旋转磁场电动式磁悬浮系统的建模与控制
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摘要
磁悬浮技术由于其运作无机械接触的优势,具有噪音小、易维护、可靠性高的优点,在交通运输、特种电机、机器人、金属加工等很多场合得到了应用。
本文提出了一种新型的磁悬浮方案——旋转磁场电动式磁悬浮系统,采用电动式磁悬浮原理,通过在盘式感应电机初级绕组中通入交变电流,在悬浮气隙中产生圆周运动的磁场,与其在轨道导体板中感应出的涡流相互作用产生悬浮力和水平力。这一磁悬浮方案结构稳定、控制简单,能够实现固有稳定的静止磁悬浮和运行导向,有较为广阔的应用范围。为能够准确分析这一全新的磁悬浮系统的性能、设计方法,设计合理的悬浮控制策略,本文提出了一整套分析方法。
首先,利用电磁场理论分析系统内部的电磁关系,为系统建模和确定控制方法提供依据。针对旋转磁场电动式磁悬浮系统的环形铁心结构,为简化计算,提高计算精度,建立了系统的分环模型,对每环按照该环参数平均值求解,并沿铁心周向展开为矩形结构,便于使用二维电磁场分析。
基于截面上的二维电磁场解析法分析了系统中横向端部效应对电磁场分布和系统磁场储能的影响,得到了等效气隙长度表达式和系统特性的动态横向端部效应修正系数。
建立了系统的多层行波磁场模型,应用Maxwell电磁场方程进行了系统的电磁场分布求解,利用表面阻抗分析得到了较为简洁的电磁场分布表达式,采用有限元方法进行了时步有限元计算验证电磁场分布结果,并根据坡印亭定理得到储能的解析表达式,作为分析系统运行性能和控制参数的依据。
其次,研究了系统的主要特性及其与系统参数的关系。根据磁场分布和储能,利用麦克斯韦张量定理和虚位移法,求得了系统的悬浮力、转矩、侧向推力、复原力和次级损耗等特性,以及这些特性与系统电流激励以及结构参数之间的关系。搭建特性试验台,分别对样机采用力特性测定试验和温升试验验证了力和损耗特性的结果。
根据现有的研究成果,研究了在系统次级采用不同的结构、材料和尺寸时的系统特性,为旋转磁场电动式系统的设计提供了理论依据。
根据悬浮力和次级损耗之间存在的固定关系以及系统的总能耗情况,提出了系统的一项评价标准,利用这一评价标准分析了不同工作状况下系统能够输出的最大悬浮力。
从电磁场波动性质的角度解释了初级磁场的运动速度与电动式磁悬浮系统的悬浮力之问的关系,通过水平方向的波矢量和角速度的等效将这一结论推广到大多数电动式磁悬浮系统,解释了系统初级极距对系统产生磁悬浮的能力的影响。
利用磁场分析求得的系统磁场储能表达式解得系统的等效电路,以气隙长度作为变量,利用等效电路参数通过坐标变换得到了两相同步旋转坐标系下的系统变气隙状态方程,用于系统的悬浮力解耦控制,对样机采用空载试验和短路试验验证了等效电路参数。
利用系统的状态方程,采用次级磁场定向策略,将悬浮力和次级磁链解耦,将悬浮高度作为主要控制对象,加入损耗最小为优化目标,设计了基于次级磁场定向控制,悬浮高度和次级磁链双闭环的矢量悬浮控制策略,实现系统的稳定悬浮控制。采用Matlab/Simulink仿真软件验证了悬浮控制策略。
最后,设计制作旋转磁场电动式磁悬浮控制系统,基于DSP设计了控制系统硬件,并在悬浮试验台上对样机进行了悬浮运行试验,证明了本文提出的数学模型的正确性和控制方法的有效性。
Magnetic levitation could operate contactlessly, has the advantages of low noise, low maintenance and high reliability, it could be used in transportation, special motors, robot and metal working.
A new configuration of maglev system--rotating field electrodynamic levitation system(RFELS) is proposed in this dissertation, the system uses electrodynamic levitation principle, rotating magnetic field (RMF) in its air-gap is generated by3-phase AC current in the primary windings, the interaction between RMF and secondary eddy current inducted by RMF produces lift force and horizontal force. This system's structural is stable, its control is simple, it can realize intrisic stable static levitation and guidance, has a widely application prospect. A series of analyzing tools was proposed to analyze the system's characteristics, structure design and levitation control system design method correctly.
