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A closed-form solution for minimizing torque pulsations or ripple in three-phase permanent magnet motors by the appropriate weighting of input current harmonics is presented. First, an analysis of torque ripple is presented by using the complex exponential Fourier series. In addition, a method to design the optimal weighting of current harmonics is developed by using constrained optimization techniques. In contrast to iterative approaches, the proposed design method determines the current harmonic weights in closed form; the procedure is especially easy to perform. Steps in the design procedure are demonstrated by a numerical example. Application of the optimal current should reduce torque-induced motor vibration and noise, as well as improve accuracy in servo applications.>
Hung et al. (Thu,) studied this question.