A Solution to ARGESIM Benchmark C 21 ’ State Events and Structural-dynamic Systems ’ based on Modelica Components

The ARGESIM C21 benchmark ’State Events and Structural-dynamic Systems’ adresses difficulties that appear in the modelling and simulation of discrete systems with state and structure-changing events. The solution presented here uses Modelica and a component based approach. It shows that even though Modelica may have conceptual problems modelling such systems, it is capable to deal with all the tasks of the benchmark in a straightforward way. Introduction The ARGESIM C21 benchmark [1] deals with systems showing state events or even structural-dynamic behaviour. It requires to investigate three different examples: a bouncing ball, an RLC circuit with a diode and a rotating pendulum with a free flight phase. The solution shown in the following applies a component based modelling approach using the Modelica language [2] and its standard library MSL. Since the benchmark is quite complex and consists of several subtasks, we concentrate here on the concrete tasks defined in the benchmark itself. The definition of the studied example systems in full detail can be found in [1]. Different approaches all based on Modelica components have been compared in [3], together with a discussion of underlying conceptions and encountered problems. With Modelica one has a choice between several simulation programs. The results presented here have been obtained using MapleSim 2017-3 from Maplesoft under Kubuntu 16.04. Using Dymola from Dassault Systemes leads to identical results in most cases. Some implementation problems that showed up in one or both systems as well as minor numerical deviations are described in [3]. The models and scripts necessary to reproduce all results presented here are available from [4]. 1 Case Study Bouncing Ball The Bouncing Ball example is a model for a falling mass with or without air resistance that is reflected when hitting the ground. The reflection is either described as a simple timeless event or as a continuous process using a spring-damper model for the deformation of the ball. 1.1 Event contact model Description of model implementation. The ‘bouncing ball’ model uses concepts and components of the Mechanics.Translational and Blocks parts of the MSL. One creates a component for each force acting on the falling mass, including a Hardstop component that is responsible for the bounce (cf. Figure 1). Except for the hardstop all components are standard or easily implemented and produce the continuous equations of the system. For the implementation of the hardstop two different versions have been studied: A simple one, based on [5, p. 57], is defined by the following Modelica code: model Hardstop1d parameter Real mu = 0.9; Position s;