Modeling and Analysis of 3D Mechanical Systems with MathModelica and Mathematica

Jan Brugård

MathCore Engineering AB, Sweden

Abstract

Several new model libraries and features have been added to MathModelica during the last year. Perhaps the most notable extension is the Multibody library, which allows for convenient modeling of 3D mechanical systems, as e.g. an inverted pendulum or a model of a robot. The image below is a screenshot of an animation of 3D robot in MathModelica. Other examples of recent additions to MathModelica are the StateGraph and Electrical.Machines libraries, dynamic sensitivity analysis, FFT analysis, import and export to SBML, and a publishing feature, for creation of interactive HTML documentation of your models.

A screenshot of an inverted pendulum model from MathModelica is shown below. The inverted pendulum consists of the pendulum itself (blue), sensors (yellow), mechanics (grey), dc motor (green), and control system (red).

An inverted pendulum is a classic control problem and the process is non linear and unstable with one input signal and several output signals. The aim is to balance a pendulum vertically on a motor driven wagon while steering the wagon to different positions with a position reference signal. The problems resembles the control systems that exist in rockets.

Using this model as an example this presentation will give an overview of the new MathModelica features and show how they can help you to analyze your systems using Mathematica and MathModelica.