Modeling and simulation of dynamic systems using Wolfram SystemModeler
Rozhdestvesky, V. Ryzhov, T. Fedorova, K. Safronov, N. Tryaskin
The guidelines is devoted to the introduction to the theory of modeling and simulation of dynamic systems using Wolfram SystemModeler (WSM). The manual has a practical orientation and is equipped with analysis of a large number of problems in mechanics and hydraulics. It is intended for students of senior undergraduate courses in technical specialties interested in virtual modeling. It is assumed that students are familiar with the theory of ordinary differential equations, the basics of numerical methods and course of physics.
The main object of research in this manual are continuous, hybrid and component mechanical systems. Comparatively simple examples show that the SystemModeler package provides future engineers and designers with powerful tools for modeling physical systems in both Modelica and an extensive library of ready-made physical and logical components.
The first chapter of the guidelines is theoretical and devoted to the theory of modeling dynamic systems. It is presented in a minimal volume and intended to remind the reader of the basic concepts, approaches, types of problems being solved. For a more detailed study of the theory of modeling dynamic systems, the textbook sends the reader to classical textbooks and monographs. In the first part of the manual, general questions of mathematical modeling of various processes and systems are considered, with special attention paid to the theory of modeling dynamic systems.
In this chapter the following sections are presented: Basic concepts of modeling; Classification of mathematical models; Properties of mathematical / computer models; Computational experiment (computer simulation); Modeling of dynamic systems: The concept of a dynamic system; Classification of models of dynamic systems; Continuous, discrete and hybrid systems; Component approach in modeling of dynamic systems.
The second chapter of the guidelines provides insights into the capabilities of the Wolfram SystemModeler, which consists of the following environments: the Model Center, the Simulation Center, and the Wolfram SystemModeler Link, a specialized package for integrating WSM models into the Wolfram Mathematica package. The reader will learn how to use the Model Center to create your own model with the Modelica Standard Libraries, and how to run and process modeling results in the Simulation Center.
The advantages of the intuitive drag-and-drop interface of Wolfram SystemModeler are described on examples of continuous mechanical systems, which greatly ease the task of creating computer models.
The process of performing a numerical experiment with the ability to change system parameters in real time and create a three-dimensional animation of mechanical components is shown in detail.
Modeling of dynamic systems is a relatively well-researched area, however, this manual demonstrates examples showing that Wolfram SystemModeler has a number of important differences and advantages.
The third chapter of the guidelines is devoted to the Modelica language, which is the basis of the Wolfram SystemModeler component-oriented modeling software. This language is developed by the Modelica Association (Linköping, Sweden) and it is a freely available, object-oriented language for modeling of large, complex and heterogeneous physical systems. Models in Modelica are mathematically described by differential, algebraic and discrete equations.
The ability to create custom components and libraries, as well as the use of Modelica standard libraries, greatly increases efficiency.
The fourth chapter of the guidelines has a practical orientation and contains a large number of examples for modeling the dynamic problems of mechanics and hydraulics in the WSM environment.
Particular attention in the manual is given to the simulation of hybrid, discrete-continuous systems. It is shown that the numerical solvers of SystemModeler define and process discontinuous data in hybrid systems, so the simulation of switches, collisions, transient states occurs correctly.
In addition to the static system modeling, Wolfram SystemModeler supports dynamic simulation of systems with the possibility of step-by-step visualization. Advantages of WSM include the ability to cover several subject areas. SystemModeler provides a completely symbolic representation of all the components of simulation. The symbolic description allows you to create the most flexible models. These possibilities are shown in the section on component modeling. Examples of hydraulic systems with varying temperature conditions are discussed in detail. It is shown that hierarchical component-oriented models better reflect the topology of real systems, easier to understand and develop than traditional block diagrams.