Synchronous vibration, arising from rotor mass unbalance, profoundly affects the levitation performance of bearingless permanent magnet slice motor (BPMSM). While the conventional phase shift notch filter (PSNF) is integrated into the BPMSM levitation control system, a critical trade-off is needed to be solved between the accuracy and responsiveness of the levitation system. Despite the adoption of PSNF, there are still vibration forces caused by displacement stiffness in BPMSM levitation system. To address these issues, firstly, the rotor levitation dynamics model under the unbalance vibration and vibration force model are created. The coupling vibration of levitation and torque systems is analyzed. Then, a full vibration compensation strategy based on the improved PSNF is proposed to suppress the synchronous vibration force in full speed domain. On one hand, taking the current decay rate as the target, an optimal phase shift angle search strategy is proposed to enhance dynamic response while preserving system accuracy. On the other hand, a feedforward compensation method is presented to eradicate residual vibration force. Through this approach, synchronous vibration is effectively suppressed. Finally, employing a 5000rpm/150W experimental BPMSM, the efficacy and superiority of the proposed strategy are validated through extensive simulations and experiments.

Bearingless motors (BMs) offer advantages such as no mechanical wear and long service life, yet their vibrations must be emphasized. This article presents the first systematic analysis of the internal-external coupling vibration in BMs, distinguishing between the rotational double-frequency internal eccentric magnetic vibration force (IVF) and the rotational co-/multiple-frequency external disturbance vibration force (EVF). A comprehensive vibration suppression strategy is proposed, with targeted approaches for each force type. For IVF, an eccentricity correction method based on minimum levitation current is proposed, aiming to ensure stable levitation of the rotor at the stator’s geometric centre, eliminating IVF at its root cause. For EVF, a resonance controller incorporating a spike-global dual-phase compensation unit and an adaptive gain coefficient method is developed to achieve effective EVF suppression across the full speed range. Experimental results on a 5000 rpm/150 W BM prototype validate the effectiveness and superiority of the proposed strategy.

Overmodulation (OVM) techniques improve dc-link voltage utilization, extending the speed-torque envelope in permanent magnet synchronous motor (PMSM) field-weakening (FW) operation. Adaptive OVM techniques are widely studied to mitigate resulting elevated current harmonics in the OVM region. However, deep OVM operation significantly exacerbates harmonic effects on the control loop, complicating harmonic suppression. This article investigates distortion amplification phenomena in the deep OVM region, revealing sharp increases in FW reference voltage ripple and current harmonics with modulation index (MI). To suppress such amplification, we propose an OVM algorithm featuring real-time adaptive control of both the dividing factor kOVM and FW reference voltage. This approach intrinsically reduces peak phase voltage THD in deep OVM by dynamically regulating reference voltage ripple, thereby attenuating current harmonics. Experimental comparisons with conventional and adaptive OVM methods confirm that the proposed algorithm substantially reduces current THD while maintaining fundamental current amplitude and voltage utilization.

Hybrid less rare-earth synchronous reluctance motors (HLR-SRMs) feature complex magnetic circuits that render back-electromotive force (back-EMF) optimization challenging, leading to torque ripple and reduced voltage utilization. This paper introduces an analytical model-based particle swarm optimization (PSO) scheme to minimize back-EMF harmonics by employing flux barrier angles as optimization variables. Analysis demonstrates that suppressing targeted orders of no-load slotless air-gap flux density harmonics is essential for enhancing back EMF performance. A simplified analytical model for the HLR SRM is developed to enable rapid calculation of the air-gap flux density. Leveraging the multi-segment distribution characteristics of the model's air-gap flux density, optimization targets the modulation of flux barrier angles to attenuate specific harmonics By minimizing dependence on finite element analysis (FEA), the proposed model-based PSO achieves efficient multi-step iterations while maintaining accuracy, thereby avoiding trapped in local optima and significantly reduces computational resource consumption. FEA and experimental validation on a prototype motor confirm the efficacy of the proposed algorithm in reducing the total harmonic distortion (THD) of the back-EMF.

A significant challenge in the radial levitation control of bearingless permanent magnet slice motors (BPMSMs) lies in eliminating inherent radial displacement measurement bias within the feedback loop. This bias induces rotor levitation eccentricity, degrading levitation precision and stability. To address this critical issue, this article develops a displacement harmonic-based self-optimizing control strategy for full compensation of inherent static eccentricity and the resulting double-frequency dynamic eccentricity. The strategy uniquely leverages the amplitude of the double-frequency displacement harmonic, whose strong positive correlation with inherent static eccentricity magnitude is rigorously derived, as a cost function. The cost function enables effective quantification of levitation eccentricity and is minimized by a closed-loop iterative algorithm. The strategy, independent of the motor's physical model parameters, offers a practical and efficient approach to compensate for levitation eccentricity, demonstrably improving levitation performance with respect to displacement fluctuation, current loss, and radial vibration.

