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Multiphysics performance of surrogate models on skewed pole surface-mounted permanent magnet motors 斜极表面安装永磁电机代用模型的多物理场性能
Pub Date : 2024-05-06 DOI: 10.1108/compel-11-2023-0607
Issah Ibrahim, David Lowther

Purpose

Evaluating the multiphysics performance of an electric motor can be a computationally intensive process, especially where several complex subsystems of the motor are coupled together. For example, evaluating acoustic noise requires the coupling of the electromagnetic, structural and acoustic models of the electric motor. Where skewed poles are considered in the design, the problem becomes a purely three-dimensional (3D) multiphysics problem, which could increase the computational burden astronomically. This study, therefore, aims to introduce surrogate models in the design process to reduce the computational cost associated with solving such 3D-coupled multiphysics problems.

Design/methodology/approach

The procedure involves using the finite element (FE) method to generate a database of several skewed rotor pole surface-mounted permanent magnet synchronous motors and their corresponding electromagnetic, structural and acoustic performances. Then, a surrogate model is fitted to the data to generate mapping functions that could be used in place of the time-consuming FE simulations.

Findings

It was established that the surrogate models showed promising results in predicting the multiphysics performance of skewed pole surface-mounted permanent magnet motors. As such, such models could be used to handle the skewing aspects, which has always been a major design challenge due to the scarcity of simulation tools with stepwise skewing capability.

Originality/value

The main contribution involves the use of surrogate models to replace FE simulations during the design cycle of skewed pole surface-mounted permanent magnet motors without compromising the integrity of the electromagnetic, structural, and acoustic results of the motor.

目的评估电机的多物理场性能是一个计算密集型过程,尤其是在电机的多个复杂子系统耦合在一起的情况下。例如,评估声学噪声需要将电机的电磁、结构和声学模型耦合在一起。如果在设计中考虑到偏斜磁极,问题就变成了纯粹的三维(3D)多物理场问题,这可能会增加天文数字般的计算负担。因此,本研究的目的是在设计过程中引入代用模型,以降低解决此类三维耦合多物理场问题的计算成本。研究结果表明,代用模型在预测斜极表面安装永磁电机的多物理场性能方面显示出良好的效果。因此,此类模型可用于处理倾斜方面的问题,而由于缺乏具有逐步倾斜能力的仿真工具,倾斜方面的问题一直是一个重大的设计挑战。原创性/价值主要贡献涉及在倾斜磁极表面安装永磁电机的设计周期中使用代用模型来替代 FE 仿真,而不会损害电机电磁、结构和声学结果的完整性。
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引用次数: 0
Comparison of a quasi Newton method using Broyden’s update formula and an adjoint method for determining local magnetic material properties of electrical steel sheets 使用布洛伊登更新公式的准牛顿法与确定电工钢片局部磁性材料特性的邻接法的比较
Pub Date : 2024-05-06 DOI: 10.1108/compel-11-2023-0566
Andreas Gschwentner, Manfred Kaltenbacher, Barbara Kaltenbacher, Klaus Roppert

Purpose

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

Design/methodology/approach

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

Findings

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

Originality/value

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.

目的在对电气传动进行精确数值模拟时,精确了解局部磁性材料特性至关重要。由于各种制造步骤(如热处理或切割技术)的影响,磁性材料特性可能会发生强烈的局部变化,因此假设全局材料参数均匀化已不再可行。本文旨在介绍利用参考和模拟数据确定局部磁性材料特性的一般方法和两种不同的解决策略。因此,使用传感器-执行器系统对电工钢片进行局部表征。根据测量数据和有限元模拟结果,采用两种不同的求解策略来解决逆问题。第一种是准牛顿法(QNM),使用布洛伊登更新公式来近似雅各布,第二种是邻接法。为了比较这两种方法的收敛性和效率,我们考虑了一个线性材料模型的人工实例。此外,考虑先验信息提高了收敛速度。原创性/价值所提出的方法能够快速、简单地确定电工钢片的局部磁性材料特性,而无需大量样本或特殊的制备程序。
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引用次数: 0
Short-voltage pulse generation for induction heating load detection on a multi-output inverter with shared power devices 在带共享功率器件的多输出逆变器上生成用于感应加热负载检测的短电压脉冲
Pub Date : 2024-05-06 DOI: 10.1108/compel-09-2023-0423
Pablo Guillén, Hector Sarnago, Oscar Lucia, José M. Burdio

Purpose

The purpose of this paper is to develop a load detection method for domestic induction cooktops. The solution aims to minimize its impact in the converter power transmission while enabling the estimation of the equivalent electrical parameters of the load. This method is suitable for a multi-output resonant inverter topology with shared power devices.

