The Language for Cyber-Physical Systems

Transcription

1 Towards Dependable Model-based Development of Cyber-Physical Systems through Modelica The Language for Cyber-Physical Systems Invited talk IPA Seminar, Tokyo, Japan October 17, 2011 Peter Fritzson Professor at Linköping University, Sweden Vice Chairman of Modelica Association Director of Open Source Modelica Consortium

2 Part I Introduction ti to Modelica 2

3 Modelica Background: Stored Knowledge Model knowledge is stored in books and human minds which h computers cannot access The change of motion is proportional to the motive force impressed d Newton 3

4 Modelica Background: The Form Equations Equations were used in the third millennium B.C. Equality sign was introduced d by Robert Recorde in 1557 Newton still wrote text (Principia, vol. 1, 1686) The change of motion is proportional to the motive force impressed CSSL (1967) introduced a special form of equation : variable = expression v = INTEG(F)/m Programming languages usually do not allow equations! 4

5 What is Modelica? A language for modeling of complex cyber-physical systems Robotics Control Automotive Aircraft Satellites Power plants Systems biology 5

6 What is Modelica? A language for modeling of complex cyber-physical systems Primary designed for simulation, but there are also other usages of models, e.g. optimization. 6

7 What is Modelica? A language for modeling of complex cyber physical systems i.e., Modelica is not a tool Free, open language specification: There exist several free and commercial tools, for example: OpenModelica from OSMC MathModelica from MathCore Dymola from Dassault systems SimulationX from ITI MapleSim from MapleSoft Available at: 7

8 Modelica The Next Generation Modeling Language Declarative language Equations and mathematical functions allow acausal modeling, high level specification, increased correctness Multi-domain modeling Combine electrical, mechanical, thermodynamic, hydraulic, biological, control, event, real-time, etc... Everything is a class Strongly typed object-oriented language with a general class concept, Java & MATLAB-like syntax Visual component programming Hierarchical system architecture capabilities Efficient, non-proprietary Efficiency comparable to C; advanced equation compilation, e.g equations, ~ lines on standard PC 8

9 Modelica Acausal Modeling What is acausal modeling/design? Why does it increase reuse? The acausality makes Modelica library classes more reusable than traditional classes containing assignment statements where the input-output causality is fixed. Example: a resistor equation: R*i = v; can be used in three ways: i := v/r; v := R*i; R := v/i; 9

10 What is Special about Modelica? Multi-Domain Modeling Visual acausal hierarchical component modeling Typed declarative equation-based textual language Hybrid modeling and simulation 10

11 What is Special about Modelica? Multi-Domain Modeling 11

12 What is Special about Modelica? Multi-Domain Modeling Acausal model (Modelica) Keeps the physical structure Visual Acausal Hierarchical Component Modeling Causal block-based model (Simulink) 12

13 What is Special about Modelica? Multi-Domain Modeling qddref qdref 1 S qref 1 S k2 i k1 i Hierarchical system modeling cut joint r3control r3motor r3drive1 1 qd tn axis6 axis5 Visual Acausal Hierarchical Component Modeling l qdref Kd 0.03 S rel qref psum - Kv 0.3 sum wsum - rate2 b(s) a(s) rate S iref Jmotor=J spring=c fric=rv0 gear=i joint=0 S axis4 axis3 rate1 tacho2 tacho1 b(s) a(s) b(s) a(s) PT1 g5 axis2 q qd Rd1=100 Rp2=50 C=0.004*D/w m Rp1=200 Ra=250 Courtesy of Martin Otter Srel = n*transpose(n)+(identity(3)- Rd2=100 n*transpose(n))*cos(q)- Ri=10 skew(n)*sin(q); wrela = n*qd; + + diff + pow er zrela = n*qdd; OpI Sb = Sa*transpose(Srel); Rd4=100 r0b = r0a; vb = Srel*va; g3 wb = Srel*(wa + wrela); g1 ab = Srel*aa; zb = Srel*(za + zrela + cross(wa, wrela)); Vs Rd3=100 hall2 hall1 La=(250/(2*D*w wm)) emf w r axis1 y x inertial g2 qd g4 q 13 Courtesy of Martin Otter

14 What is Special about Modelica? Multi-Domain Visual Acausal Modeling Hierarchical A textual class-based language Component OO primary used for as a structuring concept Modeling Behaviour described declaratively using Differential algebraic equations (DAE) (continuous-time) Event triggers (discrete-time) Variable declarations Typed Declarative Equation-based Textual Language g class VanDerPol "Van der Pol oscillator model" Real x(start = 1) "Descriptive string for x ; Real y(start = 1) "y coordinate ; ; parameter Real lambda = 0.3; equation der(x) = y; der(y) = -x + lambda*(1 - x*x)*y; x) end VanDerPol; Differential equations 14

15 What is Special about Modelica? Multi-Domain Modeling Hybrid modeling = continuous-time + discrete-time modeling Visual Acausal Component Modeling Continuous-timetime Discrete-time Typed Declarative Equation-based Textual Language g time Hybrid Modeling 15

16 16 Graphical Modeling - Using Drag and Drop Composition

17 Multi-Domain (Electro-Mechanical) Modelica Model A DC motor can be thought of as an electrical circuit which also contains an electromechanical component model DCMotor Resistor R(R=100); Inductor L(L=100); VsourceDC DC(f=10); Ground G; ElectroMechanicalElement EM(k=10,J=10, b=2); Inertia load; equation R L connect(dc.p,r.n); EM connect(r.p,l.n); DC connect(l.p, EM.n); connect(em.p, DC.n); load connect(dc.n,g.p); connect(em.flange,load.flange); G end DCMotor 17