Firstly, providing evidences to system modeling and control, analyzed the electromagnetic relationship in RFELS using electromagnetic theory. RFELS's primary core is ring-shaped, sub-loop model was set to simplify the calculation and improve the calculation accuracy, analyzed each loop using average values of the loop.Unfold the ring-shaped sub-loop model into a rectangle sub-loop model to employ2-dimension electromagnetic analysis.
Analyzed transverse end effect's influence to magnetic field distribution and energy storage based on2-dimension electromagnetic analysis, derived equivalent air-gap length expression and modified coefficients of main characteristics.
Established RFELS's multi-layer model, solved electromagnetic distribution by Maxwell equations, simplified the expressions using surface impedance method, verified the results by time-stepping finite element calculation using Ansoft Maxwell.12, derived electromagnetic field energy storage expression by Poynting theorem. The results could be used in characteristic analysis and control parameters calculation.
Secondly, the relationships between system parameters and key characteristics are investigated. According to the field distribution and energy storage, solved the lift force, torque, side force, recovery force and secondary force characteristics, relationships of the characteristics to current excitation and structure parameters. Set up test platform, performed force characteristics test an temperature rise test to testify the former characteristics. According to existing research results, investigated RFELS's main characteristics under various secondary structure, material, thickness, provided evidences to RFELS design.
Proposed evaluation criterion for the system based on the fixed relationship between lift force and secondary loss, analyzed maximam lift force outputs under various working condition using the evaluation criterion.
Analyzed the relationship between primary electromagnetic field travelling speed and lift force by electromagnetic field wave properties, generalize this conclusion to most electrodynamic levitation system by horizontal wave vector and palstance equivalent, explained how primary polar distance influent system'capacity of generating lift force.
Thirdly, the control method of the system is investigated. Calculated RFELS equivalent circuit according to field energy storage, testified the equivalent circuit parameters by no-load test and short-circuit test. Regarded air-gap length as the key variable, derived air-gap state equations under2-phases synchronous rotating coordination system through synchronous rotating reference frame by the equivalent circuit parameters, and used in lift force decoupling control.
According to the state equations, decoupled lift force and flux linkage based on secondary field orientation, took levitation height as key controlled object, added loss minimum optimization objective, designed secondary field orientation levitation height and flux linkage double closed-loop levitation vector control strategy, realized stable levitation control. Testified control strategy using Matlab/Simulink simulation software.
Lastly, designed control system hardware based on DSP, performed operation test on levitation operation test platform, RFELS and its control system realized stable static levitation in the experiments.
本文提出了一种新型的磁悬浮方案——旋转磁场电动式磁悬浮系统,采用电动式磁悬浮原理,通过在盘式感应电机初级绕组中通入交变电流,在悬浮气隙中产生圆周运动的磁场,与其在轨道导体板中感应出的涡流相互作用产生悬浮力和水平力。这一磁悬浮方案结构稳定、控制简单,能够实现固有稳定的静止磁悬浮和运行导向,有较为广阔的应用范围。为能够准确分析这一全新的磁悬浮系统的性能、设计方法,设计合理的悬浮控制策略,本文提出了一整套分析方法。
首先,利用电磁场理论分析系统内部的电磁关系,为系统建模和确定控制方法提供依据。针对旋转磁场电动式磁悬浮系统的环形铁心结构,为简化计算,提高计算精度,建立了系统的分环模型,对每环按照该环参数平均值求解,并沿铁心周向展开为矩形结构,便于使用二维电磁场分析。
基于截面上的二维电磁场解析法分析了系统中横向端部效应对电磁场分布和系统磁场储能的影响,得到了等效气隙长度表达式和系统特性的动态横向端部效应修正系数。
建立了系统的多层行波磁场模型,应用Maxwell电磁场方程进行了系统的电磁场分布求解,利用表面阻抗分析得到了较为简洁的电磁场分布表达式,采用有限元方法进行了时步有限元计算验证电磁场分布结果,并根据坡印亭定理得到储能的解析表达式,作为分析系统运行性能和控制参数的依据。
其次,研究了系统的主要特性及其与系统参数的关系。根据磁场分布和储能,利用麦克斯韦张量定理和虚位移法,求得了系统的悬浮力、转矩、侧向推力、复原力和次级损耗等特性,以及这些特性与系统电流激励以及结构参数之间的关系。搭建特性试验台,分别对样机采用力特性测定试验和温升试验验证了力和损耗特性的结果。
根据现有的研究成果,研究了在系统次级采用不同的结构、材料和尺寸时的系统特性,为旋转磁场电动式系统的设计提供了理论依据。
根据悬浮力和次级损耗之间存在的固定关系以及系统的总能耗情况,提出了系统的一项评价标准,利用这一评价标准分析了不同工作状况下系统能够输出的最大悬浮力。
从电磁场波动性质的角度解释了初级磁场的运动速度与电动式磁悬浮系统的悬浮力之问的关系,通过水平方向的波矢量和角速度的等效将这一结论推广到大多数电动式磁悬浮系统,解释了系统初级极距对系统产生磁悬浮的能力的影响。
利用磁场分析求得的系统磁场储能表达式解得系统的等效电路,以气隙长度作为变量,利用等效电路参数通过坐标变换得到了两相同步旋转坐标系下的系统变气隙状态方程,用于系统的悬浮力解耦控制,对样机采用空载试验和短路试验验证了等效电路参数。
利用系统的状态方程,采用次级磁场定向策略,将悬浮力和次级磁链解耦,将悬浮高度作为主要控制对象,加入损耗最小为优化目标,设计了基于次级磁场定向控制,悬浮高度和次级磁链双闭环的矢量悬浮控制策略,实现系统的稳定悬浮控制。采用Matlab/Simulink仿真软件验证了悬浮控制策略。
