Date of Award


Publication Type

Doctoral Thesis

Degree Name



Electrical and Computer Engineering


Control, Harmonic current, Modeling, Permanent magnet machine, Torque ripple


Kar, Narayan




This thesis investigates torque ripple modeling and minimization techniques for permanent magnet (PM) machines to achieve high-performance and reliable machine drive for practical industrial and consumer applications. At first, a comprehensive torque ripple model is proposed, in which the torque ripples resulting from the spatial harmonics of magnet flux, the time harmonics of stator currents and the cogging torque are included. Since the proposed torque ripple model involves machine operation dependent parameters, the effects of parameter variation on PM machine torque ripple modeling are investigated, to improve the accuracy and robustness of the proposed model. The key to torque ripple minimization is to determine an optimal stator current that can generate an extra torque ripple to cancel the torque ripple produced by the PM machine. Based on the proposed torque ripple model, a genetic algorithm (GA) based stator current optimization approach is proposed for torque ripple minimization, in which the GA is applied to optimize the stator currents to achieve the objectives of: 1) minimizing the peak-to-peak torque ripple; 2) minimizing the rms value of the stator current/machine losses induced by stator current; and 3) maximizing the average torque component produced by the injected harmonic currents. Then, an analytical solution to the optimal stator current design is developed from the proposed model, which can significantly reduce the computation time in finding the optimal currents for torque ripple minimization. Thus, this analytical solution is applicable for torque ripple minimization under both transient and steady states of a PM machine. Based on the proposed analytical solution, the influences of machine parameter variations including the magnet flux variations and the inductance variations on torque ripple minimization are investigated, which demonstrates that machine parameter variations have great influence on the performance of torque ripple minimization. Therefore, the feed-forward based torque ripple minimization methods are sensitive to the parameter variation and disturbance. To minimize the torque ripple more effectively, the relation between torque harmonic and speed harmonic is investigated and it is concluded that the magnitude of the speed harmonic is directly proportional to the magnitude of the torque harmonic of the same order. So, the speed harmonic can be used as a measure of torque harmonic for feedback stator current control for torque ripple minimization in PM machines. Therefore, a closed-loop fuzzy logic based current controller using the speed harmonic as the feedback control signal is proposed for PM machine torque ripple minimization. The speed harmonic is obtained from machine speed measurement, so the proposed approach does not require accurate machine parameters and is not influenced by the nonlinearity of the machine and the inverter. During the thesis investigations, the proposed torque ripple modeling and minimization approaches are extensively evaluated on a laboratory PM machine drive system under different speeds, load conditions, and temperatures.