18 Corresponding DCMotor Model Equations The following equations are automatically derived from the Modelica model: (load component not included) Automatic transformation to ODE or DAE for simulation: 18

19 Model Translation Process to Hybrid DAE to Code Modelica Graphical Editor Modelica Textual Editor Modelica Model Modelica Source code Modelica Model Modeling Environment Frontend "Middle-end" Backend Translator Analyzer Optimizer Code generator Flat model Hybrid DAE Sorted equations Optimized i sorted equations C Compiler C Code Executable Simulation 19

20 Modelica in Power Generation GTX Gas Turbine Power Cutoff Mechanism Courtesy of Siemens Industrial Turbomachinery AB, Finspång, Sweden Hello Developed by MathCore for Siemens 20

21 21 Modelica in Avionics

22 22 Modelica in Automotive Industry

23 23 Modelica in Biomechanics

24 Application of Modelica in Robotics Models Real-time Training Simulator for Flight, Driving Using Modelica models generating real-time code Different simulation environments (e.g. Flight, Car Driving, Helicopter) Developed at DLR Munich, Germany Dymola Modelica tool Courtesy of Martin Otter, DLR, Oberphaffenhofen, Germany 24

25 Combined-Cycle Cycle Power Plant Plant model system level GT unit, ST unit, Drum boilers unit and HRSG units, connected by thermo-fluid ports and by signal buses Low-temperature parts (condenser, feedwater system, LP circuits) are represented by trivial boundary conditions. GT model: simple law relating the electrical load request with the exhaust gas temperature and flow rate. Courtesy Francesco Casella, Politecnico di Milano Italy and Francesco Pretolani, CESI SpA - Italy 25

26 Combined-Cycle Cycle Power Plant Steam turbine unit Detailed model in order to represent all the startup phases Bypass paths for both the HP and IP turbines allow to start up the boilers with idle turbines, dumping the steam to the condenser HP and IP steam turbines are modelled, including inertia, electrical generator, and connection to the grid Courtesy Francesco Casella, Politecnico di Milano Italy and Francesco Pretolani, CESI SpA - Italy 26

27 Modelica Spacecraft Dynamics Library Formation flying on elliptical orbits Control the relative motion of two or more spacecraft Attitude control for satellites using magnetic coils as actuators Torque generation mechanism: interaction between coils and geomagnetic field Courtesy of Francesco Casella, Politecnico di Milano, Italy 27

28 Modelica Standard Library Open Source, Developed by Modelica Association The Modelica Standard Library contains components from various application areas, including the following sublibraries: Blocks Library for basic input/output control blocks Constants Mathematical constants and constants of nature Electrical Library for electrical models Icons Icon definitions Fluid 1-dim Flow in networks of vessels, pipes, fluid machines, valves, etc. Math Mathematical functions Magnetic Magnetic.Fluxtubes for magnetic applications Mechanics Library for mechanical systems Media Media models for liquids and gases SIunits Su Type definitions based on SI units according to ISO Stategraph Hierarchical state machines (analogous to Statecharts) Thermal Components for thermal systems Utilities Utility functions especially for scripting 28

29 Brief Modelica History First Modelica design group meeting in fall 1996 International ti group of people with expert knowledge in both language design and physical modeling Industry and academia Modelica Versions 1.0 released September released March released March released September released May released May planned Fall 2012 Modelica Association established 2000 Open, non-profit organization 29

30 30 Modelica Conferences The 1 st International Modelica conference October, 2000 The 2 nd International Modelica conference March 18-19, The 3 rd International Modelica conference November 5-6, 2003 in Linköping, Sweden The 4 th International Modelica conference March 6-7, 2005 in Hamburg, Germany The 5 th International Modelica conference September 4-5, 2006 in Vienna, Austria The 6 th International Modelica conference March 3-4, 2008 in Bielefeld, Germany The 7 th International Modelica conference Sept 21-22, 2009, Como, Italy The 8 th International Modelica conference March 20-22, 2011 in Dresden, Germany The 4th Int. OpenModelica Workshop, Febr 6, 2012, Linköping, i Sweden

31 Part II Modelica Environments and OpenModelica 31

32 MathModelica Wolfram Research System Designer Simulation Center Mathematica Modeling and Simulation and Simulation and documentation analysis analysis Courtesy of Wolfram Research Wolfram Research MathModelica kernel USA, Sweden General purpose Mathematica integration 32

33 MathModelica Car Model Graphical View Courtesy Wolfram Research 33

34 MathModelica Car Model Simulation & Animation Courtesy Wolfram Research 34

35 MWORKS Suzhou Tongyuan Software & Control Tongyuan Software & Control China Recent Modelica tool on the market Interfaces with interfaces with CAD, FEM, Matlab/Simulink and FMI Courtesy of Tongyuan Software & Control MWORKS Studio 35

36 MapleSim MapleSoft Maplesoft Canada Recent Modelica tool on the market Integration with Maple Courtesy of MapleSoft 36

37 Dymola Dassault Systémès Dassault Systémès France, Sweden First Modelica tool on the market Main focus on automotive industry Courtesy of Dassault Systemes 37

38 Simulation X ITI ITI Germany Mechatronic systems Courtesy of ITI 38

39 OpenModelica, The Most Complete Open Source Modelica Tool OpenModelica Open Source Modelica Consortium (OSMC) International Open source OMEdit, graphical editor OMOptim, optimization subsystem 39

