开关磁阻电机的非线性建模及在航空发动机多场耦合仿真中的应用
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摘要
开关磁阻电机(Switched Reluctance Machine, SRM)由于具有容错性好、稳定性高、调速范围宽、功率密度大和易冷却等优点,因而比传统电机更适合航空应用场合。随着多/全电飞机(More Electric Aircraft/All Electric Aircraft, MEA/AEA)成为未来航空的发展趋势,SRM在航空应用上面临极大的机遇。目前,美国等航空强国已把SRM作为未来的MEA/AEA电源系统的首选方案,国际上主要的航空发动机研究机构如GE、Rolls-Roys和Pratt & Whitney等公司也都将SRM作为潜在的航空起动/发电机(Starter/Generator)系统进行研究。可以预见,SRM系统将是航空发动机动力系统的一个潜在的重要组成部分。
航空发动机动力系统是一个多领域复杂物理系统,其研发进度是整个飞机研发进度的关键。基于CAE技术的仿真分析可以实现发动机动力系统的预测设计,从而缩短其研发周期并减少成本。当前,我国的航空工业正处于起步阶段,严重落后于美、俄、英、法等航空强国,尤其在以发动机为主的航空动力系统的研发方面,差距更为明显。鉴于我国航空工业的自主研制基础较弱,开发虚拟样机仿真分析的航空动力系统CAE技术对于发展我国航空工业具有重要意义。
航空发动机动力系统仿真涉及到多学科的耦合研究。目前有关发动机和开关磁阻电机的特性仿真均是单独进行的。发动机仿真往往只偏向于某一领域的诸如压气机特性、涡轮特性或燃烧特性等方面的仿真分析;开关磁阻电机的仿真研究也都将其视为独立的个体,集中在机电层面上。关于开关磁阻电机在航空发动机动力系统方面的应用,组成发动机动力系统的系统级模型,涉及机、电、液、气、热等多场耦合的实时特性仿真分析时,还鲜见相关成果。从这个意义上,本文分析了发动机各子系统的耦合作用,实现了多场耦合的发动机系统级仿真,提供了发动机各耦合子系统的实时特性,和全域内开关磁阻电机运行特性的分析依据。
由此,本课题组致力于建立一个完整的、通用化的航空动力系统元部件模型库。该模型库采用适用于多领域物理系统建模、被誉为新一代的统一建模语言——Modelica开发,具有参数化、易扩展的特点,并力求标准化和通用化。相比传统的面向块、基于信号流的如Simulink等建模平台,Modelica的面向对象性使得系统分解更接近实际物理系统结构,而其非因果性的特点则赋予模型双向计算能力,因而能较好地解决子系统之间的耦合和计算流程的问题,增加了模型的可重用性。
SRM系统是航空动力系统的一个潜在重要子系统,而开关磁阻驱动系统(Switched Reluctance Drive)本身则是个时变的强非线性系统,其控制存在着诸多难题。SRD具有可控参数多、控制灵活但难以优化的特点,常规的参数固定的PID控制方法难以取得理想的控制效果。神经网络技术具有良好的非线性逼近能力,自学习、自适应能力和并行处理信息的能力,比较适用于具有不确定性或高度非线性系统的建模和控制,因此,从20世纪90年代后,神经网络技术开始被引进SRM的建模和SRD的控制中。神经网络理论研究已形成多个流派,而多层前向神经网络是其中最富有成就、应用最广泛的研究成果之一。然而,目前网络结构还没有有效的确定方法,动态辨识与控制用的一阶梯度学习算法及其相应的衍生方法收敛过于缓慢,以及难以利用先验知识指导网络训练学习过程等问题成为制约神经网络技术实际应用的障碍。
鉴于SRM在航空方面的应用前景,本文围绕SRM的Modelica非线性建模,SRM的航空应用分析的研究展开,并致力于解决SRM神经网络控制的一些技术难点。本文主要完成的工作如下:
(1)本文基于磁路特性原理提出了SRM的一个改进的非线性解析模型。该模型原始数据基于有限元分析的静态磁特性参数,较好地实现了高精度和快速可计算性的平衡。模型分别通过静态、动态方面加以验证,精度均在误差的理想范围内。本文接着基于BP神经网络建立SRM的神经网络模型。神经网络结构采用黄金分割法确定,以求在精度和结构上找到优化计算的平衡点。相比较解析模型,神经网络模型具有更高的精度,然而,模型的计算复杂性也更强。
(2)本文采用Modelica语言并基于Dymola平台开发了SRM系统相对完整的元部件模型库。由于复杂物理系统的动态仿真具有计算量极大的特点,因此,子系统模型在确保精度的基础上,必须力求简单、可快速计算的特性。鉴于此,SRM的Modelica模型库基于非线性解析模型建立。该模型库具有参数化、通用化和易扩展的特点,既可为SRM的独立设计提供CAE分析依据,也能组建SRM系统模型与负载或原动机模型相耦合的系统级模型,提供系统级仿真分析依据。
(3)本文基于BP神经网络理论设计了SRD的自适应神经网络PID控制算法。该算法探讨了网络初始权(阈)值的问题,旨在通过先验知识指导权系数矩阵的生成,从而减小神经网络对于初始权系数矩阵的依赖性。本文提出并比较了两种改进方法,结果显示两种改进算法对于初始权系数矩阵的依赖性均有较大下降。本文进一步探讨了用于控制的多层前向神经网络的学习算法,尝试把输入向量的变化考虑进权值调整过程,进而提出动态Levenberg-Marquardt法和动态梯度法。其目的在于加速网络收敛速度并改善网络经过训练后的稳态精度,解决由静态空间建模到动态时间建模所带来的问题。
(4)最后,本文分析了SRM在航空方面的应用及其控制方法的比较。航空应用具有宽速运行的特点,传统的SRM的航空应用分析,通常是选取其典型的运行点进行分析。本文则通过搭建发动机动力系统的系统级模型提供了全域内的分析依据。仿真结果显示了SRM的航空控制方法的可行性,同时也验证了解决多场耦合的系统级模型仿真的可行性,为发动机动力系统的预测设计提供分析依据。
