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The work of this Ph.D. focuses on the investigation of advanced control algorithms for the control of constant and periodic disturbances in Permanent Magnet Synchronous Machines (PMSMs), with the discussion of different methods for improving their negative influence on the machine current and the torque produced at the shaft. The discussion of the disturbances from a control perspective starts with the study of the parameter uncertainties effect on the dynamical performances of the current control and after the detailed analysis in the frequency domain, simple methods for improving the state-of-art decoupling network are given and validated on the testbench. Thanks to the feature of the introduced estimator, the transient behavior of the proposed strategy results in a consistent fast and precise performance. The control scheme allows to avoid the implementation of anti-windup mechanisms in the current control, making the overall controller less sensitive to parameter mismatch. Further, due to the low computational burden, the algorithm is suitable for low cost hardware. Subsequently, the more complex issue of periodic disturbances has been deeply investigated. The theoretical model proposed is validated by comparing the real measured torque with an estimation based on the recovered disturbance affecting the observed voltages and currents. The results are clearly acceptable and further, the experimental validation stresses out the fact that few terms have a predominant role in producing the harmonic disturbances, compared to the others. This consideration lets develop two strategies for suppressing the different harmonic orders present in the machine torque at low-speed operation. One strategy relies on on-line adaptive policies, where the estimated information is passed through a sequence of optimization algorithms with different objectives. In this context, hints on the guaranteed stability are also provided in order to confirm the practical feasibility of the algorithm. The other strategy is based on the off-line generation of some pre-determined functions, limiting the on-line burden to the computation of look-up tables. Both methods brought satisfactory results during the experimental validation, confirming the validity of our approximations made on the original complex model. Although the hardware testbed setup limited the opportunity to validate the methodologies at low speed, this represents a realistic scenario, in fact at higher speed the artificial injection of harmonics within the machine current becomes challenging due to the high electrical rotational speed and it brings more negative effects, in terms of losses and audible noise than benefits on the shaft stress, in fact, the machine inertia acts as a natural filter for the high frequencies harmonics. In summary, it can be said that the research work on advanced control algorithms for the disturbance suppression in PMSM drives has produced affordable and reliable methodologies, which can be of practical implementation for various industrial drives.