40 OpenModelica (cont.) Advanced Interactive Modelica compiler (OMC) Supports most of the Modelica Language Basic environment for creating models OMShell an interactive command handler OMNotebook a literate programming notebook MDT an advanced textual environment in Eclipse ModelicaML UML Profile MetaModelica symbolic manipulation 40 40

41 OpenModelica (cont.) OMEdit Using Chinese Characters 41

42 OSMC Open Source Modelica Consortium 34 organizational members September 2011 Founded Dec 4, 2007 Open-source community services Website and Support Forum Version-controlled source base Bug database Development courses Code Statistics 42

43 OSMC 34 Organizational Members, Sept 2011 (initially 7 members, 2007; New: Univ Maryland) Companies and Institutes (17 members) ABB Corporate Research, Sweden Bosch Rexroth AG, Germany Siemens Turbo Machinery AB, Sweden CDAC Centre for Advanced Computing, Kerala, India CEIT Institute, Spain Creative Connections, Prague, Czech Republic Fraunhofer FIRST, Berlin, Germany Frontway AB, Sweden Equa Simulation AB, Sweden Evonik Energy Services, Dehli, India IFP, Paris, France InterCAX, Atlanta, USA Wolfram/ MathCore USA, Sweden Maplesoft, Canada TLK Thermo, Germany VI-grade, Italy VTT, Finland XRG Simulation, Germany 43 Universities (17 members) Linköping University, Sweden Hamburg University of Technology/TuTech, Germany Technical University of Berlin, Germany FH Bielefeld, Bielefeld, Germany Technical University it of Braunschweig, Institute of Thermodynamics, Germany Technical University of Dortmund, Process Dynamics Group, Germany Université Laval, modeleau, Canada University of Maryland, USA Georgia Tech, Atlanta, USA Griffith University, Australia Politecnico di Milano, Italy Mälardalen University, Sweden Technical University Dresden, Germany Telemark University College, Norway Ghent University, Belgium Ecoles des Mines, CEP, Paris, France University of Ljubljana, Slovenia

44 OMnotebook Interactive Electronic Notebook Here Used for Teaching Control Theory 44

45 45 OpenModelica Demo

46 OpenModelica MDT Eclipse Plug-in 46 Code Outline for easy navigation within Modelica files Identifier Info on Hovering 46

47 OMOptim Optimization (1) Model structure Model Variables Optimized parameters Optimized Objectives 47

48 Problems OMOptim Optimization (2) Solved problems Result plot Export result data.csv Pareto Front 48

49 Modelica Language Interoperability External Functions C, FORTRAN 77 It is possible to call functions defined outside the Modelica language, implemented in C or FORTRAN 77 function polynomialmultiply input Real a[:], b[:]; output Real c[:] := zeros(size(a,1)+size(b, 1) - 1); external end polynomialmultiply; The body of an external function is marked with the keyword external If no language is specified, the implementation language for the external function is assumed to be C. The external function polynomialmultiply can also be specified, e.g. via a mapping to a FORTRAN 77 function: function polynomialmultiply input Real a[:], b[:]; output Real c[:] := zeros(size(a,1)+size(b, 1) - 1); external FORTRAN 77 end polynomialmultiply; 49

50 General Tool Interoperability & Model Exchange Functional Mock-up Interface (FMI) The FMI development is part of the MODELISAR 29-partner project FMI development initiated by Daimler Improved Software/Model/Hardware-in-the-Loop Simulation, of physical models and of AUTOSAR controller models from different vendors for automotive applications with different levels of detail. Open Standard 14 automotive use cases for evaluation > 10 tool vendors are supporting it etc. Engine Gearbox Thermal Automated Chassis components, with ECU with ECU systems cargo door roadway, ECU (e.g. ESP) functional mockup interface for model exchange and tool coupling courtesy Daimler 50

51 OpenModelica FMI Export and Import Export: translatemodel FMU(A) importfmu( A A.f mu ) 51

52 OPENPROD Large 28-partner European Project, Vision of Cyber-Physical Model-Based Product Development Business Process Control Requirements Capture Model-Driven Design (PIM) Feedback Compilation &Code Gen (PSM) System Simulation Process models Requirements models Product models Platform models Software & Syst Product Unified Modeling: Meta-modeling& Modelica& UML & OWL OPENPROD Vision of unified modeling framework for model-driven product development from platform independent d models (PIM) to platform specific models (PSM) Current work based on Eclipse, UML/SysML, OpenModelica 52

53 OpenModelica ModelicaML UML Profile SysML/UML to Modelica OMG Standardization ModelicaML is a UML Profile for SW/HW modeling Applicable to pure UML or to other UML profiles, e.g. SysML Standardized Mapping UML/SysML to Modelica Defines transformation/mapping for executable models Being standardized by OMG ModelicaML Defines graphical concrete syntax (graphical notation for diagram) for representing Modelica constructs integrated with UML Includes graphical formalisms (e.g. State Machines, Activities, Requirements) Which do not exist in Modelica language Which are translated into executable Modelica code Is defined towards generation of executable Modelica code Current implementation based on the Papyrus UML tool + OpenModelica 53

54 Example: Representation of System Behavior State Machine of the Controller Conditional Algorithm (Activity Diagram) State Machine of the Tank 54

55 Example: Representation of System Requirements Textual Requirement Formalized Requirement 55

56 Example: Simulation and Requirements Evaluation Req. 001 is instantiated 2 times (there are 2 tanks in the system) tank-height is 0.6m Req. 001 for the tank2 is violated Req. 001 for the tank1 is not violated 56

