Modelling and simulation of complex engineering systems are often relieved by a modular approach in which the global system is decomposed into subsystems. Advantages arise from independent and parallel modelling of subsystems over easy exchange of the resulting modules to the use of different software for each module. However, the modular simulation of the global system by coupling of simulators may result in an unstable integration, if an algebraic loop exists between the subsystems. This numerical phenomenon is analyzed and two methods of simulator coupling which guarantee stability for general systems including algebraic loops are introduced. Numerical results of the modular simulation of a multibody system are presented.

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Simulation of complex engineering systems requires modelling of components from different engineering fields, e.g. mechanics, automatic control and electronics. In general, the global system has to be decomposed into subsystems due to the different engineering disciplines using engineering intuition to treat it efficiently by a team of engineers. Then, the simulation of the global system is realized by a time discrete linker and scheduler which combines the inputs and outputs of the corresponding subsystems and arranges communication between the subsystems to discrete time instants. The input-output description allows a dynamical analysis without knowledge of the internal structure of the subsystem resulting in the well known "black-box" representation of the subsystem which is accessible only by means of its input and output terminals. Since the internal structure of a subsystem is independent of the global system structure, this approach supports in particular interchangeability and reusability of system blocks. Due to the modular description of systems, independent modelling of the internal dynamics of each subsystem is possible. Coupling of the corresponding simulation tools allows system simulation by different programs avoiding the disadvantages of a block simulator. Although standard solvers can be used for each subsystem, numerical problems may arise from the coupling of the solvers. It is shown, that zero-stability for non-iterative simulator coupling is only guaranteed, if algebraic loops do not exist within the system. Otherwise, instability of the modular simulation may occur. A method is proposed to guarantee zero-stability in any case of coupled modular simulation. This iterative simulator coupling method provides a systematic and accurate way to combine simulation tools.

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