Physical Modelling Physical Modelling with with ModelVision ModelVision, , Physical Modelling with ModelVision, a DAE Simulator with Features a DAE Simulator with Features a DAE Simulator with Features for Hybrid Automata for Hybrid Automata for Hybrid Automata MVStudium Project MVStudium Project MVStudium Project D. Inikchov Inikchov, Yu. , Yu. Kolesov Kolesov D. F. Breitenecker Breitenecker F. Yu. Yu. Senichenkov Senichenkov G. Zauner Zauner G. TU Vienna TU St. Petersburg TU St. Petersburg TU Vienna Yuri Kolesov Dmitry Inikchov Yuri Senichenkov MvStudium http://www.mvstudium.com Model based design of complex dynamical systems 1
MvStudium is the tool with graphical, UML-based language for modeling and simulation of complex dynamical systems (Object Oriented Modeling) http://www.mvstudium.com Complex dynamical system is Large scale, Hierarchical, Event-driven (hybrid) mathematical model with dynamically changed number of components 2
The Model Vision Family • MV 2.1 (1994-96) • MVS 3.0 (1996-2003) • MVS 4.X – 2004-???? Glushkov V., Gusev V., Ole-Johan Dahl, Bjorn Marjanovich T., Sachnjak M. Myhrhaug, Kristen Nygaard Tools for modeling mixed SIMULA 67 continuous and discreet systems. 1975 Booch G. Jacobson I., A. Alan Pritsker. Rumbaugh J. Introduction to Simulation and The unified modeling SLAM II . language for object-oriented modeling 1986 1977 MvStudium Maler O., Manna Z, Fillipov A. Pnueli A. Differential equations with A formal approach to discontinues right-hand hybrid systems. side. 1992 1985 3
MvStudium models Classical dynamical systems Simplest user’s interface 1 st level of interface Mathematical editor Isolated systems Hybrid systems Simple graphical interface Second level of Hybrid automation editor interface Isolated systems Open hybrid automata Hybrid automation Hybrid automation with with I/O contacts Plane functional diagrams Graphical editor Third level of of functional diagrams interface Open systems Hierarchical functional diagrams Graphical editor of hierarchical functional Forth level of diagrams interface Open systems Mvstudium hybrid blocks Open hybrid automata Blocks with Blocks with Inputs/Outputs contacts Blocks with contacts Run time Final (solved) system of algebraic-differential equations Period of compyling Blocks with I/O 4
Low level language block with Input/Output contacts block Mathematical language Final (solved) system of algebraic-differential equations (Unit of measurenment) Open hybrid Open hybrid automation with automation with Inputs/Outputs contacts High level language MvStudium’s simplest mathematical models 5
Classical dynamical system (continuous time) is a system of differential equations dx n 0 = ∈ ℜ = f ( x ), x , x ( 0 ) x dt with right hand side , ensuring f ( x ) existence and uniqueness of the solution 0 x = x ( t ; x ) 6
Discreet dynamical systems (discreet time). Difference equations ( ) ⎧ 2 ⎪ = ⋅ α − − ⋅ α x x cos y x sin + n 1 n n n ⎨ ( ) ⎪ 2 ⎩ = ⋅ α − − ⋅ α y x sin y x cos + n 1 n n n 7
Discrete-continuous systems Plant or + • Object of control Environment - x = d f ( x ( t ), u ) n Controller or dt Application • Control = u G ( x ( t ), u ), + n 1 n n = = + u u ( t ), t t h , + n n n 1 n Control system 8
Hybrid systems 9
Bouncing ball MvStudium’s Blocks 10
Open I/O block with hybrid automation State_1 State_2 Activity_1 Activity_2 dx Activity: F ( , x , t ; x ) 0 dt 11
Open Contact/Flow block with hybrid automation State_1 State_2 Activity_1 Activity_2 dx Activity: F ( , x , t ; x ) 0 dt Ideal diode (test bench) 12
MvStudium’s executives MvStudium graphical language MvStudium Language (textual form) MvStudium Test bench Executable code Mathematical Mathematical.DLL Under MVS graphics 3-D Animation 2-D animation (OpenGL) Active components for control panels 13
MvStudium graphical language MvStudium Language (textual form) MvStudium.DLL Application Numerical problems • Nonlinear Algebraic Equations • Ordinary Differential Equations • Algebraic-Differential Equations 14
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MVS numerical software • Linpack, Eispack, Sparspak, MA28 • ODEPACK, Dopri5,dopri853, Radau5,Dassel MVS Numerical Library is used • Java version • Fortran version in in AnyLogic (Russia) MvStudium 4.x Open Source Physics (USA) 16
Examples Example 1: Pendulum with free point of suspension Editor of mathematics models 17
Example 2: breaking pendulum (bottom-up design) oscillation (First Class) Free fall (Second Class) Final model Example 3: statistical test:shell flight Equations A shell flight Statistical experiment 18
Example 3A: inheritance . Flight without friction and with friction . Books 19
Textbooks Thanks! Thanks! Thanks! http://www.mvstudium.com www.mvstudium.com http:// 20
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