Local bifurcation analysis of brushless DC motor

In practice, chaos is normally detrimental to brushless DC motor (BLDCM) systems. This paper investigates the Hopf, pitchfork, and general bifurcation to identify the parameter regimes associated with chaos generation. Such information helps to avoid chaos in the design of BLDCM. The original model of the BLDCM is employed to retain the physical interpretation. Pitchfork bifurcation is revealed due to the effect of direct-axis voltage. The BLDCM demonstrates Hopf bifurcation, which occurs under special motor parameter conditions for both mechanical and electrical quantities. Center manifold theorem and normal formal theory are used to prove both types of bifurcation. The bifurcation conditions in terms of the number of pole pairs are also highlighted. Different dynamical modes of the BLDCM are also investigated using numerical methods such as bifurcation diagrams and 2D Lyapunov exponent graph associated with direct-axis voltage and viscous damping coefficient.