Multiple Frequency Vibration Estimation in Controlled Electric Synchronous Motor Systems

Synchronous motors are widely used in applications demanding high efficiency, torque density, and precise velocity regulation, such as electrified transportation, industrial automation, and robotics. Their operation, however, is degraded by mechanical and electromagnetic disturbances that induce oscillatory load torque components, worsening velocity tracking and increasing mechanical stress. This paper presents a control-based reconstruction and harmonic characterization framework for multiple-frequency load torque disturbances in permanent magnet synchronous motor systems, addressing the order-based case in which the harmonic frequencies scale with the rotor speed. The proposed approach combines a robust velocity tracking control structure with a disturbance torque reconstruction scheme based on internal signals of the control system, so that the estimated torque acts as a virtual sensor. The reconstructed disturbance is resampled in the angular domain, where each speed order becomes stationary, and is processed by a hybrid Empirical–Variational mode decomposition with a blind order-identification stage; the Hilbert transform then yields the amplitude, frequency, and phase of each component without prior knowledge of the orders present. Unlike approaches based on additional sensors, specific harmonic observers, or detailed disturbance models, the proposed methodology relies solely on information already available within the control structure. The framework is validated on a surface-mounted and salient-pole permanent magnet synchronous motor under speed-dependent multiple-frequency disturbances, including a nonstationary Bézier load profile with amplitude-modulated harmonics, and remains reliable under measurement noise and abrupt load-torque steps. The yielded results evidence the proposed framework represents an efficient approach for condition monitoring, fault diagnosis, and predictive maintenance by accurate velocity tracking, adequate disturbance torque reconstruction, and precise harmonic characterization in synchronous-motor drive systems.