Abstract
A Turbo Pascal-based simulator specifically designed for continuous-time models with time delays and hysteretic phenomena is presented and its use illustrated with examples. Delays can be time- and state-dependent.
For models with hysteretic (multi-valued) behavior, use is made of a recently introduced mathematical paradigm: the differential automaton. For models defined by differ ential or delay-differential equations with jumps in the derivatives, the differential automaton formalism can be bypassed by using a switch function to indicate points of low differentiability in the model. The switch function interacts with the simulator to approximate each point of discontinuity where the numerical integrator is to be reini tialized. This interaction, transparent to the user and implemented via side effects of the switch function, replaces the explicit scheduling of state events by the user.
For models with time delays, a global approximation is constructed for each delayed state variable. Each global ap proximation is partitioned into sufficiently smooth seg ments and a smoothness index is associated with the boundary separating any two such segments. Whenever a delay crosses between two adjacent segments, should the value of the smoothness index require it, the time of crossing is approximated iteratively, the numerical integra tor is reinitialized, and a new segment is started in the partition. A new segment is also started whenever a switching takes place.
The simulator graphical output interface is self-config uring at execution time with respect to the video display adapter-display combination in use. Interactive plotting programs with on-line documentation are also provided to retrieve, then plot, problem data from save files generated during a simulation.
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