Design/methodology/approach

The considered multi-output converter presents power devices that are shared between several loads. Thus, applying load detection methods in the literature requires a halt in the power transfer to ensuring safe operation. The proposed method uses a complementary short-voltage pulse to excite the induction heating (IH) coil without stopping the power transfer to the remaining IH loads. With the current through the coil and the analytical equations, the equivalent inductance and resistance of the load is estimated. The precision of the method has been evaluated by simulation, and experimental results are provided.

Findings

The measurement of the current through the induction coil as a response to a short-time single-pulse voltage variation provides enough information to estimate the load equivalent parameters, allowing to differentiate between no-load, non-suitable IH load and suitable IH load situations.

Originality/value

The proposed method provides a solution for load detection without requiring additional circuitry. It aims for low power transmission to the load and ensures zero-voltage switching and reduced peak current even in no-load cases. Moreover, the proposed solution is extensible to less complex converters, as the half bridge.

本文旨在为家用电磁炉开发一种负载检测方法。该解决方案旨在最大限度地减少其对变流器功率传输的影响,同时能够估算出负载的等效电气参数。该方法适用于具有共享功率器件的多输出谐振逆变器拓扑结构。因此,应用文献中的负载检测方法需要停止功率传输,以确保安全运行。所提出的方法使用互补短电压脉冲来激励感应加热(IH)线圈,而不停止向其余 IH 负载的功率传输。利用通过线圈的电流和分析方程,可以估算出负载的等效电感和电阻。研究结果测量通过感应线圈的电流作为对短时单脉冲电压变化的响应,为估算负载等效参数提供了足够的信息,从而可以区分空载、非适用 IH 负载和适用 IH 负载情况。它的目标是向负载传输低功率,确保零电压开关,即使在空载情况下也能降低峰值电流。此外,所提出的解决方案还可扩展到不太复杂的转换器,如半桥转换器。
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引用次数: 0
A versatile plasma generation power supply featuring a multilevel converter for arbitrary waveforms generation 多功能等离子体发电电源,采用多电平转换器生成任意波形
Pub Date : 2024-04-30 DOI: 10.1108/compel-07-2023-0285
Ignacio Jesús Álvarez Gariburo, Hector Sarnago, Oscar Lucia

Purpose

Plasma technology has become of great interest in a wide variety of industrial and domestic applications. Moreover, the application of plasma in the domestic field has increased in recent years due to its applications to surface treatment and disinfection. In this context, there is a significant need for versatile power generators able to generate a wide range of output voltage/current ranging from direct current (DC) to tens of kHz in the range of kVs. The purpose of this paper is to develop a highly versatile power converter for plasma generation based on a multilevel topology.

Design/methodology/approach

This paper proposes a versatile multilevel topology able to generate versatile output waveforms. The followed methodology includes simulation of the proposed architecture, design of the power electronics, control and magnetic elements and test laboratory tests after building an eight-level prototype.

Findings

The proposed converter has been designed and tested using an experimental prototype. The designed generator is able to operate at 10 kVpp output voltage and 10 kHz, proving the feasibility of the proposed approach.

Originality/value

The proposed converter enables versatile waveform generation, enabling advanced studies in plasma generation. Unlike previous proposals, the proposed converter features bidirectional operation, allowing to test complex reactive loads. Besides, complex waveforms can be generated, allowing testing complex patterns for optimized cold-plasma generation methods. Besides, unlike transformer- or resonant-network-based approaches, the proposed generator features very low output impedance regardless the operating point, exhibiting improved and reliable performance for different operating conditions.

目的等离子体技术在工业和家用领域的广泛应用引起了人们的极大兴趣。此外,近年来由于等离子体在表面处理和消毒方面的应用,等离子体在家用领域的应用也在不断增加。在这种情况下,亟需能够产生从直流(DC)到千伏范围内数十千赫输出电压/电流的多功能发电机。本文旨在开发一种基于多电平拓扑结构的高通用性等离子体发电电源转换器。所采用的方法包括对拟议架构进行仿真,设计电力电子器件、控制和磁性元件,以及在建立八电平原型后进行实验室测试。所设计的发生器能够在 10 kVpp 输出电压和 10 kHz 频率下工作,证明了所提议方法的可行性。与之前的建议不同,拟议的转换器具有双向操作的特点,可以测试复杂的无功负荷。此外,还可以生成复杂的波形,从而测试优化冷等离子体生成方法的复杂模式。此外,与基于变压器或谐振网络的方法不同,拟议的发生器具有非常低的输出阻抗,不受工作点的影响,在不同的工作条件下都能表现出更好、更可靠的性能。
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引用次数: 0
Multi-objective optimization and uncertainty quantification for inductors based on neural network 基于神经网络的电感器多目标优化和不确定性量化
Pub Date : 2024-04-30 DOI: 10.1108/compel-11-2023-0552
Xiaohan Kong, Shuli Yin, Yunyi Gong, Hajime Igarashi

