Modelica

Modelica

Paradigm	declarative language
First appeared	1997
Stable release	3.2 / March 24, 2010
OS	Cross-platform
License	Modelica License Version 2
Website	www.modelica.org
Major implementations
CATIA Systems, Dymola, JModelica.org, MapleSim, MathModelica, OpenModelica, Scicos, SimulationX, Vertex, Xcos

Modelica is an object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-oriented subcomponents. The free Modelica language is developed by the non-profit Modelica Association. The Modelica Association also develops the free Modelica Standard Library that contains about 1280 generic model components and 910 functions in various domains, as of version 3.2.

Characteristics

While Modelica resembles object-oriented programming languages, such as C++ or Java, it differs in two important respects. First, Modelica is a modeling language rather than a true programming language. Modelica classes are not compiled in the usual sense, but are translated into objects which are then exercised by a simulation engine. The simulation engine is not specified by the language, although certain required capabilities are outlined.

Second, although classes may contain algorithmic components similar to statements or blocks in programming languages, their primary content is a set of equations. In contrast to a typical assignment statement, such as

x := 2 + y;,

where the left-hand side of the statement is assigned a value calculated from the expression on the right-hand side, an equation may have expressions on both its right- and left-hand sides, for example,

x + y = 3 * z;.

Equations do not describe assignment but equality. In Modelica terms, equations have no pre-defined causality. The simulation engine may (and usually must) manipulate the equations symbolically to determine their order of execution and which components in the equation are inputs and which are outputs.

History

The Modelica design effort was initiated in September 1996 by Hilding Elmqvist. The goal was to develop an object-oriented language for modeling of technical systems in order to reuse and exchange dynamic system models in a standardized format. Modelica 1.0 is based on the PhD thesis of Hilding Elmqvist and on the experience with the modeling languages Allan, Dymola, NMF ObjectMath, Omola, SIDOPS+, and Smile. Hilding Elmqvist is the key architect of Modelica, but many other people have contributed as well (see appendix E in ). In September 1997, version 1.0 of the Modelica specification was released which was the basis for a prototype implementation within the commercial Dymola software system. In year 2000, the non-profit Modelica Association was formed to manage the continually evolving Modelica language and the development of the free Modelica Standard Library. In the same year, the usage of Modelica in industrial applications started.

This table presents the timeline of the Modelica specification history:

Release	Release Date	Highlights
1.0	1997, September	First version to model continuous dynamic systems.
1.1	1998, December	Language elements to model discrete systems (pre, when)
1.2	1999, June	Interface to C and Fortran, inner/outer for global variables, refined semantics of event handling
1.3	1999, December	Improved semantics for inner/outer connections, protected elements, array expressions.
1.4	2000, December	Removed declare-before-use rule, refined package concept, refined when-clause
2.0	2002, July	Initialization of models, standardization of graphical appearance, functions with mixed positional and named arguments, record constructor, enumerations
2.1	2004, March	Overdetermined connector to model 3-dim. mechanical systems, enhanced redeclaration of submodels, array and array indices of enumerations
2.2	2005, February	Expandable connector to model signal buses, conditional component declarations, arrays with dynamic size changes in functions
3.0	2007, September	Clean-up version: specification newly written, type system and graphical appearance refined, language flaws fixed, balanced model concept to detect model errors in a much better way
3.1	2009, May	Stream connector to handle bi-directional flow of fluid, operator overloading, mapping model parts to execution environments (for use in embedded systems)
3.2	2010, March	Improved initialization with homotopy method, functions as formal inputs to functions, Unicode support, access control to protect IP, improved support of object libraries)

Implementations

Commercial front-ends for Modelica include Dymola from the Swedish company Dynasim AB (now part of Dassault Systemes), MathModelica from the Swedish company MathCore Engineering AB, SimulationX from the German company ITI GmbH, MapleSim from the Canadian company Maplesoft, and CATIA Systems from Dassault Systemes (CATIA is one of the major CAD systems).

JModelica.org is an extensible Modelica-based open source platform for optimization, simulation and analysis of complex dynamic systems. The main objective of the project is to create an industrially viable open source platform for optimization of Modelica models, while offering a flexible platform serving as a virtual lab for algorithm development and research.

OpenModelica is an open-source Modelica-based modeling and simulation environment intended for industrial and academic usage. Its long-term development is supported by a non-profit organization – the Open Source Modelica Consortium (OSMC). The goal with the OpenModelica effort is to create a comprehensive Open Source Modelica modeling, compilation and simulation environment based on free software distributed in binary and source code form for research, teaching, and industrial usage.

The free simulation environment Scicos uses a subset of Modelica for component modeling. Support for a larger part of the Modelica language is currently under development.

