SysML and Modelica: Opportunities for Synergy

1. OMG, Santa Clara, December 2008 SysML and Modelica:Opportunities for Synergy Chris Paredis, Peter Fritzson, Russell Peak Georgia Institute of Technology Linköping University

2. Intent of Presentation • Introduce Modelica to SysML community • Propose an effort to explore an integration between Modelica and SysML further: Descriptive Modeling in SysML + Formal Executable Modeling for Analyses and Trade Studies in Modelica

3. Overview • Modelica overview • What is Modelica? • What makes Modelica so appealing? • The Modelica Standard Library • The OpenModelica Project • SysML – Modelica Synergy • SysML – Modelica Correspondence • Steps Forward • Summary • Additional References

4. What is Modelica? • State-of-the-art ModelingLanguage for System Dynamics • Differential Algebraic Equations (DAE) • Discrete Events • Formal, object-oriented language • Ports represent energy flow (undirected) orsignal flow (directed) • Acausal, equation-based, declarative • Multi-domain modeling

5. Modelica is Object-Oriented model SlidingMass "Sliding mass with inertia" extendsInterfaces.Rigid; import SI = Modelica.SIunits; parameterSI.Mass m = 1 "mass o the sliding mass"; SI.Velocity v "absolute velocity of the component"; SI.Acceleration a "absolute acceleration of the component"; equation v = der(s); a = der(v); m*a = flange_a.f + flange_b.f; end SlidingMass; Class consists of declaration + equations Specify the default value for parameters Modelica is case sensitive Objects are declared as instances of classes Equations arenon-causal Use dot-notation to refer to object variables

6. Modelica is Acausal, and Port-based • Acausal, equation-based • F = m*a • a = F/m • 0 = F – m*a • Port-based • Connectors represent energy flow • Undirected connections • Semantics of Kirchhoff's laws • E.g., fluid port contains • Pressure • flow: Mass flow rate • Temperature • flow: Enthalpy flow rate

7. Textual and Graphical Views Annotations for visualization, compilation & simulation Do not affect mathematical model model myCircuit annotation(uses(Modelica(version="2.2.1"))); Modelica.Electrical.Analog.Basic.Ground Ground1 annotation (extent=[-62,-44; -42,-24]); Modelica.Electrical.Analog.Basic.Resistor Resistor1 annotation (extent=[0,-14; 20,6], rotation=270); Modelica.Electrical.Analog.Basic.Capacitor Capacitor1 annotation (extent=[-32,6; -12,26]); Modelica.Electrical.Analog.Sources.ConstantVoltage ConstantVoltage1 annotation (extent=[-62,-14; -42,6], rotation=270); equation connect(ConstantVoltage1.p, Resistor1.p) annotation (points=[-52,-24; -52,-14], style(color=3, rgbcolor={0,0,255})); connect(Resistor1.n, Capacitor1.p) annotation (points=[-52,6;-52,16;-32,16], style(color=3, rgbcolor={0,0,255})); connect(Capacitor1.n, ConstantVoltage1.n) annotation (points=[-12,16; 10,16; 10,6], style(color=3, rgbcolor={0,0,255})); connect(ConstantVoltage1.n, Ground1.p) annotation (points=[10,-14; -52,-14], style(color=3, rgbcolor={0,0,255})); end myCircuit;

8. What Makes Modelica so Appealing?  Symbolic manipulation of equations enables • Causality assignment • Simplification / elimination of algebraic loops • Index reduction • Zero-crossing functions for event detection • Symbolic differentiation for faster root-finding • Bottom Line: • Very expressive models • Very efficient simulations

9. Example: Stribeck Friction • Hybrid model • DAE +discrete events • 5 states: • locked • startForward • forward • startBackward • Backward • Dynamically reverses causalitywhen v=0 • Avoids typical stiffness at v=0

10. The Modelica Standard Library motor torque

11. Information about syntax and semantics of Modelica For working with signals & controls: generate waveforms, transfer functions, sampling, logical operators, look-up tables (interpolation) Defines constants: pi, e, G, h, … Motors and generators: DC, (a-)synchronous induction Multiphase power grids, power electronics (thyristors, etc.) Standard Mathematical functions (trig, log, interpolation,…) Mechanical 3D and 1D (for planar motion use 3D) Media = liquids and gasses; no component models Large number of units Simple models for flow of fluids with thermal properties Utilities for printing and file access The Modelica Standard Library

12. Other Modelica Libraries • Modelica association — 20+ free libs (www.modelica.org) • EUROSYSLIB project — 20+ libs under development(http://www.itea2.org/public/project_leaflets/EUROSYSLIB_profile_oct-07.pdf)

