An Overview of Hybrid Simulation Phenomena and Their Support by Simulation Packages

Continuous system dynamics can be described by possibly large systems of di erential equations These can be either ordinary di erential equations ODEs or contain algebraic constraints as well to form di erential and algebraic equations DAEs Complex systems such as aircraft often operate in di erent modes of continuous operation and when mode changes occur the continuous dynamics change abruptly Even small physical components may operate in di erent modes e g a diode can operate as a short or open circuit requiring abrupt discrete changes in the system of equations Hybrid systems combine the continuous behavior evolution speci ed by di erential equations with discontinuous changes speci ed by discrete event switching logic Numerical simulation of continuous behavior and of discrete behavior is well understood However to facilitate simulation of mixed continuous discrete systems a number of speci c hybrid sim ulation issues must be addressed This paper presents an overview of phenomena reported in previously published literature that emerge in simulation of hybrid systems They can be classi ed as i event handling ii run time equation processing iii discontinuous state changes iv event iteration v chattering and vi comparing Dirac pulses Based on these phenomena numerical simulation requires the imple mentation of speci c hybrid simulation features An evaluation of ex isting simulation packages with respect to these features is presented No assessment of the quality of particular implementations is given The evaluation shows that some of the hybrid simulation features are incor porated in a number of simulation packages whereas a number of other features are only implemented by a few or none The aim of this paper is to categorize issues in hybrid simulation to benchmark the quality of simulation packages and to refer to possible methods of implementation Pieter J Mosterman is supported by a grant from the DFG Schwerpunktprogramm KONDISK