57 vvdr virtual Verification of Design Requirements vvdr Roles and Tasks Requirements Analyst -Select requirements to be verified using simulations -Formalize textual requirements System Designer System Tester -Support Requirements Analyst in selecting requirements -Create system design models to be verified against requirements -Support System Tester in deciding which requirements are to be verified using which test cases -Support System Tester in linking requirement properties to design model properties -Create test modes including test cases and decide which requirement are to be verified using which test cases -Link requirements to design models -Simulate and create a Simulation Summary Report 57

58 1) Select Requirements To Be Evaluated by Means of Simulation 1. Read a requirement Agreed textual requirements Requirements Analyst in collaboration with System Designer 2. Decide if this requirement shall be evaluated using a simulation model (involve the System Designer) Selected textual requirements 3. Is this requirement complete, unambiguous and testable by using a simulation model? 4. If yes: Mark this requirement as selected 58

59 1) Select Requirements to Be Evaluated by Means of Simulation Example of selected requirements: If at any time the controller calculates l a "caution" " signal, it shall, within 0.5 seconds, enable the alarm in the driver cabin. If the alarm in the driver cabin has been activated due to a "caution" signal and the train speed is not decreasing by at least 0.5 m/s^2 within 2 seconds after activation of alarm, then the controller shall within 0.5 seconds activate the automatic braking. If at any time the controller calculates a "danger" signal it shall within 0.5 seconds activate the braking system and enable the alarm in the driver cabin. 59

60 1) Select Requirements to Be Evaluated by Means of Simulation Example of requirements that are not selected: The sensors shall be attached to the side of the train and read information from approaching track-side signals, i.e. they detect what the signal is signaling to the train driver. Why not? We do not plan to create a model that will contain all information required to detect whether the sensors are attached to the side of the train. Simulation may not be best suited means to verify this requirement. Inspection of the design may be more appropriate. The ATP system shall consist of a central controller and five boundary subsystems that manage the sensors, speedometer, brakes, alarm and a reset mechanism. Why not? This is a design constraint to be taken into account. Inspection of the design will be sufficient to verify this requirement. 60

61 2) Formalize Textual Requirements Selected textual requirements Requirements Analyst 61

62 2) Formalize Textual Requirements Textual requirement example: If at any time the controller calculates a "caution" signal, it shall, within 0.5 seconds, enable the alarm in the driver cabin. Requirements Analyst 1. Identify measurable properties addressed in the requirement statement 2. Formalize properties and define requirement violation monitor Formalized requirement: 62

63 3) Select or Create Design Model To Be Verified Against Requirements System Requirements System Design Alternatives System Designer 63

64 4) Create Test Models, Instantiate Models System Tester in collaboration with System Designer Define test models that will contain a test case, requirements models and a design model to be verified against requirements This model will contain the information required for reproducing tests results Define test cases for evaluating requirements One test case can be used for evaluating one or more requirements Create additional models if necessary For example, models that simulate the environment of the system, models that stimulate the system, models that monitor specific values, etc. 64

65 4) Create Test Models, Instantiate Models System Tester in collaboration with System Designer Test Case description 65

66 5) Link Requirement Properties to Design Model Properties Instantiated requirement System Tester in collaboration with System Designer Instantiated design model 66 Requirement properties are linked to design model properties

67 6) Simulate and Observe Requirement Violations System Tester Requirement violation indication 67

68 7) Analyze Simulation Results Create a Simulation Summary Report including: For each test model include the simulation configuration: Which design model, test cases and requirements were included Requirements violations, if any. This configuration allows the reproducing of test results The reports can be used as reference for product verification Requirements Analyst System Designer Simulation Summary Report System Tester 68

69 vvdr Summary vvdr is a method for the verification of design against requirements by using simulations The method applicability depends on Design simulation models that are planned to be created Quality (testability, t completeness and correctness) of requirements to be verified Formalization and modeling activities are performed by different roles according to their competencies The separation of requirements, designs and test cases Enables reuse and combination of requirements in different test cases for different design alternatives Enables a automated re-evaluation of requirements along the system design evolution 69

70 Interactive Simulation with OpenModelica Online manipulation of parameters Simulation Control Examples of Simulation Visualization Plot View Requirements Evaluation View Liquid Source MaxLevel Level h Level h Domain-Specific Visualization View Tank 1 Tank 2 70

71 MetaModelica Language Extension Meta-Level Operations on Models Model Operations Creation, Query, Manipulation, Composition, Management Manipulation of model equations for Optimization purposes Parallelization, Model checking Simulation with different solvers MetaModelica language features Lists, trees, pattern matching, symboli transformations Garbage collection Very Large MetaModelica Application OpenModelica compiler, implemented in lines of MetaModelica, compiles itself efficiently. 71

72 Faster Simulation Compiling Modelica to Multi-Core Automatic Parallelization of Mathematical Models Parallelism over the numeric solver method. Parallelism over time. Parallelism over the model equation system... with fine-grained task scheduling Coarse-Grained Explicit Parallelization Using Components The programmer partitions the application into computational components using strongly-typed communication interfaces. Co-Simulation, Transmission-Line Modeling g( (TLM) Explicit Parallel Programming Providing general, easy-to-use explicit parallel programming constructs within the algorithmic part of the modeling language. OpenCL, CUDA,... 72

73 Example Task Graphs and Parallelized Application Speedup # Proc Clustered Task Graph Thermofluid Pipe Application 73

74 Task Merging vs Approach with Pipelining/Inlining g S 74 Equation tasks S Eq quation ta asks Eq quation t asks Equ ation tas sks Equation tasks Eq quation ta asks Use a graph rewriting system to merge tasks into larger tasks, based on latency and bandwidth. Some tasks are duplicated to avoid communication within a step S S S S S S S S S S S Try to keep communication as close as possible Only communicate in one direction inside a time step. Solver Inlining distribute the solver across all the processors

