Modeling and bifurcation research of phase-locked loop speed control of induction motor drive

This paper is concerned with the nonlinear analyses of phase locked loop (PLL) speed control of induction motor drive. The modeling strategy of a PLL with voltage pump phase frequency detector (VPPFD) is put forward, and the nonlinear model of VPPFD is achieved. This model is valid for the whole lock-in process of PLL drive system and is much more efficient than normal linear model which is only available for phase detection. On the basis of the nonlinear model, the nonlinear characteristics of PLL drive system are analyzed comprehensively. Center manifold reduction is performed and the unfolding of the reduced system discovers the presence of Hopf bifurcation. Finally, the periodic solution of bifurcation is also given.