19 September 2001 Accuracy and stability tradeoffs in multirate simulation
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Many dynamic systems can be separated into identifiable fast and slow subsystems. Computational efficiency in simulating such systems can be improved significantly by using a faster integration frame rate (smaller integration time step) in the numerical simulation of the fast subsystems, compared with the frame rate used for the slow subsystems. In real- time simulations the use of multi-rate simulation may be the only way in which acceptable real-time accuracy can be achieved using a given processor. To convert slow data- sequence outputs form the slow-subsystem simulation to the required fast data sequence inputs for the fast subsystems, extrapolation formulas must be used. Overall simulation accuracy can be improved by using high-order extrapolation formulas. On the other hand, the use of high-order extrapolation can result in numerical instability, especially when the fast and slow subsystems are tightly coupled. Thus there is an accuracy-stability tradeoff in the choice of extrapolation formulas for the slow-to-fast data sequence conversion. In this paper the problem is studied by using fast and slow second-order systems connected in a feedback loop. For various levels of coupling between the two subsystems, dynamic accuracy and numerical stability of the overall simulation is studied. To reduce the number of parameters needed to describe the dual-speed system, the bandwidth of the fast subsystem is assumed to be infinite, with an exact simulation achieved by using an infinite integration frame rate. Numerical stability of the multi-rate simulation is studied by examining the stability boundaries in the λh plane, where λ is the eigenvalue of the overall system and h is the time-step used in numerical simulation of the slow subsystem. For various levels of coupling between fast and slow subsystems, it is shown that the λh-plane stability boundaries shrink when higher-order extrapolation is used for slow-to-fast data sequence conversion. On the other hand, overall simulation accuracy improves with the use of the higher order extrapolation formulas.
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Robert M. Howe, Robert M. Howe, } "Accuracy and stability tradeoffs in multirate simulation", Proc. SPIE 4367, Enabling Technology for Simulation Science V, (19 September 2001); doi: 10.1117/12.440011; https://doi.org/10.1117/12.440011

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