75 Some Speedup Measurements on NVIDIA Modelica Model, Generated Code, Function of Problem Size 75

76 Bayesian Network Based Fault and Failure Analysis Developing a Fault and Failure analysis tool for the engineers, containing the following features: Modelica/UML/SysML-like intuitive GUI design interface with simulation Functionality Generate Failure Mode and Effect Analysis, FMEA table Generate Fault Tree, FTA table Answer to Queries Probability of hazards Root cause of hazards Infer hazards, given the root cause 76

77 Bayesian Network Based Fault and Failure Analysis Association of Services to the Components Legend 77

78 Bayesian Network Based Fault and Failure Analysis Illustration of the Work-Flow Modelica Model Model Parser Equation Type Equations System Reference Systems struct Interfacing Evaluate Parsed Model and Generate the Causal Network SMILE & GeNIe Interfacing 78 Bayesian Network FMEA FTA

79 Efficient Traceable Model-Based Dynamic Optimization EDOp Research Project Integrated modeling & optimization in OpenModelica Equation oriented tool, generation of efficient parallel code Based on OpenModelica, cooperation with Open-Source Consortium Including model error traceability and localization Efficient solution methods for model-based optimization problems Methods can exploit structure of the problem and their equations Exploit models for parallel computing Utilize equations to analytically compute gradients and hessians, faster search routines Optimized Heavy Industrial Applications Trucks (Scania), Wheel Loaders (Volvo CE) Bearing applications in mechanical systems (e.g. wind power, SKF) Siemens: Gas turbines, Frontway: Process industry 79

80 Extending Modelica with PDEs for 2D, 3D flow problems class PDEModel HeatNeumann h_iso; Dirichlet h_heated(g=50); HeatRobin h_glass(h_heat=30000); HeatTransfer ht; Rectangle2D dom; equation dom.eq=ht; dom.left.bc=h_glass; dom.top.bc=h_iso; dom.right.bc=h_iso; dom.bottom.bc=h_heated; end PDEModel; Insulated boundary: Conducting boundary: u 60 Poorly insulated boundary: T 20 inf 80

81 Part III Future Modelica and Modelica 4 81

82 Motivation for Modelica 4 1) Modelica is getting large and complicated, with many special cases Increasingly harder to extend the language Increasingly harder to implement the language in a correct way 2) Current Modelica 3.2 problems with the synchronous (event-handling) features in embedded systems contexts Improvements needed for a fast and correct Embedded Systems Library Goal is good support for embedded systems development 82

83 Improved Synchronous Features in Modelica More precise synchronous features, clock, subsampling, etc. Can be separated from the continuous-time parts Usage in generating fast code for embedded systems New version will be developed of Embedded Systems Library First version scheduled for release in the Modelica 3.3 Language; g Planned for December

84 Approach to Modelica 4 Simplify and generalize language features Partly Library-based definition Define many Modelica language features by modeling the language features in a Core Library This needs core language extensions symbolic recursive data structures (trees, lists) pattern matching for transformations some higher-order language features. Ongoing design work in Modelica Association Advantages improved correctness language modularity and extensibility 84

85 Language Features and Symbolic Data Structures Needed for Modelica 4 More higher-order functions (function arguments to functions, returning functions, etc.) Subtyping polymorphism Recursive data structures (trees, lists, etc.) Pattern-matching for model transformations Such language features have been designed in the MetaModelica language extension One version implemented in the OpenModelica compiler Bootstrapping Paper in Modelica conference, March 2011 Innovative application, Paper Debugging Symbolic Transformations in Equation Systems, EOOLT, Sept

86 OpenModelica Large Test Case Collective and symbolic operations Large application for symbolic operations, the OpenModelica compiler, > lines Very large (and difficult) test model! First object-oriented equation-based language compiler that compiles itself = bootstrapping Advantages of bootstrapped compiler Faster compilation for the developers Complete Modelica language for easier programming Better error messages and maintainability Makes a more advanced Modelica debugger possible Makes performance analysis possible Supports some Modelica 4 like features 86

87 OMC Performance Compiled Using Itself Flattening small models OMC compiling itself Task MMC OMC Factor Task MMC OMC Factor Translate sources to C 98.8s 49.7s 0.50x drmodelica, 104 flattening 2.136s 2.049s 0.96x tests mofiles, 548 flattening s s 1.05x tests msl 1.5, 60 flattening tests 1.726s 1.578s 0.91x mosfiles, 120 simulation test s s 1.03x Compile C, gcc O s 152.0s 0.65x Executable size 18.7MB 5.43MB 0.29x Compile C, gcc Os 218.9s 102.8s 0.47x Executable size 10.3MB 5.10MB 0.50x Debug version, gcc g O3 1405s 152.5s 0.11x Executable size 125MB 25MB 0.20x 87

88 Part IV Modelica language concepts and textual modeling Typed Declarative Equation-based Textual Language Hybrid Modeling 88

89 Acausal Modeling The order of computations is not decided at modeling time Acausal Causal Visual Component Level Equation Level A resistor equation: R*i = v; Causal possibilities: i := v/r; v := R*i; R := v/i; 89

