Numerically robust co-simulation using transmission line modeling and the Functional Mock-up Interface

Abstract

Modeling and simulation are important tools for efficient product development. There is a growing need for collaboration, interdisciplinary simulation, and re-usability of simulation models. This usually requires simulation tools to be coupled together for co-simulation. However, the usefulness of co-simulation is often limited by poor performance and numerical instability. Achieving stability is especially hard for stiff mechanical couplings. A suitable method is to use transmission line modeling (TLM), which separates submodels using physically motivated time delays. The most established standard for tool coupling today is the Functional Mock-up Interface (FMI). Two example models in one dimension and three dimensions are used to demonstrate how the next version of FMI for co-simulation can be used in conjunction with TLM. The stability properties of TLM are also proven by numerical analysis. Results show that numerical stability can be ensured without compromising on performance. With the current FMI standard, this requires tailor-made models and custom solutions for the interpolation of input variables. Without using custom solutions, variables must be exchanged using sampled communication and extrapolation. In this case, stability properties can be improved by reducing communication step size. However, it is shown that stability cannot be achieved even when using unacceptably small communication steps. This motivates the need for the next version of FMI to include an intermediate update mode, where variables can be interchanged in between communication points. It is suggested that the FMI standard should be extended with optional callback functions for providing intermediate output variables and requesting intermediate input variables.

Discrete-event simulation of continuous-time systems: evolution and state of the art of quantized state system methods

“…The initial stage of this conversion (flattening) has already been proposed in the work by Marzorati et al 75 With a similar goal of allowing Modelica tools to use QSS algorithms, another approach that can be adopted is that of using Functional Mockup Interfaces so that the models are co-simulated by both tools. 76…”

“…of this conversion (flattening) has already been proposed in the work by Marzorati et al 75 With a similar goal of allowing Modelica tools to use QSS algorithms, another approach that can be adopted is that of using Functional Mockup Interfaces so that the models are co-simulated by both tools. 76 Another open research line is that of automatic partitioning of models for load balancing in parallel simulation. Following the initial work done in the work by Floros 77 the current work is aimed to exploit the tools based on SBG so the automatic partitioning stage becomes computationally efficient.…”