The fHan tracking differentiator (TD)-based active disturbance rejection control (ADRC) is widely adopted in permanent magnet synchronous motor (PMSM) drives to suppress setpoint jumps. However, this work uncovers a critical drawback: the optimal value of the parameter r in fHan-TD, which is designed to achieve rapid and overshoot-free control, exhibits strong dependence on speed step commands and load variations. Consequently, existing fixed r configurations fail to sustain stability and dynamic performance under varying operating conditions. To address this, this paper proposes a self-regulating fHan-TD algorithm that dynamically tunes r in real-time. Experimental validation on a PMSM drive platform confirms that the proposed algorithm reduces the speed settling time by up to 50% relative to the conventional fixed-r fHan-TD, while maintaining no overshoot across diverse operating scenarios.

The problem of the rotor mass imbalance is unavoidable in the process of mechanical manufacturing, which will lead to the vibration of the magnetic levitation pump (MLP) system with the rotational speed co-frequency. The influence of the rotor mass imbalance is first analyzed in detail in this paper by building a dynamic rotor model. The resonant controller can better filter out the rotational co-frequency signal component in the system to achieve the effect of vibration suppression. However, introducing the resonant controller will lead to the instability of the low-frequency operating conditions of MLP and the corresponding compensation scheme must be implemented. An improved resonant controller is proposed to suppress the vibration caused by the rotor mass imbalance of MLP, and the low-frequency instability is solved by reasonable phase compensation, ensuring stable operation in the full-speed domain. Adequate simulations are given to verify the effectiveness of the proposed vibration suppression scheme.

The bearingless permanent magnet slice motor is capable of achieving five-degree-of-freedom suspension. Due to its passive suspension in the axial direction, the system demonstrates limited robustness and is prone to axial deviation and torsion under external disturbances or sudden load variations. To enhance axial stability and disturbance resistance, this article proposes an enhanced axial suspension force/torque strategy. First, mathematical models for axial deviation and torsion are established. The influences of axial force/torque stiffness and damping coefficients on rotor vibration are analyzed. Based on these analyses, an axial control strategy is introduced, which generates additional axial suspension force/torque through current regulation. Control strategies with different polarity factors are optimized and compared to ensure that the proposed control strategy remains effective across various operating conditions without imposing excessive demands on the controller. Finally, sufficient simulations and experiments validate the effectiveness of the proposed control strategy in suppressing axial deviation and torsion.

A proper sensing scheme for the bearingless motor (BM), which is designed for the detection of rotational angle position and translational radial displacements of the rotor, is a vital component from the BM control system point of view. However, adopting independent angle and radial displacement sensing methods make a challenge to the integration of BM system. To further improve integration level of BM, a composite sensing scheme only using four Hall sensors to simultaneously detect the rotational angle position and translational radial displacements of the rotor for BM under levitating orthogonal coordinate system is proposed in this article, and the proposed composite sensing scheme is easy implementation with digital control by carrying out simple algebraic operation on four Hall signals. Meanwhile, for the problem of eccentricity of the solved levitation center position due to nonideal factors, such as assembly errors and inconsistent device characteristics, a compensation strategy based on the tracking of the minimum levitation current is proposed, and with the target of the minimum antieccentric levitation current, the levitation position of BM is dynamically adjusted in real-time in two dimensions, and the stable levitation at the optimal point (stator geometric center) is finally achieved. Detailed parameter selection principles of the proposed scheme are also given. Simulations and experiments are carried out on a 5000 rpm/150 W BM to verify the effectiveness and superiority of the proposed composite sensing scheme and levitation position eccentricity compensation scheme.

To address compatibility issues between ferrite and rare-Earth (RE) materials in hybrid less RE (HLRE) motors, caused by differences in magnetic properties and cost, this article proposes a simplified and systematic optimization method for permanent magnet (PM) dimensions in HLRE PM-assisted synchronous reluctance motors (PmaSRM). First, the analytical model of the motor is simplified to reduce analysis complexity. Then, PM dimension variation rules for two types of PMs are designed to ensure the motor's output performance within a limited cost. Simultaneously, demagnetization criteria are proposed. By adjusting the thickness of the two types of PMs to meet these criteria, the demagnetization robustness can be enhanced. The final optimized motor achieves significant cost and computational savings while maintaining output torque and demagnetization resistance. Finite element analysis (FEA) and experimental results confirm that the prototype motor meets design expectations.