Examples

The following code fragment shows a very simple example of a first order system (${\dot {x}}=-c\cdot x$):

model FirstOrder
  parameter Real c=1 "Time constant";
  Real x "An unknown";
equation
  der(x) = -c*x "A first order differential equation";
end FirstOrder;

Interesting things to note about this example are the 'parameter' qualifier, which indicates that a given variable is time-invariant and the 'der' operator, which represents (symbolically) the time derivative of a variable. Also worth noting are the documentation strings that can be associated with declarations and equations.

The main application area of Modelica is the modeling of physical systems. The most basic structuring concepts are shown at hand of simple examples from the electrical domain:

Built-in and user derived types

Modelica has the 4 built-in types Real, Integer, Boolean, String. Typically, user-defined types are derived, to associate physical quantity, unit, nominal values and other attributes:

type Voltage = Real(quantity="ElectricalPotential", unit="V");
type Current = Real(quantity="ElectricalCurrent", unit="A");
  ...

Connectors describing physical interaction

The interaction of a component to other components is defined by physical ports, called connectors, e.g., an electrical pin is defined as:

connector Pin "Electrical pin"
   Voltage      v "Potential at the pin";
   flow Current i "Current flowing into the component";
end Pin;

When drawing connection lines between ports, the meaning is that corresponding connector variables without the "flow" prefix are identical (here: "v") and that corresponding connector variables with the "flow" prefix (here: "i") are defined by a zero-sum equation (the sum of all corresponding "flow" variables is zero). The motivation is to automatically fulfill the relevant balance equations at the infinitesimal small connection point.

Basic model components

A basic model component is defined by a model and contains equations that describe the relationship between the connector variables in a declarative form (i.e., without specifying the calculation order):

model Capacitor
   parameter Capacitance C;
   Voltage u "Voltage drop between pin_p and pin_n";
   Pin pin_p, pin_n;
equation
            0 = pin_p.i + pin_n.i;
            u = pin_p.v - pin_n.v;
   C * der(u) = pin_p.i;
end Capacitor;

The goal is that a connected set of model components leads to a set of differential, algebraic and discrete equations where the number of unknowns and the number of equations is identical. In Modelica this is achieved by requiring so called balanced models. This means that when "using" a model (making a model instance), all missing equations must be provided. From this requirement and the possibilities to provide missing equations for a model instance, e.g., by connecting connectors, Modelica requires in its simplest form that:

Number of model equations = Number of unknowns - number of flow variables - number of inputs

The Capacitor model above is balanced, since

number of equations =   5 (number of unknowns:
                           pin_p.v, pin_p.i, pin_n.v, pin_n.i, u)
                      - 2 (number of flow variables: pin_p.i, pin_n.i)
                    =   3.

Hierarchical models

A hierarchical model is built-up from basic models, by instantiating basic models, providing suitable values for the model parameters, and by connecting model connectors. A typical example is the following electrical circuit:

model Circuit
   Capacitor C1(C=1e-4) "A Capacitor instance from the model above";
   Capacitor C2(C=1e-5) "A Capacitor instance from the model above";
     ...
equation
   connect(C1.pin_p, C2.pin_n);
   ...
end Circuit;

Via the language element annotation(...) definitions can be added to a model that do not have an influence on a simulation. Annotations are used to define graphical layout, documentation and version information. A basic set of graphical annotations is standardized in order that the graphical appearance and layout of models in different Modelica tools is the same.

Applications

Modelica is designed to be domain neutral and, as a result, is used in a wide variety of applications, such as fluid systems (e.g. steam power generation, hydraulics, etc), automotive applications (especially powertrain) and mechanical systems (e.g. multi-body systems, mechatronics, etc).

In the automotive sector, many of the major automotive OEMs are using Modelica. These include Ford , General Motors, Toyota, BMW and Daimler. Modelica is also been increasingly used for the simulation of thermo-fluid and energy systems.

See also

• AMPL
• APMonitor
• ASCEND
• Dymola
• Domain-Specific Modeling DSM
• EcosimPro: Continuous and Discrete Modelling and Simulation Software
• EMSO
• GAMS
• MapleSim
• MathModelica
• MATLAB
• SimulationX

External links

• Modelica Association, the homepage of the non-profit Modelica Association (developing Modelica).
• Introduction to Physical Modeling with Modelica, book by Michael Tiller
• Fritzson, Peter (2004). Principles of Object-Oriented Modeling and Simulation with Modelica 2.1 (PDF). Wiley-IEEE Press. ISBN 978-0-471-47163-9. {{cite book}}: Unknown parameter |month= ignored (help)
• Commercial Modelica tools: Dymola, LMS Imagine.Lab AMESim, MapleSim, MathModelica, Modelica Physical Modeling Toolbox for Matlab, SimulationX, Vertex
• Open source Modelica tools: OpenModelica (GPL or OSMC-PL), JModelica.org (GPL)