Purpose

The prolonged training time of the neural network (NN) has sparked considerable debate regarding their application in the field of optimization. The purpose of this paper is to explore the beneficial assistance of NN-based alternative models in inductance design, with a particular focus on multi-objective optimization and uncertainty analysis processes.

Design/methodology/approach

Under Gaussian-distributed manufacturing errors, this study predicts error intervals for Pareto points and select robust solutions with minimal error margins. Furthermore, this study establishes correlations between manufacturing errors and inductance value discrepancies, offering a practical means of determining permissible manufacturing errors tailored to varying accuracy requirements.

Findings

The NN-assisted methods are demonstrated to offer a substantial time advantage in multi-objective optimization compared to conventional approaches, particularly in scenarios where the trained NN is repeatedly used. Also, NN models allow for extensive data-driven uncertainty quantification, which is challenging for traditional methods.

Originality/value

Three objectives including saturation current are considered in the multi-optimization, and the time advantages of the NN are thoroughly discussed by comparing scenarios involving single optimization, multiple optimizations, bi-objective optimization and tri-objective optimization. This study proposes direct error interval prediction on the Pareto front, using extensive data to predict the response of the Pareto front to random errors following a Gaussian distribution. This approach circumvents the compromises inherent in constrained robust optimization for inductance design and allows for a direct assessment of robustness that can be applied to account for manufacturing errors with complex distributions.

目的神经网络(NN)的训练时间较长,这引发了有关其在优化领域应用的大量讨论。本文旨在探索基于 NN 的替代模型在电感设计中的有益帮助,尤其侧重于多目标优化和不确定性分析过程。设计/方法/途径在高斯分布的制造误差条件下,本研究预测了帕雷托点的误差区间,并选择了误差幅度最小的稳健解决方案。此外,本研究还确定了制造误差与电感值差异之间的相关性,为确定适合不同精度要求的允许制造误差提供了实用方法。研究结果与传统方法相比,NN 辅助方法在多目标优化方面具有显著的时间优势,尤其是在反复使用训练有素的 NN 的情况下。原创性/价值在多目标优化中考虑了包括饱和电流在内的三个目标,通过比较单目标优化、多目标优化、双目标优化和三目标优化等方案,深入探讨了 NN 的时间优势。本研究提出了帕累托前沿的直接误差区间预测,利用大量数据预测帕累托前沿对高斯分布随机误差的响应。这种方法规避了电感设计约束稳健优化中固有的折衷方法,并允许对稳健性进行直接评估,该评估可用于考虑具有复杂分布的制造误差。
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引用次数: 0
3D electromagnetic analytical model for radial-flux eddy-current couplers 径向通量涡流耦合器的三维电磁分析模型
Pub Date : 2024-04-25 DOI: 10.1108/compel-11-2023-0558
Mohammed Messadi, Larbi Hadjout, Noureddine Takorabet

Purpose

This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

Design/methodology/approach

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

Findings

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

Practical implications

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

Originality/value

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

目的 本文旨在开发一种新的圆柱坐标三维分析模型,以研究径向磁通涡流耦合器(RFECC),同时考虑磁边缘和三维曲率效应,以及感应电流引起的场反应。空气和磁体区域的磁标量势公式和导电区域的电流密度公式。磁场和涡流表达式是通过在三维圆柱坐标中使用变量分离法求解三维麦克斯韦方程得到的。扭矩表达式是利用麦克斯韦应力张量从磁场求解中导出的。除了三维磁边缘效应外,所提出的模型还考虑了导电部分感应电流引起的反作用力场效应。为了显示所开发的三维分析模型的准确性,我们将其结果与三维有限元模拟的结果进行了比较。三维分析模型与二维模拟结果的对比证明,这些器件具有强烈的磁边缘效应影响(轴向),必须在建模时加以考虑。新的分析模型无需任何校正因子即可考虑磁边缘效应,并在精度和计算时间之间实现了良好的折衷。实用意义与三维有限元仿真相比,所提出的三维分析模型大大缩短了计算时间,使其成为径向磁通涡流装置的有效精确设计和优化工具。原创性/价值开发了一种新的三维圆柱坐标分析模型,用于计算径向磁通涡流耦合器中的电磁扭矩。该模型考虑了磁边缘效应、三维曲率效应和磁场反作用力(不含修正系数),同时改进了计算时间。
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引用次数: 0
Analysis of current distribution and termination conditions in 2D metasurfaces 二维元表面中的电流分布和终止条件分析
Pub Date : 2024-04-22 DOI: 10.1108/compel-10-2023-0548
Sami Barmada, Nunzia Fontana, Leonardo Sandrolini, Mattia Simonazzi