High-precision position detection is pivotal for ensuring the stable operation of the bearingless permanent magnet synchronous motors (BPMSMs). Addressing the issue of rotor position estimation errors in sensorless control, which caused by the introduction of third-harmonic components in the observed back electromotive force (EMF) due to variations in the mutual inductance matrix model under rotor eccentricity, an enhanced sliding mode observer scheme based on an adaptive notch filter is proposed in this paper, grounded in the mathematical model of bearingless motors that accounts for the mutual inductance between levitation and torque windings. Simulation results demonstrate that the proposed scheme effectively eliminates the third-harmonic components in the observed back EMF, reduces position estimation errors, and significantly enhances the accuracy of sensorless control.

Inherent levitation eccentricity, which results from sensor detection errors, is an inevitable problem in bearingless permanent magnet synchronous motor (BPMSM) systems. It will drastically degrade the levitation performance, and even damage the system due to rotor hitting boundary. In this article, quantitative investigations of the above issue are developed from two dimensions, i.e., mechanism analysis and suppression technology. First, the double-frequency pulsating magnetic force (DFPMF), which characterizes the nonlinear perturbation from eccentricity, is proposed and analyzed by developing the eccentric radial force model. Accordingly, the expression of radial displacement under DFPMF is derived, which accounts for the intrinsic cause of displacement pulsation increase. Second, a DFPMF compensation scheme based on quasi-resonant controllers is proposed. Through the adaptive optimization of resonant gain, great effect of reducing displacement pulsation could be achieved while ensuring absolute stability. Finally, sufficient experiments verify the correctness of mechanism derivation and the effectiveness of proposed suppression scheme.

As the output voltage amplitude and frequency of the non-isolated ultrasonic motor drive circuit increase, the common-mode voltage issue of the ultrasonic motor becomes more prominent, severely affecting the system’s operating accuracy and efficiency. This paper conducts research on the V-shaped ultrasonic motor, analyzing the mechanism of common-mode voltage generation and the electrical model. It summarizes methods to reduce common-mode voltage, providing a theoretical basis for optimizing the structure design and assembly dimensions of ultrasonic motors. Finally, the proposed model is verified through simulations, proving the accuracy of the presented theory.

The magnetic levitation planar motor (MLPM) is a multi-degree-of-freedom planar driver system widely used in ultra-clean environments such as semiconductor manufacturing. However, due to the end effects and nonlinear characteristics of the air-gap magnetic field, the electromagnetic force modeling of MLPM is complex, and there exists coupling between the levitation and horizontal forces in the drive unit. To address these issues, this paper proposes an accurate analytical model of electromagnetic force, which includes harmonics of higher order force and considers the influence of magnetic field end effects. Based on this model, a decoupled control strategy for MLPM electromagnetic forces is designed using a virtual current coordinate system. Experimental results verify the accuracy of the proposed electromagnetic force model and the effectiveness of the decoupling control strategy.

Given the urgent challenges posed by global climate change and the ongoing energy crisis, fuel cell electric vehicles (FCEVs) have emerged as a promising solution. Incorporating sophisticated energy management strategies (EMSs) into FCEVs can significantly enhance the efficiency of the complex powertrain under diverse driving conditions. In this paper, a dual-model predictive control energy management strategy based on long short-term memory (LSTM)-based driving condition recognition is proposed to enhance the economic performance of FCEVs and robustness across diverse driving conditions. Firstly, to improve the generalization capability and adaptability of the LSTM model and to enhance the accuracy of driving condition recognition, wavelet transform (WT) is introduced into both the offline training and online application of LSTM. Secondly, to enhance the real-time performance and control effectiveness of the EMS, model predictive control (MPC) and explicit model predictive control (eMPC) are established based on a unified optimization objective and constraints. Thirdly, a dual MPC switching logic is developed using the information of driving condition prediction, ensuring the coordination of dual MPCs in practical applications and enhancing their adaptability to various conditions. Finally, an evaluation of the simulations demonstrates that the proposed dual-model predictive control energy management strategy based on wavelet transform LSTM driving condition recognition (WTL-DMPC EMS) can improve economic performance. Compared with other baselines, the energy-saving capability is remarkable, showcasing its promising performance.

