Bifurcation and chaos phenomena appearing in induction motor under variation of PI controller parameters

Bifurcation theory deals with the change of qualitative behavior in a parameter space of dynamical systems. This paper provides a numerical approach to better understand the dynamic behavior of an indirect field oriented control (IFOC) of a current-fed induction motor. The focus is on bifurcation analysis of the IFOC motor model parameters, with a particular emphasis on the change that affects the dynamics and stability under small variations of Proportional Integral controller (PI) parameters. In fact, the dynamical properties of this electrical machine exhibit a rich behavior. Indeed equilibrium point and complex oscillatory phenomena such as limit cycle and chaos are observed. Since a perturbation of PI control gains led to the existence of regular behavior and region where chaotic phenomena may occur. Properties of both parametric and phase plane singularities are carried out by using numerical simulations. Furthermore, bifurcation diagrams for the equilibrium points and the 2-parametric bifurcation curves are computed based on continuation methods for solving differential equations. This paper also attempts to discuss various types of the transition to chaos in the induction motor model. The analysis of the obtained bifurcation simulations gives useful guidelines for adjusting both motor model and PI controller parameters.