A Julia package for equation-based 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.
Sims builds on top of ModelingToolkit. The following are exported:
t: independent variable
der: aliases for
system: flattens a set of hierarchical equations and returns a simplified
Unknown: helper function to create variables
default_value: return the default (starting) value of a variable
compatible_values: return the base value from a variable to use when creating other variables
Branch: marks nodes and flow variables
Equations are standard ModelingToolkit equations. The main difference in Sims is
that variables should be created with
Unknown(val; name) or one of the helpers like
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.
Sims uses a functional style as opposed to the more object-oriented
approach of ModelingToolkit, Modia, and Modelica. Because
ODESystem, models can be built up of Sims components and
standard ModelingToolkit components.
This package is for non-causal modeling in Julia. The idea behind non-causal 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. Non-causal 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 highest-profile 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 Simscape that uses Matlab notation. Modelica is an object-oriented, 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. Sims is most similar to Modelyze by David Broman (report).
Sims is an installable package. To install Sims, use the following:
Sims.jl has one main module named
Sims and the following submodules:
Sims.Lib-- the standard library
Sims.Examples-- example models, including:
Sims 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.
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.
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 top-level 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 (
Unnamed components can also be used, but then variables used
in components have anonymized naming (
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 = 5.0e-3) ] end ckt = Circuit()