Physical Modelling Physical Modelling with with ModelVision - - PDF document

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Physical Modelling with ModelVision, a DAE Simulator with Features for Hybrid Automata

MVStudium Project

Physical Physical Modelling Modelling with with ModelVision ModelVision, , a DAE Simulator with Features a DAE Simulator with Features for Hybrid Automata for Hybrid Automata

MVStudium MVStudium Project Project

D.

• D. Inikchov

Inikchov, Yu. , Yu. Kolesov Kolesov Yu.

• Yu. Senichenkov

Senichenkov TU St. Petersburg TU St. Petersburg

F.

• F. Breitenecker

Breitenecker G.

• G. Zauner

Zauner TU Vienna TU Vienna

Yuri Kolesov Dmitry Inikchov

MvStudium

http://www.mvstudium.com

Model based design of complex dynamical systems Yuri Senichenkov

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MvStudium

http://www.mvstudium.com

is the tool with graphical, UML-based language for modeling and simulation

• f complex dynamical systems

(Object Oriented Modeling)

Complex dynamical system is

Large scale, Hierarchical, Event-driven (hybrid) mathematical model with dynamically changed number of components

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The Model Vision Family

• MV 2.1 (1994-96)
• MVS 3.0 (1996-2003)
• MVS 4.X – 2004-????

MvStudium

Ole-Johan Dahl, Bjorn Myhrhaug, Kristen Nygaard SIMULA 67 Maler O., Manna Z, Pnueli A. A formal approach to hybrid systems. 1992 Booch G. Jacobson I., Rumbaugh J. The unified modeling language for object-oriented modeling 1977 Glushkov V., Gusev V., Marjanovich T., Sachnjak M. Tools for modeling mixed continuous and discreet systems. 1975

• A. Alan Pritsker.

Introduction to Simulation and SLAM II . 1986 Fillipov A. Differential equations with discontinues right-hand side. 1985

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Classical dynamical systems Hybrid systems Open hybrid automata Plane functional diagrams Hierarchical functional diagrams Simplest user’s interface Mathematical editor Isolated systems 1st level of interface Second level of interface Simple graphical interface Hybrid automation editor Isolated systems Hybrid automation with I/O Hybrid automation with contacts Third level of interface Graphical editor

• f functional diagrams

Open systems Graphical editor

• f hierarchical functional

diagrams Open systems Forth level of interface

MvStudium models

Open hybrid automata Blocks with Inputs/Outputs Blocks with contacts

Mvstudium hybrid blocks

Final (solved) system of algebraic-differential equations

Blocks with contacts Blocks with I/O

Run time Period of compyling

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block with contacts Input/Output block Mathematical language Final (solved) system of algebraic-differential equations (Unit of measurenment) Open hybrid automation with contacts Open hybrid automation with Inputs/Outputs Low level language High level language

MvStudium’s simplest mathematical models

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Classical dynamical system (continuous time)

is a system of differential equations with right hand side , ensuring existence and uniqueness of the solution

) ( , ), ( x x x x f dt dx

n

= ℜ ∈ =

) (x f

) ; ( x t x x =

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( ) ( )

⎪ ⎩ ⎪ ⎨ ⎧ ⋅ − − ⋅ = ⋅ − − ⋅ =

+ +

α α α α cos sin sin cos

2 1 2 1 n n n n n n n n

x y x y x y x x

Discreet dynamical systems (discreet time). Difference equations

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Discrete-continuous systems

• Object of control
• Control

) ), ( (

n

t dt d u x f x =

, ), ( ), ), ( (

1 1

h t t t t

n n n n n n n

+ = = =

+ +

u u u x G u

Plant or Environment Controller or Application +

• Control system

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Hybrid systems

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Bouncing ball MvStudium’s Blocks

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State_1 Activity_1 State_2 Activity_2

) ; , , ( x t x dt dx F

Activity: Open I/O block with hybrid automation

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State_1 Activity_1 State_2 Activity_2

) ; , , ( x t x dt dx F

Activity: Open Contact/Flow block with hybrid automation

Ideal diode (test bench)

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MvStudium’s executives

MvStudium graphical language MvStudium Language (textual form) Executable code Under MVS Mathematical.DLL Mathematical graphics 3-D Animation (OpenGL) 2-D animation Active components for control panels

MvStudium Test bench

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MvStudium graphical language MvStudium Language (textual form) MvStudium.DLL Application

Numerical problems

• Nonlinear Algebraic

Equations

• Ordinary Differential

Equations

• Algebraic-Differential

Equations

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MVS numerical software

• Linpack, Eispack, Sparspak, MA28
• ODEPACK, Dopri5,dopri853,

Radau5,Dassel

MVS Numerical Library is used

• Fortran version
• Java version

in AnyLogic (Russia) Open Source Physics (USA) in MvStudium 4.x

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Examples

Example 1: Pendulum with free point of suspension

Editor of mathematics models

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Example 2: breaking pendulum (bottom-up design)

• scillation (First Class)

Free fall (Second Class)

Final model

Example 3: statistical test:shell flight

A shell flight

Equations

Statistical experiment

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Example 3A: inheritance. Flight without friction and

with friction .

Books

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Textbooks Thanks! Thanks! Thanks!

http:// http://www.mvstudium.com www.mvstudium.com