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A model partitioning method based on dynamic decoupling for the efficient simulation of multibody systems

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Abstract

The presence of different time scales in a dynamic model significantly hampers the efficiency of its simulation. In multibody systems the fact is particularly relevant, as the mentioned time scales may be very different, due, for example, to the coexistence of mechanical components controled by electronic drive units, and may also appear in conjunction with significant nonlinearities. This paper proposes a systematic technique, based on the principles of dynamic decoupling, to partition a model based on the time scales that are relevant for the particular simulation studies to be performed and as transparently as possible for the user. In accordance with said purpose, peculiar to the technique is its neat separation into two parts: a structural analysis of the model, which is general with respect to any possible simulation scenario, and a subsequent decoupled integration, which can conversely be (easily) tailored to the study at hand. Also, since the technique does not aim at reducing but rather at partitioning the model, the state space and the physical interpretation of the dynamic variables are inherently preserved. Moreover, the proposed analysis allows us to define some novel indices relative to the separability of the system, thereby extending the idea of “stiffness” in a way that is particularly keen to its use for the improvement of simulation efficiency, be the envisaged integration scheme monolithic, parallel, or even based on cosimulation. Finally, thanks to the way the analysis phase is conceived, the technique is naturally applicable to both linear and nonlinear models. The paper contains a methodological presentation of the proposed technique, which is related to alternatives available in the literature so as to evidence the peculiarities just sketched, and some application examples illustrating the achieved advantages and motivating the major design choice from an operational viewpoint.

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Notes

  1. It is known that any multistep method can be reduced to a single-step method with an increased state space vector. Thus, in this paper we focus only on the case of single-step methods without loss of generality.

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Authors and Affiliations

  1. Department of Automatic Control, Lund University, Lund, Sweden

    Alessandro Vittorio Papadopoulos

  2. Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy

    Alberto Leva

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  1. Alessandro Vittorio Papadopoulos
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  2. Alberto Leva
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Correspondence to Alessandro Vittorio Papadopoulos.

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Papadopoulos, A.V., Leva, A. A model partitioning method based on dynamic decoupling for the efficient simulation of multibody systems. Multibody Syst Dyn 34, 163–190 (2015). https://doi.org/10.1007/s11044-014-9415-x

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