Simulation of high-index DAEs and ODEs with constraints in FMI

Abstract

In the current FMI standard the dynamical behavior of a model can only be defined as a system of Ordinary Differential Equations (ODE). The dynamics of many physical systems, such as the equations of motion of constrained mechanical multibody systems, are expressed by high-index Differential Algebraic Equations (DAE) so they cannot be simulated directly using standard ODE or DAE solvers. These systems can be converted through index-reduction into ODE or index 1 DAE systems. However FMUs based solely on these latter systems suffer from drift in hidden constraints on the states. As a consequence, the simulation may results in physically meaningless solutions. In this paper, we propose an extension of the FMI standard to handle DAE Systems of index 1 or higher and ODE with constraints. This FMI extension requires only few additions to the FMI specification, all of which can be omitted for FMUs that represent ODE systems or FMUs that do not support DAE handling. The extension has been implemented in solidThinking ActivateTM and two examples that illustrate the ease of implementation and the effectiveness of the method will be discussed.