Methods and Tools for Co-Simulation of Dynamic Systems with the Functional Mock-up Interface

Simulation of coupled dynamical systems, where the subsystems are bundled with their own internal solver, is important in industry. This is due to that in many cases, with complex systems, this is the only viable option. In this setting, the dynamics of each system is hidden and information between subsystems is exchanged through sampled inputs and outputs, 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. Methods, within scope of the FMI, are further proposed which offer improved stability properties, compared to the classical case.

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 that the performance of the method is poor. In this thesis, a modification of the predictor in a multistep method is proposed achieving increased performance.

Furthermore, two software packages are presented. The package PyFMI is a high-level package for working with models following the FMI and contains methods for simulation of weakly coupled systems. The package Assimulo connects different solvers under a common interface which, together with PyFMI, provides an environment for 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 the proposed modification to the predictor, as well as being successfully used in a number of different applications outside the authors work.