On the limits of chaotic simulations by classic software - application to the step motor

Abstract

The well known butterfly effect which induces the divergence of two initially infinitely near trajectories in a bounded space hardly damage chaotic dynamic systems simulation quality. The integration step truncation which stands in numbers representation produced when not precisely controlled ghost solutions like split in two cycles first observed under long time simulations. This is not simply a question of precision decrease but rather a qualitative change in the simulated solution nature. This paper shows that a sharp analysis of the numerical integrator manages to justify rewriting the algorithm. The dynamic system under study is a hybrid two-phased step motor. After briefly describing the motor model, this paper compares classic simulation using Matlab and experimental results in order to point out strange and meaningless behaviours appearing during long time simulations. In the third part we will analyse the numerical reasons of this divergence. At last the fourth part explains how to remedy those drawbacks and presents the improved results.