Purpose

The purpose of this paper is to gain a better understanding on how metasurfaces behave, in terms of currents in each unit cell. A better knowledge of their behavior could lead to an ad-hoc design for specific applications.

Design/methodology/approach

The methodology used is both theoretical and numerical; it is based on circuit theory and on an optimization procedure.

Findings

The results show that when the knowledge of the current in each unit cell of a metasurface is needed, the most common approximations currently used are often not accurate. Furthermore, a procedure for the termination of a metasurface, with application-driven goals, is given.

Originality/value

This paper investigates the distribution of the currents in a 2D metamaterial realized with magnetically coupled resonant coils. Different models for the analysis of these structures are illustrated, and the effects of the approximations they introduce on the current values are shown and discussed. Furthermore, proper terminations of the resonators on the boundaries have been investigated by implementing a numerical optimization procedure with the purpose of achieving a uniform distribution of the resonator currents. The results show that the behavior of a metasurface (in terms of currents in each single resonator) depends on different properties; as a consequence, their design is not a trivial task and is dependent on the specific applications they are designed for. A design strategy, with lumped impedance termination, is here proposed.

目的本文旨在更好地了解元表面在每个单元格中的电流表现。研究结果研究结果表明,当需要了解元表面每个单元格中的电流时,目前最常用的近似方法往往并不准确。此外,本文还给出了以应用为导向的超表面终止程序。原创性/价值本文研究了用磁耦合谐振线圈实现的二维超材料中的电流分布。文中阐述了分析这些结构的不同模型,并展示和讨论了这些模型引入的近似值对电流值的影响。此外,通过实施数值优化程序,研究了谐振器在边界上的适当终端,目的是实现谐振器电流的均匀分布。研究结果表明,元表面的行为(就每个单个谐振器中的电流而言)取决于不同的特性;因此,元表面的设计并非易事,而且取决于设计的具体应用。本文提出了一种采用叠加阻抗终端的设计策略。
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引用次数: 0
Modelling permanent magnet excited uniform fields with rational approximations 用有理近似值模拟永磁体励磁均匀场
Pub Date : 2024-04-18 DOI: 10.1108/compel-11-2023-0584
Stefano Costa, Eugenio Costamagna, Paolo Di Barba

Purpose

A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

Design/methodology/approach

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

Findings

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

Research limitations/implications

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

Originality/value

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

目的 研究一种基于有理函数数值近似的新型永磁体建模方法。本研究旨在介绍 AAA 算法和其他最新开发的前沿数学工具,这些工具可对磁势和矢量场进行快速准确的数值计算。然后,通过 AAA 最小二乘法对带有单极对的圆形哈尔巴赫阵列进行分析,重点是孔中的矢量势能和通量密度,并通过经典的有限元软件对结果进行验证。最后,通过有限差分分析完成了研究。结果与有限元模型提供的结果非常吻合,而且与有限差分的结果非常吻合,这表明未来还将有改进。它们还易于编程;MATLAB 代码不到 200 行。研究局限/启示AAA 方法在磁静力学中是一种新方法,但将其扩展到类似物理问题似乎很简单。作为一种无网格方法,不太可能考虑局部非线性问题。一个特别值得关注的方面是处理非均质域的能力,即解决一般界面问题,这也是未来研究的重点。
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引用次数: 0
An FEM framework for modeling forces between NdFeB magnets and HTS bulks 用于模拟钕铁硼磁体与 HTS 磁体之间作用力的有限元框架
Pub Date : 2024-04-16 DOI: 10.1108/compel-10-2023-0526
Guilherme Homrich, Aly Ferreira Flores Filho, Paulo Roberto Eckert, David George Dorrell

Purpose

This paper aims to introduce an alternative for modeling levitation forces between NdFeB magnets and bulks of high-temperature superconductors (HTS). The presented approach should be evaluated through two different formulations and compared with experimental results.

