to true in the position1 component:

SSModel = WSMLinearize[Model1, Method -> "NumericDerivative"] // Chop
SystemModelLinearize::bld: -- Message text not found -- (GroundSimple)
SystemModelLinearize::bldl: -- Message text not found -- (Error) (<<4209>>)

It does it well when it's set to false but the unwanted effect of the filter becomes obvious. I have the impression setting exact=true is not compatible with an input not being connected. The rationale of the code defining the position1 component is not clear from reading it.

Nevertheless, I think you have pointed out the correct way of obtaining the transfer function in Mathematica from SystemModeler. I just have to find a workaround to the effect of the position1 component.

Thank you indeed.

Regards,

Fabian

Hello Neil,

Thank you very much for your kind help.

I was able to reproduce the Modelica model, however, Mathematica does not recognize the command

nlsm =WSM`LocalizedSystemModel[eigensys,"StopTime"];

Instead I can use

WSMFindEquilibrium[Model1] ;
WSMLinearize[Model1] ;

but Mathematica fails to find an equilibrium position and returns an error. The only way in which an equilibrium position is found is by connecting body2 directly to world, in which case its position cannot be an input.

Any suggestion would be appreciated.

I'm using SystemModeler 5.1.0 and Mathematica 11.3.0.0.

Regards,

Fabian