Chaotic dynamic behavior of switched reluctance motor taking into account of magnetic saturation effects

The aim of this paper is to present a mathematical model of 6/2 SRM that takes into account magnetic saturation effects which is unavoidable in a SRM for some values of phase current and rotor position and to study its global dynamics according to the control frequency in open loop. A mathematical model of the SRM characterizing its overall dynamical behavior is presented. Using a semi-analytical approach, flux-linkage and static torque are fast computed to determine the incremental inductance and voltage per unit speed. These parameters are integrated in the dynamical model in order to take into account geometric design and magnetic saturation of the SRM. The obtained precise model and close to the Finite Element Analysis, is thereafter used to study the chaotic behavior of the SRM using standard nonlinear analysis techniques. The bifurcation diagrams, phase portrait, Poincare maps and time series analysis of the 6/2 SRM was given. As a result, the global dynamics of the SRM (periodicity, sub-harmonic and chaotic behavior) is clearly reported. The 6/2 SRM presents a chaotic behavior for an operating frequency beyond 275 Hz. This work can be useful for machine engineers since the dynamic instability can be the cause of vibration and noise in the machine. The results obtained could then be useful and help avoid such noisy operation of the machine for industrial applications.