Design/methodology/approach

The T-A and H-ϕ formulations are among the most efficient approaches for modeling superconducting materials. COMSOL Multiphysics was used to apply them to magnetic levitation models and predict the forces involved.The permanent magnet movement is modeled by combining moving meshes and magnetic field identity pairs in both 2D and 3D studies.

Findings

It is shown that it is possible to use the homogenization technique for the T-A formulation in 3D models combined with mixed formulation boundaries and moving meshes to simulate the whole device’s geometry.

Research limitations/implications

The case studies are limited to the formulations’ implementation and a brief assessment regarding degrees of freedom. The intent is to make the simulation straightforward rather than establish a benchmark.

Originality/value

The H-ϕ formulation considers the HTS bulk domain as isotropic, whereas the T-A formulation homogenization approach treats it as anisotropic. The originality of the paper lies in contrasting these different modeling approaches while incorporating the external magnetic field movement by means of the Lagrangian–Eulerian method.

目的 本文旨在介绍一种替代方法,用于模拟钕铁硼磁体与高温超导体(HTS)块体之间的悬浮力。设计/方法/途径 T-A 和 H-ϕ 公式是超导材料建模最有效的方法之一。研究结果表明,可以在三维模型中使用 T-A 公式的均质化技术,结合混合公式边界和移动网格来模拟整个设备的几何形状。原创性/价值H-j 公式将 HTS 体域视为各向同性,而 T-A 公式均质化方法将其视为各向异性。本文的独创性在于对比了这些不同的建模方法,同时通过拉格朗日-欧勒方法纳入了外部磁场运动。
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引用次数: 0
Modeling of novel cross-type hybrid 4-pole carrier system and experimental air gap control 新型交叉式混合 4 极载波系统建模与气隙控制实验
Pub Date : 2024-04-16 DOI: 10.1108/compel-05-2023-0193
Enes Mahmut Göker, Ahmet Fevzi Bozkurt, Kadir Erkan

Purpose

The purpose of this paper is to introduce a novel cross (+) type yoke with hybrid electromagnets and new reluctance modeling to precisely calculate attraction force is given.

Design/methodology/approach

The comparison of attraction force and torque analyses between the proposed formulation and the existing formulation in the literature is comparatively presented. For the correctness of the force and torque values calculated in the model created, the system was created in ANSYS Maxwell and its accuracy was proved by making analyses. The maglev carrier system is inherently unstable from the point of view of control engineering. For that, it needs an active controller to eliminate this instability. For the levitation of the carrier system, it is necessary to design a controller in three axes (z, α and β). I-PD controller was designed for the air gap control of the carrier system in three axes and the controller parameters were determined by the canonical method.

Findings

While the new formulation proposed in the modeling of the carrier system has a maximum error of 1.03%, the existing formula in the literature has an error of 16.83% in the levitation distance point.

Originality/value

A novel cross-type hybrid carrier system has been proposed in the literature. With the double integral used in modeling the system, it takes a long time to solve symbolically, and it is difficult to simulate dynamic behavior in control validation. To solve this problem, attraction force and inclination torque values are easily characterized by new formulation and besides the simulations are conducted easily. The experimental setup was manufactured and assembled, and the carrier system was successfully levitated, and reference tracking was performed without overshoot.

目的本文旨在介绍一种新型交叉(+)式混合电磁铁磁轭,并给出了精确计算吸引力的新磁阻模型。为确保所创建模型中计算的力和扭矩值的正确性,在 ANSYS Maxwell 中创建了该系统,并通过分析证明了其准确性。从控制工程的角度来看,磁悬浮运载系统本身是不稳定的。因此,它需要一个主动控制器来消除这种不稳定性。为了使载体系统悬浮,有必要在三个轴(z、α 和 β)上设计一个控制器。研究结果在载体系统建模中提出的新公式的最大误差为 1.03%,而文献中现有公式在悬浮距离点的误差为 16.83%。原创性/价值文献中提出了一种新型交叉型混合载体系统。由于系统建模采用双积分,符号求解时间长,难以在控制验证中模拟动态行为。为了解决这个问题,采用新的计算公式可以轻松表征吸引力和倾斜力矩值,而且易于进行仿真。实验装置已制造完成并组装完毕,载体系统悬浮成功,并进行了无过冲的参考跟踪。
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引用次数: 0
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