Switched Reluctance Machine (SRM) boasts lots of excellent characteristics like high fault tolerance, high reliability, high power density, wide-speed operation ability and being easy to cool etc. The distinctive advantages of SRM lead to its better suitability for aerospace applications than the conventional drives. As a matter of fact, since More Electric Aircraft (MEA) and All Electric Aircraft (AEA) become the trend of future aircraft power system, SRM is facing great opportunities in aerospace applications. Big aviation countries like USA have selected SRM as the first scheme of the electrical power system for future MEA/AEA, and main research institutions of aircraft engine like GE, Rolls-Roys and Pratt & Whitney etc have carried out researches on SRM as potential aircraft engine Starter/Generator (S/G). In the foreseeable future, SRM system should be one of the potential important subsystems in the aircraft power systems.
An aircraft power system is a complex, multi-disciplinary physical system. Its development is the key factor in the progress of the development of an aircraft. CAE technology-based simulation ensures the predictive design technique, which is important in that it saves the cost and shortens the development period. The aviation industry in China is still in its beginning stage. It’s by no way comparable to the conventional aviation powers such as USA, Russia, Britain and France. In the research and development of the aircraft engine power system, the disparity is especially huge. Given that the foundation of independent development in aviation industry is strongly weak in China, It’s meaningful to develop virtual prototype-based aircraft power system CAE technology to improve China’s aviation industry.
Simulation of aircraft power system involves coupling of multi-physics. Up to now, all the research on simulation of aircraft engine and SRM was confined to their individual characteristics. The previous simulation of aircraft engine mainly focused on some specific aspects like the compressor map, the turbine map or the combustion characteristics etc; likewise, simulation of SRM was carried out alone and was focused on the electromechanical field. As for applications of SRM in aerospace, system-level simulation of aircraft power system together with SRM as a whole would be helpful for dynamic analysis. It should involve the coupling of multi-domains like mechanics, electrics, hydraulics, pneumatics and thermodynamics etc. However, very few research findings could be found in this aspect. On this account, this paper is devoted to analyze the coupling sub-systems of aircraft power system, and to realize multi-domain system-level simulation of aircraft power system. It’s aimed to provide dynamic analysis of the coupling sub-systems and that of SRM on the global operation range.
