Co-Simulation of Dynamic Systems with the Functional Mock-up Interface

Welcome to PhD defense on May 4, in Lund

Modelon is pleased to announce a new PhD Thesis coming out as result of a collaboration with Lund University (Centre for Mathematical Sciences and Department of Automatic Control).

The title of this thesis is Methods and Tools for Co-Simulation of Dynamic Systems with the Functional Mock-up Interface. Author and Modelon engineer Christian Andersson will defend his work on the 4th of May, 10:15 at MH:A at the Centre for Mathematical Sciences, Lund, Sweden.

Simulation of coupled dynamical systems, where each subsystem is bundled with an internal solver, is an important industrial method to support model-based design workflows. This is due to that in many cases, with complex systems, this is the only viable option in heterogeneous simulation landscapes where different parts of a system are modeled in different simulation tools.

In this setting, the dynamics of each system is hidden and information between subsystems is exchanged through sampled inputs and outputs. This is often denoted as a weakly coupled system. While a new industrial standard for exchanging models, the Functional Mock-up Interface (FMI), gains increasing acceptance, the numerical consequences of treating complex systems in this way are not completely understood.

In this thesis, stability questions of weakly coupled linear systems with feed-through are studied. New methods, within the scope of the FMI, are proposed which offer improved stability properties compared to the classical approaches.

A simulation of a weakly coupled system introduces discontinuities due to input changes for the internal solvers. If the internal solver is a multistep method, these discontinuities will result in performance degradation. To avoid the degradation, a modification of the predictor in a multistep method is proposed achieving increased performance.

Furthermore, two Python packages are presented. The package PyFMI is a high-level package for working with models compliant with the FMI standard. PyFMI also contains co-simulation masters for simulation of weakly coupled systems. The package Assimulo unifies different integrators under a common interface which, together with PyFMI, provides an environment for using and evaluating solvers on industrial models. The packages are demonstrated by various examples ranging from simple test cases to a more extensive industrial application. Additionally, they have been used to verify the proposed methods and predictor modification.

Fig. 1 Visualization of a race car modeled in Modelica using the commercial Vehicle Dynamics Library. The car is driven by a virtual driver that tries to stay onto an eight shaped course with increasing velocity in order to investigate the dynamic response of the car, especially when changing the turning direction. Initialization of the race car is done in a co-simulation setting. There are five coupled models, the chassis and the four wheels, with 172 connections between them. 

Fig. 2 Visualization of the couplings in the race car in a co-simulation setup where the wheel and chassis have been divided into separate models. Shown in the figure is the direct feed-through in the wheels between the hubFrame and spinVelocity with t[I-4] and f[I-4]. 

To learn more attend the defense on May 4th in Lund.

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