13. The OpenModelica Project • Open source Modelica environment • OMC, The Modelica Compiler/Interpreter • OMShell, The Interactive Session Handler • OMNotebook, DrModelica Simple Electronic notebook • Graphic Model Editor – SimForge(developed by Technical University of Milan) • Modelica Development Tooling (MDT) as Eclipse Plugin • Modelica XML conversion • Debugger for extended subset algorithmic code • Supported by the Open Source Modelica Consortium • European ITEA2 project OPENPROD • PI: P. Fritzson; 25 Partners;  €11M • More info: http://www.openmodelica.org  

14. SysML – Modelica Synergies • Modelica = state-of-the-art modeling language for system dynamics • Complements SysML Parametrics • Very expressive, formal language for differential algebraic equations and discrete events • Is (more or less) Compatible with SysML • Object-oriented, port-based • Broad Range of (Open Source) Libraries • Addresses need for domain models in SysML • Access to Free, Open Source Solvers

15. Overview • Modelica overview • What is Modelica? • What makes Modelica so appealing? • The Modelica Standard Library • The OpenModelica Project • SysML – Modelica Synergy • SysML – Modelica Correspondence • Steps Forward • Summary • Additional References

16. SysML – Modelica Correspondence:Model Definitions Modelica SysML Block or Constraint Block Modelica connectors could map to flow ports, or a stereotyped constraint property Stereotyped connector or stereotyped binding connector No formal equivalent textual constraint • Class • Has restricted classes: package, record, function,… • "connector" is crucial • Connection • For energy-flow, the connections have the semantics of Kirchhoff's laws • Equations and Algorithms • Initial equations and algorithms

17. SysML – Modelica Correspondence:Model Usage Modelica SysML Properties (usages) No equivalents new stereotypes? Multiplicities Not sufficiently expressive Property-specific types Somewhat vaguely defined Not (well) supported by tools Fixed visualization • Component clauses • discrete, constant, parameter  indicates time variance • input, output, flow • Arrays • Modifiers • Change default values • Redeclare type • Arbitrarily deep in hierarchy • Visualization annotations NOTE: this is just an illustration – much work remains

18. Initial Work towards Integration • ModelicaML UML profile • Pop, A., and Akhvlediani, D., and Fritzson, P. (2007). "Towards Unified Systems Modeling with the ModelicaML UML Profile." International Workshop on Equation-Based Object-Oriented Languages and Tools. Berlin, Germany, Linköping University Electronic Press. • SysML-Modelica profile and mapping • Johnson, T. A., C. J. J. Paredis and R. M. Burkhart (2008). "Integrating Models and Simulations of Continuous Dynamics into SysML." 6th International Modelica Conference, Bielefeld, Germany, March 3-4, Modelica Association, 135-145. • Tool prototype • Automated mapping from SysML (MagicDraw) to Modelica • Model transformation with MOFLON • Model simulation with Dymola

19. Example: Hydraulic Circuit DiagramPressure-Compensated, Load-Sensing Excavator—ISO 1219 notation

20. SysML Schematic (ibd) — Basic ViewPressure-Compensated, Load-Sensing Excavator

21. Hydraulics Subsystem Simulation Modelbdd

22. D i g C y c l e h y d r a u l i c s environment world y p _ amb = 101325 T _ amb = 288 . 15 x Excavator Case StudyCorresponding Modelica Models Hydraulics Model Multi-Body System Dynamics Model(linkages, ...)

23. Simulationin Dymola Simulation Results ModelicaLexical Representation (auto-generated from SysML) [Johnson, 2008 - Masters Thesis]

24. How to Move Forward from Here? • Further develop and refine SysML-Modelica profile and mapping • In parallel with other SysML 2.0 efforts • Provide input to future SysML 2.0 submissions • Team members: Roger Burkhart,Sandy Friedenthal, Peter Fritzson,Chris Paredis, Russell Peak, …

25. Summary • Modelica = state-of-the-art modeling language for system dynamics • Strong SysML-Modelica synergy • Complements Parametrics • Is (more or less) Compatible with SysML • Broad range of libraries • Access to Free Solvers • Good high-level correspondence,but some (minor) differences • Team: extensive experience in both Modelica and SysML

26. Additional References • Modelica Specification: http://www.modelica.org/documents/ModelicaSpec30.pdf • Fritzson, P. (2004). Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. New York, NY, Wiley-IEEE Press. • Akhvlediani, D. (2006). Design and implementation of a'UML profile for Modelica'/SysML. M.S. Thesis. Linköping University. LITH-IDA-EX--06/061—SE. • Johnson, T. A. (2008). Integrating Models and Simulations of Continuous Dynamic System Behavior into SysML. M.S. Thesis. G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology. Atlanta, GA. • Peak, R., McGinnis, L., Paredis, C. Integrating System Design with Simulation and Analysis Using SysML – Phase 1 Final Report, (available from russell.peak@gatech.edu)