FunctionalModels.jl (formerly Sims.jl)
A Julia package for equationbased modeling and simulations. For more information, see the documentation:
NOTE: This is a work in progress to convert the package to use ModelingToolkit.
Some of the components and/or examples do not work, yet. This especially includes models requiring events and discrete systems.
FunctionalModels builds on top of ModelingToolkit. The following are exported:
t
: independent variableD
andder
: aliases forDifferential(t)
system
: flattens a set of hierarchical equations and returns a simplifiedODESystem
Unknown
: helper function to create variablesdefault_value
: return the default (starting) value of a variablecompatible_values
: return the base value from a variable to use when creating other variablesRefBranch
andBranch
: marks nodes and flow variables
Equations are standard ModelingToolkit equations. The main difference in FunctionalModels is
that variables should be created with Unknown(val; name)
or one of the helpers like Voltage()
.
Variables created this way include metadata to ensure that variable names don't clash.
Multiple subcomponents can all have a v(t)
variable for example.
Once the model is flattened, the variable names will be normalized.
FunctionalModels uses a functional style as opposed to the more objectoriented
approach of ModelingToolkit, Modia, and Modelica. Because system
return an ODESystem
, models can be built up of FunctionalModels components and
standard ModelingToolkit components.
Background
This package is for noncausal modeling in Julia. The idea behind noncausal modeling is that the user develops models based on components which are described by a set of equations. A tool can then transform the equations and solve the differential algebraic equations. Noncausal models tend to match their physical counterparts in terms of their specification and implementation.
Causal modeling is where all signals have an input and an output, and the flow of information is clear. Simulink is the highestprofile example. The problem with causal modeling is that it is difficult to build up models from components.
The highest profile noncausal modeling tools are in the Modelica family. The MathWorks company also has FunctionalModelscape that uses Matlab notation. Modelica is an objectoriented, open language with multiple implementations. It is a large, complex, powerful language with an extensive standard library of components.
This implementation follows the work of David Broman (thesis and code) and George Giorgidze (Hydra code and thesis) and Henrik Nilsson and their functional hybrid modeling. FunctionalModels is most similar to Modelyze by David Broman (report).
Installation
FunctionalModels is an installable package. To install FunctionalModels, use the following:
Pkg.add("FunctionalModels")
Model Libraries
FunctionalModels.jl has one main module named FunctionalModels
and the following submodules:

FunctionalModels.Lib
 the standard library 
FunctionalModels.Examples
 example models, including:FunctionalModels.Examples.Basics
FunctionalModels.Examples.Lib
FunctionalModels.Examples.Neural
Basic example
FunctionalModels uses ModelingToolkit to build up models. All equations use the ModelingToolkit variables and syntax. In a simulation, the unknowns are to be solved based on a set of equations. Equations are built from device models.
A device model is a function that returns a vector of equations or other devices that also return lists of equations.
Electrical example
This example shows definitions of several electrical components. Each is again a function that returns a list of equations.
Arguments to each function are model parameters. These normally include nodes specifying connectivity followed by parameters specifying model characteristics.
Models can contain models or other functions that return equations.
The function Branch
is a special function that returns an equation
specifying relationships between nodes and flows. It also acts as an
indicator to mark nodes. In the flattening/elaboration process,
equations are created to sum flows (in this case electrical currents)
to zero at all nodes. RefBranch
is another special function for
marking nodes and flow variables.
Nodes passed as parameters are unknown variables. For these electrical examples, a node is simply an unknown voltage.
function Resistor(n1, n2; R::Real)
i = Current()
v = Voltage()
[
Branch(n1, n2, v, i)
R * i ~ v
]
end
function Capacitor(n1, n2; C::Real)
i = Current()
v = Voltage()
[
Branch(n1, n2, v, i)
D(v) ~ i / C
]
end
What follows is a toplevel circuit definition. In this case, there are no input parameters. The ground reference "g" is assigned zero volts.
All of the equations returned in the list of equations are other models with various parameters.
In this example, the model components are named (:vs
, :r1
, ...).
Unnamed components can also be used, but then variables used
in components have anonymized naming (c1₊i(t)
vs. var"##i#1057"(t)
).
function Circuit()
@named n1 = Voltage()
@named n2 = Voltage()
g = 0.0 # A ground has zero volts; it's not an unknown.
[
:vs => SineVoltage(n1, g, V = 10.0, f = 60.0)
:r1 => Resistor(n1, n2, R = 10.0)
:r2 => Resistor(n2, g, R = 5.0)
:c1 => Capacitor(n2, g, C = 5.0e3)
]
end
ckt = Circuit()