AbstractThe paper suggests a design and optimisation approach for a consequent‐pole line‐start permanent magnet motor (CPLSPM) with flexible pole arc coefficients and high utilisation of rare‐earth (RE) materials, without the need for a variable frequency drive. The presence of dual‐sided slots and adjustable pole arc coefficient sets CPLSPM apart from other types of motors, making the analysis of its cogging torque more complex. Taking into account the double‐sided slotted and flexible adjustable pole arc coefficient, a cogging torque and airgap flux density model was established, and the influence of the pole arc coefficient on the characteristics of the cogging torque and airgap flux density of CPLSPM was analysed. The authors conduct multidimensional optimisation considering the coupling of multiple parameters to obtain a CPLSPM with minimal RE material usage, low cogging torque and excellent start‐up and steady‐state performance. Finite element simulation data are presented to validate the factors affecting the cogging torque and the feasibility of the proposed less‐magnetic CPLSPM design. Finally, a prototype of a 750 rpm/2.2 kW CPLSPM is built, and performance testing is carried out for comparison, and applied to submersible mixers.

Synchronous vibration, resulting from rotor mass imbalance, significantly impacts the operational performance of bearingless motor (BM). To address this issue, a full compensation strategy of vibration is proposed to suppress the synchronous vibration force. Firstly, the motion model of the rotor under imbalance vibration is derived, and the mechanism of synchronous vibration is revealed. A phase shift notch filter is a common choice to suppress vibration. Furthermore, based on the common strategy where the synchronous current is minimized, a feed-forward compensation is presented to eliminate the residual vibration force caused by displacement stiffness. The synchronous vibration is fully compensated. Finally, based on a 5000rpm/150W experimental BM, sufficient simulation verifies the effectiveness and superiority of the proposed strategy.

The consequent-pole permanent magnet synchronous motor (CPPM) has flexible pole arc coefficients. However, the pole arc coefficient significantly influence the cogging torque. In this article, the relationship between the pole arc coefficient and cogging torque of CPPM was derived by establishing a Fourier series analytical expression for the unit airgap magnetic permeability and the rotor permanent magnet magnetic excitation using the energy method. Firstly, the equivalent magnetic circuit model of CPPM was established using magnetic circuit analysis and Fourier series methods, and the influence of the pole arc coefficient on the cogging torque was analyzed. By using an unequal pole arc coefficient combination and skew slots, the cogging torque could be weakened. Secondly, through finite element simulation analysis, the cogging torque of different pole arc coefficients and unequal pole arc coefficient combinations were compared to verify the effectiveness of the proposed methods for reducing the influence of the pole arc coefficient on the cogging torque.

The error of the radial displacement sensor causes a deviation between the rotor levitation position of the bearingless motor (BM) and the geometric center of the stator. As a theoretical basis, force analysis of the rotor is performed first to analyze the effects caused by the aforementioned deviation. A radial levitation force modeling scheme for BM is proposed in this article, whose derivation is directly on the rotor coordinate system. The proposed modeling scheme has a simpler form of expression and a more straightforward physical concept than the traditional scheme. To completely compensate for the aforementioned deviation, a levitation position eccentricity compensation scheme for BM based on the tracking of the minimum antieccentric levitation current is proposed in this article. The proposed scheme takes the amplitude of the antieccentric levitation current vector as the index, which characterizes the degree of eccentricity of the rotor and dynamically adjusts the rotor levitation position in two dimensions and, finally, makes the rotor stably levitated at the optimal point, where the amplitude of the antieccentric levitation current vector is minimum. The absence of parameter dependence, ease of implementation, and generality makes the proposed scheme attractive. Meanwhile, the design of the displacement regulator can also be simplified. Sufficient simulation and experiments verify the effectiveness of the proposed scheme.

The Hybrid Less Rare-Earth Synchronous Reluctance Motor (HLRE-SRM) has garnered widespread attention due to its economic advantages. This paper addresses the back EMF optimization for HLRE-SRM by constructing a simplified no-load magnetic circuit model to derive the relationship between the barrier angle and the motor's magnetic flux harmonics. Then, the Particle Swarm Optimization (PSO) algorithm, which does not rely on finite element analysis, is used to optimize the barrier position angle, reducing specific harmonic magnetic densities and enhancing the sinusoidality of the back EMF. Simulation results demonstrate that the proposed optimization scheme achieves a total harmonic distortion of less than 4%.