Analytical Routes to Chaos and Controlling Chaos in Brushless DC Motors

Abstract

This study examines the dynamics in a brushless DC motor (BLDCM) and methods used to control potentially chaotic behavior or behavior similar to chaotic processes in these systems. Bifurcation diagrams revealed complex nonlinear behaviors over a range of parameter values. In the resulting bifurcation diagram, period-doubling bifurcation, period-three bifurcation, and chaotic behavior can clearly be seen. We used Lyapunov exponents and Lyapunov dimensions to show the occurrence of chaos in a BLDCM. We then used the state feedback method to control chaos behaviors in the same BLDCM. Numerical simulations show the feasibility of the suggested means. Analysis of robustness against parametric perturbation in a BLDCM was performed from the perspective of Lyapunov stability theory and by using numerical simulations. We believe that studying the nonlinear dynamics and controlling chaos in BLDCMs will help to advance the development of high-performance electric vehicles.