Stability of multi-rate simulation algorithms

ABSTRACT

Multi-rate simulation, in which a differential-equation model is partitioned into segments that are solved using different integration step lengths, has the potential to speed up simulations significantly. This is an important consideration especially for studies that involve many repeated simulation runs (e.g. multi-parameter, multi-objective optimizations) as well as for real-time simulation of systems with a wide dynamic range.

The multi-rate approach does however raise questions of accuracy and stability arising from the methods of communicating data between segments and the effects of using different integration step lengths.

A stability analysis of multi-rate integration is presented in which a general form of vector difference equation is developed that can be applied to the combination of a given system and an explicit, single-step integration algorithm. This yields stability criteria that provide information about permissible step lengths and system parameters. For the purposes of this analysis a number of simplifying assumptions are made. It is assumed that the system is divided into two regions, that the differential equations are linear and that a zero-order hold is used in communicating data between segments.

REFERENCES

• 1: A. Haraldsdottir and R. M. Howe, "Multiple Frame Rate Integration," Proc. of the AIAA Flight Simulation Technologies Conference, Sept. 7--9, 1988.
• 2: K. C. Lin and R. M. Howe, "Simulation Using Staggered Integration Steps. Part II: Implementation on Dual-speed Systems," Transactions of the Society for Computer Simulation, Vol. 10, No. 4, Dec., 1993, pp. 239--262.
• 3: R. M. Howe, "Some Techniques with Potential Application to Real-time Simulation of Power Electronic Systems" in Proceedings of Huntsville Simulation Conference, Huntsville, AL, October 2006.
• 4: Dale Word , John J. Zenor , Richard Bednar , Roy E. Crosbie , Narain G. Hingorani, Multi-rate real-time simulation techniques, Proceedings of the 2007 summer computer simulation conference, July 16-19, 2007, San Diego, California
• 5: J. J. Zenor , J. G. Pearce , R. Bednar, Testing of multi-rate simulations using the ESL simulation language, Proceedings of the 2007 summer computer simulation conference, July 16-19, 2007, San Diego, California

INDEX TERMS

Keywords:
discrete state equations, multi-rate, numerical integration, stability