Weak Coupling of Multibody Dynamics and Block Diagram Simulation Tools

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Dynamic simulation of complex mechatronic systems can be carried out in an efficient and modular way making use of weakly coupled co-simulation setups. When using this approach, multirate methods are often needed to improve the efficiency, since the physical components of the system usually have different frequencies and time scales. However, most multirate methods have been designed for strongly coupled setups, and their application in weakly coupled co-simulations is not straightforward due to the limitations enforced by the commercial simulation tools used for mechatronics design. This work describes a weakly coupled multirate method applied to combine a block diagram simulator (Simulink) with a multibody dynamics simulator in a co-simulation setup. A double-mass triple-spring system with known analytical solution is used as test problem in order to investigate the behavior of the method as a function of the frequency ratio (FR) of the coupled subsystems. Several synchronization schemes (fastest-first and slowest-first) and interpolation/extrapolation methods (polynomials of different order and smoothing) have been tested. Results show that the slowest-first methods deliver the best results, combined with a cubic interpolation (for FR < 25) or without interpolation (for 25 < FR < 50). For FR > 50, none of the tested methods can deliver precise results, although smoothing techniques can reduce interpolation errors for certain situations.