90 90 Typical Simulation Process

91 Simple model - Hello World! Equation: x = - x Initial condition: x(0) = 1 Continuous-time variable Parameter, constant during simulation Name of model Initial condition model HelloWorld "A simple equation" Real x(start=1); parameter Real a = -1; equation der(x)= a*x; end HelloWorld; Simulation in OpenModelica environment 1 Differential equation simulate(helloworld, stoptime = 2) plot(x)

92 Modelica Variables and Constants Built-in primitive data types Boolean true or false Integer Integer value, e.g. 42 or 3 Real Floating point value, e.g. 2.4e-6 String String, e.g. Hello world Enumeration Enumeration literal e.g. ShirtSize.Medium Parameters are constant during simulation Two types of constants in Modelica constant constant Real PI= ; parameter constant String redcolor = "red"; constant Integer one = 1; parameter Real mass = 22.5; 92

93 A Simple Rocket Model Rocket apollo13 mg thrust thrust mass gravity acceleration mass mass masslossrate abs thrust altitude velocity velocity acceleration new model parameters (changeable before the simulation) floating point type differentiation with regards to time class Rocket "rocket class" parameter String name; Real mass(start= ); Real altitude(start= 59404); Real velocity(start= -2003); Real acceleration; Real thrust; // Thrust force on rocket Real gravity; // Gravity forcefield parameter Real masslossrate= ; equation (thrust-mass*gravity)/mass t = acceleration; der(mass) = -masslossrate * abs(thrust); der(altitude) = velocity; der(velocity) = acceleration; end Rocket; declaration comment start value name + default value mathematical ti equation (acausal) 93

94 Celestial Body Class A class declaration creates a type name in Modelica class CelestialBody constant Real g = 6.672e-11; parameter Real radius; parameter String name; parameter Real mass; end CelestialBody; An instance of the class can be declared by prefixing the type name to a variable name... CelestialBody moon;... The declaration states that moon is a variable containing an object of type CelestialBody 94

95 Moon Landing Rocket apollo13 mg thrust apollo. gravity moon. g moon. mass apollo. altitude moon. radius 2 altitude CelestialBody only access inside the class access by dot notation outside the class class MoonLanding parameter Real force1 = 36350; parameter Real force2 = 1308; protected parameter Real thrustendtime = 210; parameter Real thrustdecreasetime = 43.2; public Rocket apollo(name="apollo13"); CelestialBody moon(name="moon",mass=7.382e22,radius=1.738e6); equation apollo.thrust = if (time < thrustdecreasetime) then force1 else if (time < thrustendtime) then force2 else 0; apollo.gravity=moon.g*moon.mass/(apollo.altitude+moon.radius)^2; end MoonLanding; 95

96 Simulation of Moon Landing simulate(moonlanding, stoptime=230) plot(apollo.altitude, xrange={0,208}) plot(apollo.velocity, xrange={0,208}) It starts at an altitude of (not shown in the diagram) at time zero, gradually reducing it until touchdown at the lunar surface when the altitude is zero The rocket initially has a high negative velocity when approaching the lunar surface. This is reduced to zero at touchdown, giving a smooth landing 96

97 Specialized Class Keywords Classes can also be declared with other keywords, e.g.: model, record, block,, connector,, function,,... Classes declared with such keywords have restrictions or enhancements These apply to the contents of specialized classes After Modelica 3.0 the class keyword means the same as model Example: A model is a class that cannot be used as a connector class Example: A record is a class that only contains data, with no equations Example: A block is a class with fixed input-output causality model CelestialBody constant Real g = 6.672e-11; parameter Real radius; parameter String name; parameter Real mass; end CelestialBody; 97

98 Modelica Functions Modelica Functions can be viewed as a special kind of specialized class A function can be called with arguments, and is instantiated dynamically when called function sum input Real arg1; input Real arg2; output t Real result; algorithm result := arg1+arg2; end sum; 98

99 Function Call Example Function with for-loop Example Modelica function call:... p = polynomialevaluator({1,2,3,4},21) function PolynomialEvaluator input Real A[:]; // array, size defined // at function call time input Real x := 1.0;// default value 1.0 for x output Real sum; protected Real xpower; // local variable xpower algorithm sum := 0; xpower := 1; for i in 1:size(A,1) loop sum := sum + A[i]*xpower; xpower := xpower*x; end for; end PolynomialEvaluator; {1,2,3,4} becomes the value of the coefficient vector A, and 21 becomes the value of the formal parameter x. The function PolynomialEvaluator computes the value of a polynomial given two arguments: a coefficient vector A and a value of x. 99

100 Inheritance parent class to Color restricted kind of class without equations child class or subclass keyword denoting inheritance record ColorData parameter Real red = 0.2; parameter Real blue = 0.6; Real green; end ColorData; class Color extends ColorData; equation red + blue + green = 1; end Color; class ExpandedColor parameter Real red=0.2; parameter Real blue=0.6; Real green; equation red + blue + green = 1; end ExpandedColor; Data and behavior: field declarations, equations, and certain other contents are copied into the subclass 100

101 Multiple Inheritance Multiple Inheritance is fine inheriting both geometry and color class Point class Color Real x; parameter Real red=0.2; Real y,z; parameter Real blue=0.6; end Point; Real green; equation red + blue + green = 1; multiple l inheritance it end Color; class ColoredPoint extends Point; extends Color; end ColoredPoint; class ColoredPointWithoutInheritance Real x; Real y, z; parameter Real red = 0.2; parameter Real blue = 0.6; Real green; equation red + blue + green = 1; end ColoredPointWithoutInheritance; Equivalent to 101

102 Simple Class Definition Simple Class Definition Shorthand h Case of Inheritance Example: class SameColor = Color; Often used for introducing new names of types: inheritance Equivalent to: class SameColor extends Color; end SameColor; type Resistor = Real; connector MyPin = Pin; 102

