Skip to content IOP Science home Accessibility Help Journals Books Publishing Support Login Physica Scripta Inclusive Publishing Trusted Science, find out more. Purpose-Led Publishing, find out more. Paper A vibration analysis of the permanent magnet synchronous motor under the effect of proportional derivative control H S Bauomy, Y A Amer, A T Elsayed and M M Agwa Published 11 April 2024 • © 2024 IOP Publishing Ltd Physica Scripta, Volume 99, Number 5 Focus on Recent Trends in Nonlinear Dynamics and Pattern Formation Citation H S Bauomy et al 2024 Phys. Scr. 99 055233 DOI 10.1088/1402-4896/ad398b Authors References Open science Article metrics 74 Total downloads Submit Submit to this Journal Permissions Get permission to re-use this article Share this article Article information Abstract In industrial environments, excessive vibration can pose a safety risk since it can weaken the structural integrity of PMSMs and adjacent equipment. Vibration levels can be understood and controlled to help assure safe operation and avoid mishaps or equipment breakdowns. Friction and mechanical resistance are examples of vibration-induced losses that can lower PMSMs' overall efficiency. Through the optimization of motor design and operation, engineers may minimize vibration and increase energy efficiency while lowering operating costs. Since an electric motor's tendency to overheat after a brief period of use is linked to oscillating vibration, this study employs a proportional derivative control (PD control) to demonstrate the potential effectiveness of a permanent magnet synchronous motor (PMSM). The external force is a component of the non-linear dynamical system. The equation of the (PMSM) system is explained with two-degree-of-freedom (2dof) differential coupled equations, consisting of the major body (motor current) and cutting drive system. The present study uses the approximate method of multiple scales perturbation technique (MSPT) to get an approximate solution, showing the response equation before using (PD) and to achieve the highest effect on the control system so as to ensure the highest efficiency at the lowest possible cost. Different numerical tests have been conducted (NPDCVF, NVC, PPF, PD, delay velocity) and showed that (PD) has the best effect and is able to control the vibrations with more accuracy than others. Then, the vibration value of the system has been studied numerically before and after applying the control method of (MSPT). By combining the analysis of the resonance situation via both the phase plane techniques and the frequency response equation within the utilization of Runge–Kutta of the fourth-order, the stability of the numerical solution has been investigated. Then, by employing the MATLAB tool, the impact of various parameters on model performance has been examined numerically. Lastly, a comparison is made with earlier research and other techniques used in prior work using other types of control mechanisms for other systems.