The vibration caused by torque ripple may degrade the performance of drivetrain, thus the reduction of torque ripple are necessary for hybrid electrical vehicle/electrical vehicle application, while an analytical description of torque will be the basis. In this study, two-dimensional Fourier series supplemented by polynomial fitting is introduced to reconstruct the numerical solution of magnetic coenergy (MCE) from finite element analysis. An analytical torque model, which can describe torque ripple precisely at all working points, is derived from the reconstructed MCE. On the basis of the torque model, the expressions of harmonic currents used to reduce torque ripple are obtained. The proposed expression also satisfies the principle of maximum torque per ampere. Then, a feedforward torque controller based on the expression of harmonic currents is introduced. Meanwhile, a feedback torque controller based on a torque observer is developed as a comparison. The results of simulation and experiments show that both two controllers can reduce the torque ripple in steady state, but the feedforward torque controller has obviously better effects when motor speed increases. Furthermore, the feedforward torque controller is also beneficial to decline torque ripple during transient process of torque response.

Aiming at the torque ripple problem of direct torque control that is based on space vector pulse width modulation (SVPWM-DTC) caused by the spatial harmonics and magnetic saturation characteristics of permanent magnet synchronous motor (PMSM), a feedforward controller based on an analytical model of PMSM was designed. An analytical motor model taking the spatial harmonics and magnetic saturation characteristics of PMSM into account by reconstructing the numerical solution of magnetic co-energy (MCE) from finite element analysis (FEA) was proposed. Based on that, the optimal stator flux linkage that minimizes the torque ripple is calculated and then a feedforward controller is designed and added to the SVPWM-DTC framework. Simulations and experiments are carried out and the results show that the proposed feedforward controller can effectively reduce the torque ripple of SVPWM-DTC.

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