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This paper studies the segregation behavior of binary granular particles with diameters at approximately 10:1 in a vertically vibrated container. An array of transitional separation patterns between reversed Brazilian nut (RBN) and Brazilian nut (BN) separations are observed, with their geometrical features carefully measured. The binary particle system develops into either a stable separation pattern when f and Γ are relatively low or an oscillating pattern when f and Γ are relatively high. We regard these patterns as different phases, in which the stable patterns can be divided into phases of RBN, RBN transitional (RBNT), BNT, and BN. A phase parameter λ between-1 and 1 is defined to describe the separation patterns based on the mass center height difference in large and small particles. By drawing f-Γ-λ phase diagrams, the system's tendency toward BN separation was found to increase with f and decrease with Γ. Furthermore, the range of the tendency toward BN separation expands when the size of small particles rises. As the total mass of the small particles increases, the system's tendency toward RBN separation is enhanced. Abnormal points are also observed in the stable phase regions, and the oscillating phase shifts among the four stable phases with time. These stable phases can be explained via an analysis of the distribution of the dissipation energy, whereas the mechanism of the oscillating phase remains to be discovered.

A novel direct torque control (DTC) method based on sliding-mode-control (SMC) strategy is proposed for permanent magnet synchronous motor (PMSM) which is used in electric vehicles (EVs). In order to improve the dynamic response time and enhance the robustness performance against the external loading disturbances and motor parameter's variation, a kind of SMC-based torque controller and speed controller are designed to regulate the torque angle increment and the speed respectively. The torque controller is designed based on a sliding mode controller with an asymmetric boundary layer to reduce the overshoot. Compared with other DTC methods based on space vector modulation (SVM) in the literature, the proposed DTC scheme adopts the asymmetric boundary layer SMC instead of the proportional-integral (PI) regulator. The simulation results have validated the effectiveness of the proposed SMC-based DTC method.