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 dcmotor (bldcm) and permanent magnet synchronous motor (pmsm), exposed to externaldisturbances, 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 thatthe parameters of bldcm and pmsm are fully unknown, and appropriate adaptive lawsare derived to tackle the unknown parameters of the systems. besides, the eects of modelsuncertainties and external disturbances are also taken into account. afterwards, basedon the adaptive laws and robust nite-time control idea, a robust adaptive sliding modecontroller is proposed to ensure the occurrence of the sliding motion in nite time. it ismathematically proved that the introduced nonsingular terminal sliding mode technique hasnite-time convergence and stability in both reaching and sliding mode phases. numericalsimulations are presented to verify the eciency of the proposed method and to validatethe theoretical results of the paper.