Nizar Jabli^1,, Hedi Khammari², Mohamed Faouzi Mimouni³, Sultan Aljahdali²

The main purpose of this paper is to give a reasonably comprehensive discussion of what is commonly referred to as the bifurcation analysis applied to an indirect field oriented control of induction machines (IFOC). In the current work, we study the appearance of self-sustained oscillations in AC drives and compute their corresponding stability margins. As the dynamics is explored, a transition mode to chaotic states via codimension one Hopf bifurcations is detected. Based on qualitative approach, investigations of both parametric and phase plane singularities in IFOC induction motor lead to put into evidence equilibrium points and complex oscillatory phenomena such as limit cycles and chaotic behaviors. Furthermore we found out the bifurcation sets and the attraction basins related to such nonlinear phenomena. Bifurcations originated by system and control parameter fluctuations may lead to stability loss. The adequate remedy is to keep the parameters and the state variables inside the well known normal operating domains computed in this paper. It is worth noting that a rational use of the main analysis tools such as bifurcation sets and attraction basins permits to cancel non desired oscillations and limit cycles by choosing the appropriate initializations leading to the desired behavior. The interpretation of these results contributes to widen the understanding of the mechanism of certain types of singularities and the stability domain boundaries either in phase space or in parameter space and to demonstrate the suitability of bifurcation theory to solve stability problems in electric machines.

attractors, multistability, attraction basins, bifurcation, chaos, induction machine