最后,设计制作旋转磁场电动式磁悬浮控制系统,基于DSP设计了控制系统硬件,并在悬浮试验台上对样机进行了悬浮运行试验,证明了本文提出的数学模型的正确性和控制方法的有效性。
Magnetic levitation could operate contactlessly, has the advantages of low noise, low maintenance and high reliability, it could be used in transportation, special motors, robot and metal working.
A new configuration of maglev system--rotating field electrodynamic levitation system(RFELS) is proposed in this dissertation, the system uses electrodynamic levitation principle, rotating magnetic field (RMF) in its air-gap is generated by3-phase AC current in the primary windings, the interaction between RMF and secondary eddy current inducted by RMF produces lift force and horizontal force. This system's structural is stable, its control is simple, it can realize intrisic stable static levitation and guidance, has a widely application prospect. A series of analyzing tools was proposed to analyze the system's characteristics, structure design and levitation control system design method correctly.
Firstly, providing evidences to system modeling and control, analyzed the electromagnetic relationship in RFELS using electromagnetic theory. RFELS's primary core is ring-shaped, sub-loop model was set to simplify the calculation and improve the calculation accuracy, analyzed each loop using average values of the loop.Unfold the ring-shaped sub-loop model into a rectangle sub-loop model to employ2-dimension electromagnetic analysis.
Analyzed transverse end effect's influence to magnetic field distribution and energy storage based on2-dimension electromagnetic analysis, derived equivalent air-gap length expression and modified coefficients of main characteristics.
Established RFELS's multi-layer model, solved electromagnetic distribution by Maxwell equations, simplified the expressions using surface impedance method, verified the results by time-stepping finite element calculation using Ansoft Maxwell.12, derived electromagnetic field energy storage expression by Poynting theorem. The results could be used in characteristic analysis and control parameters calculation.
Secondly, the relationships between system parameters and key characteristics are investigated. According to the field distribution and energy storage, solved the lift force, torque, side force, recovery force and secondary force characteristics, relationships of the characteristics to current excitation and structure parameters. Set up test platform, performed force characteristics test an temperature rise test to testify the former characteristics. According to existing research results, investigated RFELS's main characteristics under various secondary structure, material, thickness, provided evidences to RFELS design.
Proposed evaluation criterion for the system based on the fixed relationship between lift force and secondary loss, analyzed maximam lift force outputs under various working condition using the evaluation criterion.
Analyzed the relationship between primary electromagnetic field travelling speed and lift force by electromagnetic field wave properties, generalize this conclusion to most electrodynamic levitation system by horizontal wave vector and palstance equivalent, explained how primary polar distance influent system'capacity of generating lift force.
Thirdly, the control method of the system is investigated. Calculated RFELS equivalent circuit according to field energy storage, testified the equivalent circuit parameters by no-load test and short-circuit test. Regarded air-gap length as the key variable, derived air-gap state equations under2-phases synchronous rotating coordination system through synchronous rotating reference frame by the equivalent circuit parameters, and used in lift force decoupling control.
According to the state equations, decoupled lift force and flux linkage based on secondary field orientation, took levitation height as key controlled object, added loss minimum optimization objective, designed secondary field orientation levitation height and flux linkage double closed-loop levitation vector control strategy, realized stable levitation control. Testified control strategy using Matlab/Simulink simulation software.
Lastly, designed control system hardware based on DSP, performed operation test on levitation operation test platform, RFELS and its control system realized stable static levitation in the experiments.
引文
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