Approximated beats exact Interface Jacobians at model-based co-simulation - explanation and impact

This work deals with the effect of approximated and exact Interface Jacobians according the stability of the overall co-simulation, which is coupled via the Model-based Pre-Step Stabilization Method. At the co-simulation of a helicopter and its controller, the exact Interface Jacobian based co-simulation results in an instable behaviour, whereas with approximated ones the results are accurate and stable. This leads to the question why is there this paradoxical behaviour? For a detailed analysis, the dual mass oscillator, a co-simulation benchmark example, is additionally investigated and also a simulation study of more than 2500 runs has been performed. Leading to the conclusion that for industrial use cases the usage of approximated Interface Jacobians is favourable against exact ones due to the so-called mutual influence between the subsystems.