103 Inheritance Through Modification Modification is a concise way of combining inheritance with declaration of classes or instances A modifier modifies a declaration equation in the inherited class Example: The class Real is inherited, modified with a different start value equation, and instantiated as an altitude variable:... Real altitude(start= 59404);

104 Discrete Events and Hybrid Systems Picture: Courtesy Hilding Elmqvist 104

105 Hybrid Modeling Hybrid modeling = continuous-time + discrete-time modeling Events time Continuous-time i Real x; Discrete-time Voltage v; Current i; A point in time that is instantaneous, i.e., has zero duration An event condition so that the event can take place A set of variables that are associated with the event discrete Real x; Integer i; Boolean b; Some behavior associated with the event, e.g. conditional equations that become active or are deactivated at the event 105

106 Event creation if if-equations, if-statements, and if-expressions if <condition> then <equations> elseif <condition> then <equations> else <equations> end if; model Diode "Ideal diode" extends TwoPin; Real s; Boolean off; equation off = s < 0; if off then v=s else v=0; end if; i = if off then 0 else s; end Diode; False if s<0 If-equation choosing equation for v If-expression 106

107 Event creation when when-equations when <conditions> then <equations> end when; event 1 event 2 event 3 time Time event when time >= 10.0 then... end when; Equations only active at event times State event when sin(x) > 0.5 then... end when; Only dependent on time, can be scheduled in advance Related to a state. Check for zero-crossing 107

108 Generating Repeated Events The call sample(t0,d) returns true and triggers events at times t0+i*d, where i=0,1, true sample(t0,d) Variables need to be discrete false t0 t0+d t0+2d t0+3d t0+4d time model SamplingClock Integer i; discrete Real r; equation when sample(2,0.5) then i = pre(i)+1; r = pre(r)+0.3; end when; end SamplingClock; Creates an event after 2 s, then each 0.5 s pre(...) takes the previous value before the event. 108

109 Reinit - discontinuous changes The value of a continuous-time state variable can be instantaneously changed by a reinit-equation equation within a when-equation equation model BouncingBall "the bouncing ball model" parameter Real g=9.81; //gravitational acc. parameter Real c=0.90; //elasticity constant Real height(start=10),velocity(start=0); equation der(height) = velocity; der(velocity)=-g; when height<0 then reinit(velocity, -c*velocity); end when; end BouncingBall; Reinit assigns continuous-time variable velocity a new value Initial conditions 109

110 Part V Components, Connectors and Connections Modelica Libraries 110

111 Software Component Model Interface Connector Acausal coupling Component Connection Component Causal coupling A component class should be defined independently of the environment, very essential for reusability A component may internally consist of other components, i.e. hierarchical modeling Complex systems usually consist of large numbers of connected components 111

112 Connectors and Connector Classes Connectors are instances of connector classes electrical connector connector class keyword flow indicates that currents of connected pins sum to zero. connector Pin Voltage v; flow Current i; end Pin; Pin pin; v + i pin an instance pin of class Pin mechanical connector connector class connector Flange Position s; flow Force f; end Flange; s flange an instance flange of class Flange Flange flange; f 112

113 The flow prefix Two kinds of variables in connectors: Non-flow variables potential or energy level Flow variables represent some kind of flow Coupling Equality coupling, for non-flow variables Sum-to-zero coupling, forflow variables The value of a flow variable is positive when the current or the flow is into the component positive flow direction: v i + pin 113

114 Physical Connector Classes Based on Energy Flow Domain Type Potential Flow Carrier Electrical Voltage Current Charge Translational Position Force Linear momentum Rotational Angle Torque Magnetic Magnetic potential ti Magnetic flux rate Angular momentum Magnetic flux Modelica Library Electrical. l Analog Mechanical. Translational Mechanical. Rotational Hydraulic Pressure Volume flow Volume HyLibLight Heat Temperature Heat flow Heat HeatFlow1D Chemical Chemical potential Particle flow Particles Under construction Pneumatic Pressure Mass flow Air PneuLibLight 114

115 connect-equationsequations Connections between connectors are realized as equations in Modelica connect(connector1,connector2) The two arguments of a connect-equation equation must be references to connectors, either to be declared directly within the same class or be members of one of the declared variables in that class pin1 + v v + pin2 i i Pin pin1,pin2; //A connect equation //in Modelica: connect(pin1,pin2); Using Kirschoff s Laws Corresponds to pin1.v = pin2.v; pin1.i + pin2.i =0; 115

116 Common Component Structure The base class TwoPin has two connectors p and n for positive and negative pins respectively p.v p.i i + TwoPin - p n i i n.v n.i partial class (cannot be instantiated) positive pin negative pin partial model TwoPin Voltage v connector Pin Current i Voltage v; Pin p; flow Current i; Pin n; end Pin; equation v = p.v - n.v; 0 = p.i + n.i; i = p.i; end TwoPin; // TwoPin is same as OnePort in // Modelica.Electrical.Analog.Interfaces electrical connector class 116

117 Electrical Components model Resistor Ideal electrical resistor extends TwoPin; parameter Real R; equation R*i = v; end Resistor; p.i p.v + v n.i n.v model Inductor Ideal electrical inductor extends TwoPin; parameter Real L Inductance ; equation L*der(i) = v; end Inductor; p.i p.v + v n.i n.v model Capacitor Ideal electrical capacitor extends TwoPin; parameter Real C ; equation i=c*der(v); end Capacitor; p.i p.v + v n.i n.v 117