Therefore, our research group is devoted to developing a rather complete, generic aircraft power system model library. The model library is built based on Modelica, which is especially suitable for the modeling of complex, multi-disciplinary system, and is honored as the next generation unified modeling language (UML). The library is parameterized, expandable and it’s also aimed to be standard and generic. Compared to the conventional block-oriented, signal-flow modeling software like Simulink, the object-oriented characteristic of Modelica makes the system decomposition more similar to the real physical system, and the non-causal characteristic of Modelica endows the model with bidirectional calculation ability, which is a good solution to problems of the calculation flow and the mutual coupling of sub-systems.
SRM system is a potential important subsystem in aircraft power system, whereas SRM drive (SRD) itself is a time-varying, strongly nonlinear system. There exist many problems in the control of SRM. SRD characterizes flexible control but being hard to optimize. The conventional parameter-fixed PID control is not good enough to achieve satisfactory control effect. Neural network (NN) technique boasts strong nonlinear approximation, self-study, self-adaptability and parallel processing ability, and thus it’s suitable to be used in the modeling and control of uncertain or nonlinear systems. NN technique has been applied in the modeling and control of SRM ever since 1990s. There has been quite a lot of school in the research of NN technology, and multi-layer feed-forward NN is one of the most fruitful and the most widely used techniques. However, there have still been some problems in NN research: the NN structure can not be derived analytically; there’s no particular learning algorithm for dynamic identification and control; it’s hard to apply the empirical knowledge in the initialization and training of the networks.
Considering the potential application of SRM in aerospace, this dissertation carries out the research work on the Modelica-based nonlinear modeling of SRM, the application and control analysis of SRM in aerospace, and it’s also aimed to improve or present solutions to some key technical problems in the NN control of SRM. The following are the achievements that are fulfilled in this dissertation:
(1) Based on the analysis of the magnetic field characteristics, an improved nonlinear analytical model of SRM is presented. The original static magnetic characteristics data are derived from FEM and the model is verified through comparison with FEM,statically and dynamically. The model is proved to be satisfactory in accuracy and it also ensures rapid calculation due to its analyticity. Further on, this dissertation derives a BP neural network (NN) model of SRM. The structure of the network is based on gold section method in order for a balance between accuracy and complexity. Compared to the analytical model, the BP NN model of SRM is more accurate. However, the model is much more complex for calculation.
(2) A comparatively complete SRM system model library is developed on Modelica/Dymola. For dynamic simulation of a complex physical system, the calculation is very intense. Therefore, models for sub-systems should be rapidly computable besides precise in accuracy. Thus, the nonlinear analytical model of SRM is chosen for the SRM Modelica model. The model library is parameterized, generic and conveniently expandable. It can be used as an independent modeling software package for the CAE analysis of SRM design alone, and it can also serve the whole aircraft power system model library to assemble a system-level model for system-level simulation analysis.
(3) A BP NN PID controller is developed for the adaptive speed control of SRM. The interest of the dissertation is to explore on the utilization of the prior empirical knowledge as guidance in the initializing and the training of the neural networks. It’s aimed to make the networks less sensitive on the initial weights and biases. Two proposed algorithms are compared. Simulation results show that the two proposed algorithms are much less sensitive on the initial weights. Learning algorithms of feed-forward NN for control applications are further discussed. This dissertation explores to involve the variation of the inputs into the adjusting of the weights. Subsequently, two algorithms, namely Dynamic Levenberg-Marquardt (DLM) and Dynamic Gradient Method (DGM), are presented. The purpose is to accelerate the training of the networks, and to improve the output accuracy after training as well, and also to solve problems caused by the transformation from static-space modeling to dynamic-time modeling.
(5) In the end, this paper analyzes SRM’s aerospace applications and the respective control. Aerospace applications characterize wide-speed operation. Therefore, selective operating points’analysis, which is mostly used in previous research papers, is not enough to evaluate the SRM’s global performance. System-level models of Switched reluctance generator (SRG) coupled with an aircraft engine are constructed on Modelica/Dymola. Dynamic simulation results verify the control methods. The example also verifies the validation of the idea of system-level simulation with multi-field coupling, and thus makes a way to the predictive design of the aircraft power system.
