The Permanent Magnet Synchronous Motors (PMSM) have wide application in the robotics field due to its efficiency and reliability. As a servo system, it demands high precision in different control applications. Torque ripple is a critical issue resulting in mechanical vibrations and shortening the life of PMSMs, especially at low speeds. Because the magnitude of speed harmonics is proportional to the magnitude of the torque harmonics of the same order, methods to reduce speed harmonics can be utilized for torque ripple minimization. This thesis work proposes three methods for torque ripple reduction. One method is based on harmonic speed control (HSC) and harmonic current control (HCC). Another method uses the fuzzy to adjust PI parameters based on HSC-HCC. The third method utilizes torque ripple estimation (TRE) and HCC. In the proposed methods, torque ripples are estimated using a torque ripple model (TRM). At low speeds, speed harmonics and current harmonics are obtained based on an adaptive linear neural-based filter. The errors between the optimal harmonic current reference from HSC or TRE and the harmonic current from extraction are used to generate harmonic voltage in HCC. This harmonic voltage is fed back to compensate and reduce torque ripple. Furthermore, a feedforward compensation method is proposed to minimize torque ripple across a range of speeds based on the feedback compensation results. Finally, simulations and experiments are carried out to demonstrate the validity and performance of the proposed torque ripple reduction methods.