Introducing a new sliding manifold applied for control of uncertain nonlinear brushless DC and permanent magnet synchronous motors

In this paper, the problem of controlling chaotic uncertain brushless DC motor (BLDCM) and Permanent Magnet Synchronous Motor (PMSM), exposed to external disturbances, is considered. First, a new nonsingular terminal sliding surface is introduced, and its nite-time convergence to the zero equilibrium is proved. Then, it is assumed that the parameters of BLDCM and PMSM are fully unknown, and appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Besides, the eects of models uncertainties and external disturbances are also taken into account. Afterwards, based on the adaptive laws and robust nite-time control idea, a robust adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in nite time. It is mathematically proved that the introduced nonsingular terminal sliding mode technique has nite-time convergence and stability in both reaching and sliding mode phases. Numerical simulations are presented to verify the eciency of the proposed method and to validate the theoretical results of the paper.