航空发动机动力系统是一个多领域复杂物理系统,其研发进度是整个飞机研发进度的关键。基于CAE技术的仿真分析可以实现发动机动力系统的预测设计,从而缩短其研发周期并减少成本。当前,我国的航空工业正处于起步阶段,严重落后于美、俄、英、法等航空强国,尤其在以发动机为主的航空动力系统的研发方面,差距更为明显。鉴于我国航空工业的自主研制基础较弱,开发虚拟样机仿真分析的航空动力系统CAE技术对于发展我国航空工业具有重要意义。
航空发动机动力系统仿真涉及到多学科的耦合研究。目前有关发动机和开关磁阻电机的特性仿真均是单独进行的。发动机仿真往往只偏向于某一领域的诸如压气机特性、涡轮特性或燃烧特性等方面的仿真分析;开关磁阻电机的仿真研究也都将其视为独立的个体,集中在机电层面上。关于开关磁阻电机在航空发动机动力系统方面的应用,组成发动机动力系统的系统级模型,涉及机、电、液、气、热等多场耦合的实时特性仿真分析时,还鲜见相关成果。从这个意义上,本文分析了发动机各子系统的耦合作用,实现了多场耦合的发动机系统级仿真,提供了发动机各耦合子系统的实时特性,和全域内开关磁阻电机运行特性的分析依据。
由此,本课题组致力于建立一个完整的、通用化的航空动力系统元部件模型库。该模型库采用适用于多领域物理系统建模、被誉为新一代的统一建模语言——Modelica开发,具有参数化、易扩展的特点,并力求标准化和通用化。相比传统的面向块、基于信号流的如Simulink等建模平台,Modelica的面向对象性使得系统分解更接近实际物理系统结构,而其非因果性的特点则赋予模型双向计算能力,因而能较好地解决子系统之间的耦合和计算流程的问题,增加了模型的可重用性。
SRM系统是航空动力系统的一个潜在重要子系统,而开关磁阻驱动系统(Switched Reluctance Drive)本身则是个时变的强非线性系统,其控制存在着诸多难题。SRD具有可控参数多、控制灵活但难以优化的特点,常规的参数固定的PID控制方法难以取得理想的控制效果。神经网络技术具有良好的非线性逼近能力,自学习、自适应能力和并行处理信息的能力,比较适用于具有不确定性或高度非线性系统的建模和控制,因此,从20世纪90年代后,神经网络技术开始被引进SRM的建模和SRD的控制中。神经网络理论研究已形成多个流派,而多层前向神经网络是其中最富有成就、应用最广泛的研究成果之一。然而,目前网络结构还没有有效的确定方法,动态辨识与控制用的一阶梯度学习算法及其相应的衍生方法收敛过于缓慢,以及难以利用先验知识指导网络训练学习过程等问题成为制约神经网络技术实际应用的障碍。
鉴于SRM在航空方面的应用前景,本文围绕SRM的Modelica非线性建模,SRM的航空应用分析的研究展开,并致力于解决SRM神经网络控制的一些技术难点。本文主要完成的工作如下:
(1)本文基于磁路特性原理提出了SRM的一个改进的非线性解析模型。该模型原始数据基于有限元分析的静态磁特性参数,较好地实现了高精度和快速可计算性的平衡。模型分别通过静态、动态方面加以验证,精度均在误差的理想范围内。本文接着基于BP神经网络建立SRM的神经网络模型。神经网络结构采用黄金分割法确定,以求在精度和结构上找到优化计算的平衡点。相比较解析模型,神经网络模型具有更高的精度,然而,模型的计算复杂性也更强。
(2)本文采用Modelica语言并基于Dymola平台开发了SRM系统相对完整的元部件模型库。由于复杂物理系统的动态仿真具有计算量极大的特点,因此,子系统模型在确保精度的基础上,必须力求简单、可快速计算的特性。鉴于此,SRM的Modelica模型库基于非线性解析模型建立。该模型库具有参数化、通用化和易扩展的特点,既可为SRM的独立设计提供CAE分析依据,也能组建SRM系统模型与负载或原动机模型相耦合的系统级模型,提供系统级仿真分析依据。
(3)本文基于BP神经网络理论设计了SRD的自适应神经网络PID控制算法。该算法探讨了网络初始权(阈)值的问题,旨在通过先验知识指导权系数矩阵的生成,从而减小神经网络对于初始权系数矩阵的依赖性。本文提出并比较了两种改进方法,结果显示两种改进算法对于初始权系数矩阵的依赖性均有较大下降。本文进一步探讨了用于控制的多层前向神经网络的学习算法,尝试把输入向量的变化考虑进权值调整过程,进而提出动态Levenberg-Marquardt法和动态梯度法。其目的在于加速网络收敛速度并改善网络经过训练后的稳态精度,解决由静态空间建模到动态时间建模所带来的问题。
(4)最后,本文分析了SRM在航空方面的应用及其控制方法的比较。航空应用具有宽速运行的特点,传统的SRM的航空应用分析,通常是选取其典型的运行点进行分析。本文则通过搭建发动机动力系统的系统级模型提供了全域内的分析依据。仿真结果显示了SRM的航空控制方法的可行性,同时也验证了解决多场耦合的系统级模型仿真的可行性,为发动机动力系统的预测设计提供分析依据。
Switched Reluctance Machine (SRM) boasts lots of excellent characteristics like high fault tolerance, high reliability, high power density, wide-speed operation ability and being easy to cool etc. The distinctive advantages of SRM lead to its better suitability for aerospace applications than the conventional drives. As a matter of fact, since More Electric Aircraft (MEA) and All Electric Aircraft (AEA) become the trend of future aircraft power system, SRM is facing great opportunities in aerospace applications. Big aviation countries like USA have selected SRM as the first scheme of the electrical power system for future MEA/AEA, and main research institutions of aircraft engine like GE, Rolls-Roys and Pratt & Whitney etc have carried out researches on SRM as potential aircraft engine Starter/Generator (S/G). In the foreseeable future, SRM system should be one of the potential important subsystems in the aircraft power systems.