118 Electrical Components cont model Source extends TwoPin; parameter Real A,w; equation v = A*sin(w*time); end Resistor; p.i p.v + v(t) n.i n.v model Ground Pin p; equation p.v = 0; end Ground; p.v p.i 118

119 Resistor Circuit Very Simple Example i 1 i 2 n R1 p p R2 n v 1 v 2 v 3 i 3 p R3 n model ResistorCircuit Resistor R1(R=100); Resistor R2(R=200); Resistor R3(R=300); equation connect(r1.p, R2.p); connect(r1.p, R3.p); end ResistorCircuit; Corresponds to R1.p.v = R2.p.v; R1.p.v = R3.p.v; R1.p.i + R2.p.i + R3.p.i = 0; 119

120 Modelica Standard Library - Graphical Modeling Modelica Standard Library (called Modelica) is a standardized di d predefined d package developed d by Modelica Association It can be used freely for both commercial and noncommercial purposes under the conditions of The Modelica License. Modelica libraries are available online including documentation ti and source code from 120

121 Modelica Standard Library cont The Modelica Standard Library contains components from various application areas, including the following sublibraries: Blocks Library for basic input/output control blocks Constants Mathematical constants and constants of nature Electrical Library for electrical models Icons Icon definitions Fluid 1-dim Flow in networks of vessels, pipes, fluid machines, valves, etc. Math Mathematical functions Magnetic Magnetic.Fluxtubes for magnetic applications Mechanics Library for mechanical systems Media Media models for liquids and gases SIunits Su Type definitions based on SI units according to ISO Stategraph Hierarchical state machines (analogous to Statecharts) Thermal Components for thermal systems Utilities Utility functions especially for scripting 121

122 Modelica.Blocks Continuous, discrete, and logical input/output blocks to build block diagrams. Library Continuous Examples: 122

123 Modelica.Electrical Electrical components for building analog, digital, and multiphase circuits Library Library Library Library Analog Digital Machines MultiPhase Examples: V2 R2 R4 Gnd9 R1 Transistor1 C2 Gnd3 Gnd6 C4 Transistor2 R3 V1 C1 I1 C5 C3 Gnd4 Gnd1 Gnd2 Gnd7 Gnd8 Gnd5 123

124 Modelica.Mechanics Package containing components for mechanical systems Subpackages: Rotational 1-dimensional rotational mechanical components Translational 1-dimensional translational mechanical components MultiBody 3-dimensional mechanical components 124

125 Modelica.Stategraph Hierarchical state machines (similar to Statecharts) 125

126 Other Free Libraries WasteWater Wastewater treatment plants, 2003 ATPlus Building simulation and control (fuzzy control included), 2005 MotorCycleDymanics Dynamics and control of motorcycles, 2009 NeuralNetwork Neural network mathematical models, 2006 VehicleDynamics Dynamics of vehicle chassis (obsolete), 2003 SPICElib Some capabilities of electric circuit simulator PSPICE, 2003 SystemDynamics y System dynamics modeling a la J. Forrester, 2007 BondLib Bond graph modeling of physical systems, 2007 MultiBondLib Multi bond graph modeling of physical systems, 2007 ModelicaDEVS DEVS discrete event modeling, 2006 ExtendedPetriNets Petri net modeling, 2002 External.Media Library External fluid property computation, 2008 VirtualLabBuilder ild Implementation ti of virtual labs, 2007 SPOT Power systems in transient and steady-state mode,

127 Some Commercial Libraries Powertrain SmartElectricDrives VehicleDynamics AirConditioning HyLib PneuLib CombiPlant HydroPlant 127

128 Connect Components from Multiple Domains Block domain Mechanical domain Electrical domain R2 emf ex ac iner vsen Block domain Mechanical domain model Generator Modelica.Mechanics.Rotational.Accelerate ac; Modelica.Mechanics.Rotational.Inertia iner; Modelica.Electrical.Analog.Basic.EMF emf(k=-1); Modelica.Electrical.Analog.Basic.Inductor ind(l=0.1); Modelica.Electrical.Analog.Basic.Resistor R1,R2; Modelica.Electrical.Analog.Basic.Ground i l l i d G; Modelica.Electrical.Analog.Sensors.VoltageSensor vsens; Modelica.Blocks.Sources.Exponentials ex(risetime={2},risetimeconst={1}); equation connect(ac.flange_b, b iner.flange_a); a); connect(iner.flange_b, b emf.flange_b); flange connect(emf.p, ind.p); connect(ind.n, R1.p); connect(emf.n, G.p); connect(emf.n, R2.n); connect(r1.n, R2.p); connect(r2.p, vsens.n); connect(r2.n, vsens.p); connect(ex.outport, ac.inport); end Generator; G ind R1 Electrical domain

129 Get More Information, Download Software Peter Fritzson Pi Principles i of fobject toi Oriented Modeling and Simulation with Modelica 2.1 Wiley-IEEE Press, 2004, 940 pages OpenModelica Modelica Association 129

130 New Introductory Book September pages Wiley IEEE Press For Introductory Short Courses on Object Oriented Mathematical Modeling 130

131 Announcements, Coming Workshops Call for Presentations OpenModelica Workshop Feb 6, Linköping, Sweden Applications and tool developments in the OpenModelica Open Source Effort. MODPROD Workshop on Model-Based Development Feb 7-8, 2012, Linköping, Sweden 131

132 Summary Multi-Domain Modeling Visual Acausal Component Modeling Typed Declarative Textual Language Thanks for listening! Hybrid Modeling 132