From Fold to Fold-Hopf Bifurcation in IFOC Induction Motor: a Computational Algorithm

Abstract Analytical determination of the bifurcation thresholds is of important interest for practical electrical machine design and analysis control. This paper presents mathematical investigation of the qualitative behavior of indirect filed oriented control induction motor based on bifurcation theory. In this context, steady-state responses analysis of the motor model is discussed and an analytical study of generic bifurcations was made. Particular attention is paid to the codimension two bifurcation namely Fold-Hopf bifurcation. The paper introduces some elementary mechanisms of transit from Fold to Fold-Hopf parameter singularity, to derive some analytical rigorous existence conditions and to develop an algorithm for Fold-Hopf bifurcation detection. Some numerical results of equilibrium properties and bifurcation diagrams are then performed to outline our methodology.