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 LibraryThe Modelica Standard Library is available for download here that contains about 1400 generic model components and 1200 functions in various domains, as of version 4.0.0.
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 conventional programming language. Modelica classes are not compiled in the usual sense, but they 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,Jeandel A., Boudaud F.: Physical System Modelling Languages: from ALLAN to Modelica, Building Simulation'97, IBPSA Conference, Prague, September 8–10, 1997. Dymola, NMF ObjectMath, Omola,S.E. Mattsson, M. Andersson and K.J..Aström: Object-oriented modeling and simulation. In: Linkens, ed., CAD for Control Systems (Marcel Dekker, 1993) pp. 31-69. SIDOPS+, and Smile.Ernst T., Jähnichen S., Klose M.: Object-Oriented Physical Systems Modeling, Modelica, and the Smile/M Simulation Environment. 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Berlin, August 24–29, 1997. Hilding Elmqvist is the key architect of Modelica, but many other people have contributed as well (see appendix E in the Modelica specification). 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 Highlights1.01997, SeptemberFirst version to model continuous dynamic systems.1.11998, DecemberLanguage elements to model discrete systems (pre, when)1.21999, JuneInterface to C and Fortran, inner/outer for global variables, refined semantics of event handling1.31999, DecemberImproved semantics for inner/outer connections, protected elements, array expressions.1.42000, DecemberRemoved declare-before-use rule, refined package concept, refined when-clause2.02002, JulyInitialization of models, standardization of graphical appearance, functions with mixed positional and named arguments, record constructor, enumerations2.12004, MarchOverdetermined connector to model 3-dim. mechanical systems, enhanced redeclaration of submodels, array and array indices of enumerations2.22005, FebruaryExpandable connector to model signal buses, conditional component declarations, arrays with dynamic size changes in functions3.02007, SeptemberClean-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 way3.12009, MayStream connector to handle bi-directional flow of fluid, operator overloading, mapping model parts to execution environments (for use in embedded systems)3.22010, MarchImproved initialization with homotopy method, functions as formal inputs to functions, Unicode support, access control to protect IP, improved support of object libraries3.32012, MayAdded language elements to describe periodic and non-periodic synchronous controllers based on clocked equations, as well as synchronous state machines.3.42017, AprilAutomatic conversion of models. Many minor improvements3.52021, FebruaryAnnotations for predefined plots. Change of specification format, with many editorial changes. Clarifications to synchronous language elements and state machines. Many minor clarifications to functions, model conversions, and several other parts of the specification. 3.62023, MarchRemoving modifiers with break and selective model extensions. Multilingual support to present Modelica libraries in multiple languages.
Implementations Commercial front-ends for Modelica include AMESim from the French company Imagine SA (now part of Siemens Digital Industries Software), Dymola from the Swedish company Dynasim AB (now part of Dassault Systèmes), Wolfram SystemModeler (formerly MathModelica) from the Swedish company Wolfram MathCore AB (now part of Wolfram Research), SimulationX from the German company ESI ITI GmbH, MapleSim from the Canadian company Maplesoft, JModelica.org (open source, discontinued) and Modelon Impact, from the Swedish company Modelon AB, and CATIA Systems Announcement of DS' acquisition of Dynasim from Dassault Systèmes (CATIA is one of the major CAD systems).
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,Adrian Pop, David Akhvlediani, Peter Fritzson Integrated UML and Modelica System Modeling with ModelicaML in Eclipse, In Proceedings of the 11th IASTED International Conference on Software Engineering and Applications (SEA 2007), Cambridge, MA, USA compilation and simulation environment based on free software distributed in binary and source code form for research,Håkan Lundvall and Peter Fritzson Automatic Parallelization of Object Oriented Models Executed with Inline Solvers, In Proceedings of EuroPvm/Parsim, Springer Verlag LNCS, Volume 4757, 2007 teaching,Anders Fernström, Ingemar Axelsson, Peter Fritzson, Anders Sandholm, Adrian Pop OMNotebook - Interactive WYSIWYG Book Software for Teaching Programming, In Proc. of the Workshop on Developing Computer Science Education - How Can It Be Done?, 2006. Linköping University, Dept. Computer & Inf. Science, Linköping, Sweden 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. Nevertheless, there is still some incompatibility and diverging interpretation between all the different tools concerning the Modelica language.Jörg Frochte Modelica Simulator Compatibility - Today and in Future, The 8th International Modelica Conference, March 20–22, 2011, Technical University, Dresden, Germany
Examples The following code fragment shows a very simple example of a first order system ():
model FirstOrder parameter Real c=1 "Time constant"; Real x (start=10) "An unknown"; equation der(x) = -c*x "A first order differential equation"; end FirstOrder;
The following code fragment shows an example to calculate the second derivative Introduction to Physical Modeling with Modelica, Michael Tiller of a trigonometric function, using OMShell, as a means to develop the program written below.
model second_derivative Real l; Real z=sin(w*time); Real m; parameter Real w = 1; equation l=der(z); m=der(l); end second_derivative;
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 four 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 infinitesimally 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.
The full rules for defining balanced models are rather complex, and can be read from in section 4.7.
However, for most cases, a simple rule can be issued, that counts variables and equations the same way as most simulation tools do: A model is balanced when the number of its equations equals the number of its variables. given that variables and equations must be counted according to the following rule:
->Number of model equations = Number of equations defined in the model + number of flow variables in the outside connectors
->Number of model variables = Number of variables defined in the model (including the variables in the physical connectors)
Note that standard input connectors (such as RealInput or IntegerInput) do not contribute to the count of variables since no new variables are defined inside them.