Analysis of multistability, hidden chaos and transient chaos in brushless DC motor

The dynamics of brushless DC motor (BLDCM), a type of permanent magnet synchronous motor (PMSM) is investigated. The dynamical model of the BLDCM is compared to a mostly used model of PMSM. The BLDCM transition to chaos is briefly investigated both on the local level through local bifurcations and global level through manifold and invariant sets. All the transition parameter values are given. Apart from transition, multistability of the BLDCM is observed and assessed with stability basin. For some parameter values all dynamic modes (stable fixed point, limit cycle, chaotic attractor) coexist. For other parameter values multistability concerns different stable equilibria. Also, hidden chaos which is of non-Shilnikov type is examined and reported in BLDCM with the method of homotopy. Hidden chaos is defined from the basin of attraction. Transient features of the hidden chaotic set are studied. Finally, transient time of hidden chaos improves with two methods: critical velocity (acceleration) surfaces and Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. (C) 2020 Elsevier Ltd. All rights reserved.