Dynamics of Brushless DC Motor and its Generalized Bound, Generalized Extremal Ellipsoid and Control Through Hamiltonian Energy

The nonlinear dynamics of Brushless Direct-Current Motor (BLDCM) is investigated. The energy-based approach is used in order to explain the occurrence of different dynamical behaviors (chaos, stability, limit cycle). In particular, the generalized Hamiltonian energy and its derived generalized Hamiltonian power are exploited to explain the complex dynamics of BLDCM, including the energy cycle while keeping physical meaning in sight. By using the two functions, the optimal generalized bound for the chaotic attractor is identified for the first time. The bound includes generic parameter, which means that it is actually a family of bounds. Different bounds are even compared to show the impact of generic parameters. Also, the generalized extremal ellipsoid that explains the chaotic oscillations is also identified for the first time. Some comparison from the generic parameters is made. Finally, chaos is controlled using the same generalized Hamiltonian energy on one state. The control parameter, which is derived analytically and verified experimentally, introduces not only stability but also limit cycle, chaos and even divergence (explosion).