High-speed maglev trains, which combine the advantages of high speed, low noise, and low maintenance cost, have become integral to modern transportation systems owing to their electromagnetic suspension guidance and linear motor drive characteristics. However, during high-speed operation, long-wavelength track irregularities induced by deflection under load constitute the primary source of vibration excitation. These excitations exhibit broad frequency bandwidth, vary dynamically with vehicle speed, and contain multiple harmonic components, markedly compromising ride comfort and posing potential safety risks, representing a key technological bottleneck limiting the performance enhancement of high-speed maglev trains. Traditional control methods, such as neural network-optimized PI control and robust control, have partially improved vibration suppression through parameter optimization or frequency-domain design; however, they struggle to adapt to the dynamic frequency variations associated with long-wavelength irregularities, failing to achieve adaptive control for time-varying multi-frequency vibrations, thus falling short of fundamentally resolving the problem. To address this challenge, this paper focuses on the single-electromagnet suspension system of high-speed maglev trains and develops targeted control strategies.

First, based on track beam irregularity characteristics and electromagnetic mechanics principles, while neglecting minor disturbances such as magnetic reluctance and leakage, a physical model of the single-electromagnet suspension system is established, clarifying the mathematical relationships among coil voltage, current, suspension gap, and electromagnetic force. Through Taylor expansion around the static equilibrium point and by ignoring higher-order small terms, the system is linearized. Using Newton’s second law, the open-loop dynamic equation of the suspension system is derived, thereby laying a theoretical foundation for controller design. Second, to address the core issue that the fundamental frequency of long-wavelength irregularities varies dynamically with speed, a second-order generalized integrator frequency-locked loop (SOGI-FLL) is designed: the SOGI extracts specific frequency components, while the FLL detects frequency deviation in real time and adjusts resonance characteristics, enabling precise and real-time identification of the fundamental frequency and providing the basis for adaptive control parameter adjustment. Building on this foundation, a fractional-order repetitive control method based on Lagrange interpolation finite impulse response (FIR) filtering is proposed. To overcome the internal model tracking error that arises when the delay order n in traditional repetitive control is non-integer, n is decomposed into integer and fractional parts. An integer delay is realized via an integer-period delay module, whereas a fractional delay is approximated using a FIR filter designed through Lagrange interpolation, thereby accurately matching the excitation frequency. A second-order Butterworth low-pass filter is introduced to suppress high-frequency resonance, and a phase compensation term z^k corrects phase lag, completing the repetitive control architecture. This architecture is then integrated with displacement-velocity-acceleration state feedback control to form a synergistic strategy. To validate its effectiveness, a Simulink simulation platform was built with parameters including a reference suspension gap of 0.01 mm, a sampling frequency of 1 kHz, and a beam span of 24 m. A half-sine wave track deformation of 0.05 mm was simulated at speeds of 100 km/h and 400 km/h for comparative testing.

The results demonstrate that the proposed method achieves both marked vibration suppression and excellent frequency adaptability. At 100 km/h, the electromagnet vibration amplitude under traditional control reached 4 mm, while the proposed method reduced it to 0.6 mm. Under high-speed conditions of 400 km/h, traditional control exhibited severe vibration, whereas the proposed method enabled rapid, stable convergence of the suspension gap to 10 mm without overshoot and with fast dynamic response, fully adapting to the frequency dynamics demanded at high speeds. By employing the SOGI-FLL to track the fundamental frequency in real time and integrating a fractional-delay compensation mechanism, the method precisely matches the disturbance fundamental frequency and suppresses all harmonic components, overcoming the technical limitations of conventional approaches.

The proposed control method overcomes the limitations of traditional control technologies in suppressing time-varying multi-frequency disturbances. It achieves accurate and efficient suppression of vibrations induced by long-wavelength track irregularities in high-speed maglev trains through the organic integration of dynamic modeling, fundamental frequency adaptive identification, and fractional-order repetitive control architecture. Offering marked vibration suppression, excellent dynamic response, and strong frequency adaptability, the method effectively enhances ride comfort and operational safety of maglev trains at medium-to-high speeds, providing essential theoretical and technical support for the engineering application of these technologies.

The integral commutation error compensation method demonstrates strong performance in suppressing high- frequency noise. However, its effectiveness diminishes at high motor speeds. This paper addresses the limitations of integral compensation accuracy owing to sampling frequency and the presence of commutation misalignment. After analyzing the relationship between commutation error and the DC-link current waveform, a closed-loop control system is constructed using DC-link current characteristics. Consequently, we propose a commutation error correction method based on DC-link current reconstruction.

Given the negligibly small phase inductance of the coreless stator structure, this study analyzes the symmetry characteristics of DC-link current waveforms. In a commutation cycle, the difference in the area on both sides of the symmetry axis of the DC-link current waveform directly correlates with the magnitude of the commutation error and can be used as a characteristic parameter for commutation error. Moreover, the integration link can attenuate high-frequency disturbances, while higher values provide a more accurate error quantification. To divide the DC-link current with the symmetry axis as the boundary, we combine the three-phase commutation signals to produce a logic signal. By delaying this logic signal and performing an XOR operation on the pre- and post-delay logic signals, we construct a window signal. This window signal can be used as a control signal for two analog switches simultaneously. The DC-link current, once passing through the analog switches, is split into two parts. To avoid the accuracy problem of software integration at high speeds, we obtain the area value of these two signals through hardware depth filtering. These values are sampled by the controller and subtracted to obtain the error characterization parameter. This parameter serves as the feedback to establish the commutation error PI controller. The PI controller calculates and generates the error compensation amount, which is subsequently used to correct the commutation error of the commutation signal through the phase shift module.

Our experimental results demonstrate the efficacy of the commutation error correction method based on the reconstructed DC-link current. We found the following: 1) This method, which relies on hardware filtering to obtain the integral, is not limited by the sampling frequency. It delivers high precision and accurate compensation without any overshoot or oscillation during the control process, indicating that the system has good dynamic performance and anti-interference ability. 2) Summing the integral of the reconstructed DC-link current for motor current loop control allows us to directly obtain the DC component of the DC-link current. This eliminates the need for additional filtering and conditioning, thus simplifying the hardware circuit.

Compared to traditional methods, our approach circumvents the influence of high-frequency interference during the sampling process of the DC-link current. Simultaneously, the integral value of the reconstructed DC-link current can be accurately obtained through our proposed hardware circuit. This prevents the error compensation accuracy from being affected by the sampling frequency, addressing the shortcomings of the integral compensation method in high-speed scenarios. The proposed method facilitates high-precision closed-loop correction of the commutation signal phase, thereby improving the operational efficiency of the brushless DC motor.