Modelling and analysis of the non-iterative coupling process for co-simulation

Concerning non-iterative co-simulation, stepwise extrapolation of coupling signals is required to solve an overall system of interconnected subsystems. Each extrapolation is some kind of estimation and is directly associated with an estimation error. The introduced disturbance depends significantly on the macro-step size, i.e. the coupling step size, and influences the entire system behaviour. In addition, for synchronization purposes, sampling of the coupling signals can cause aliasing. Instead of analysing the coupling effects in the time domain, as it is commonly practised, we concentrate on a model-based approach to gain more insight into the coupling process. In this work, we consider commonly used polynomial extrapolation techniques and analyse them in the frequency domain. Based on this system-oriented point of view of the coupling process, a relation between the coupling signals and the macro-step size is available. In accordance to the dynamics of the interconnected subsystems, the model-based relation is used to select the most critical parameter, i.e. the macro-step size. Besides a ‘rule of thumb’ for meaningful step-size selection, a co-simulation benchmark example describing a two degree of freedom (2-DOF) mechanical system is used to demonstrate the advantages of modelling and the efficiency of the proposed method.