QSS and multi-rate simulation of object-oriented models

Abstract

Object-Oriented (O--O) languages like Modelica allow the description of multi-domain dynamical models. These models represent a Differential Algebraic Equation (DAE) that is usually converted to an Ordinary Differential Equation (ODE) formulation and simulated using numerical integration methods. Most Modelica tools include Single-Rate integration methods based on time discretization. Recently developed ODE numerical integration methods like Quantized State Systems (QSS) and Multi-Rate algorithms have some features (sparsity exploitation, efficient stiffness handling, efficient integration of loosely coupled systems of equations) that makes them suitable for many applications. By their nature, efficient implementation of these methods requires a different perspective on the model than classical methods, thus it is not a trivial task to implement them in Modelica tools. The Functional Mock-up Interface (FMI) is a tool independent standard for model exchange and co-simulation. Models are exchanged as compiled binaries (Functional Mockup Unit - FMU) with an API that allows the evaluation and simulation of the model. The FMU presents the model as a hybrid ODE on which numerical integration methods (such as Euler, Runge-Kutta) are applied for simulation. In this article we propose an extension to the FMU API to allow QSS and Multi-Rate simulation of O--O oriented models by means of FMI Model-Exchange. This extension opens up the possibility of testing and fine tuning QSS and Multi-Rate algorithms on a wide range of system models. Some results obtained with a prototype implementation on two example cases are reported.