Extended Poincaré model and non‐linear analysis of permanent‐magnet synchronous motor scalar drive system

Abstract

In this paper, bifurcation diagrams, modified Poincaré map and Lyapunov exponents characteristic are developed for studying non-linear phenomenon in dynamics of permanent-magnet synchronous machine scalar drive systems (PMSMSDS). For this, extended Poincaré model of the system is introduced analytically taking into account voltage saturation effects. Using this proposed discrete map model, chaotic and stable region of the PMSMSDS in voltage frequency plane of the system are determined. Furthermore, bifurcation diagram of the system is derived when reference command speed is considered as a bifurcation parameter. Lyapunov exponents are calculated numerically in order to prove the chaotic response of the system and evaluate the accuracy of simulation and numerical results. Experimental test is implemented to investigate the occurrence of chaotic behaviour in the system. It is shown that the proposed map model of the PMSMSDS is capable to predict the chaotic behaviour of the system at any conditions.