An aircraft power system is a complex, multi-disciplinary physical system. Its development is the key factor in the progress of the development of an aircraft. CAE technology-based simulation ensures the predictive design technique, which is important in that it saves the cost and shortens the development period. The aviation industry in China is still in its beginning stage. It’s by no way comparable to the conventional aviation powers such as USA, Russia, Britain and France. In the research and development of the aircraft engine power system, the disparity is especially huge. Given that the foundation of independent development in aviation industry is strongly weak in China, It’s meaningful to develop virtual prototype-based aircraft power system CAE technology to improve China’s aviation industry.
Simulation of aircraft power system involves coupling of multi-physics. Up to now, all the research on simulation of aircraft engine and SRM was confined to their individual characteristics. The previous simulation of aircraft engine mainly focused on some specific aspects like the compressor map, the turbine map or the combustion characteristics etc; likewise, simulation of SRM was carried out alone and was focused on the electromechanical field. As for applications of SRM in aerospace, system-level simulation of aircraft power system together with SRM as a whole would be helpful for dynamic analysis. It should involve the coupling of multi-domains like mechanics, electrics, hydraulics, pneumatics and thermodynamics etc. However, very few research findings could be found in this aspect. On this account, this paper is devoted to analyze the coupling sub-systems of aircraft power system, and to realize multi-domain system-level simulation of aircraft power system. It’s aimed to provide dynamic analysis of the coupling sub-systems and that of SRM on the global operation range.
Therefore, our research group is devoted to developing a rather complete, generic aircraft power system model library. The model library is built based on Modelica, which is especially suitable for the modeling of complex, multi-disciplinary system, and is honored as the next generation unified modeling language (UML). The library is parameterized, expandable and it’s also aimed to be standard and generic. Compared to the conventional block-oriented, signal-flow modeling software like Simulink, the object-oriented characteristic of Modelica makes the system decomposition more similar to the real physical system, and the non-causal characteristic of Modelica endows the model with bidirectional calculation ability, which is a good solution to problems of the calculation flow and the mutual coupling of sub-systems.
SRM system is a potential important subsystem in aircraft power system, whereas SRM drive (SRD) itself is a time-varying, strongly nonlinear system. There exist many problems in the control of SRM. SRD characterizes flexible control but being hard to optimize. The conventional parameter-fixed PID control is not good enough to achieve satisfactory control effect. Neural network (NN) technique boasts strong nonlinear approximation, self-study, self-adaptability and parallel processing ability, and thus it’s suitable to be used in the modeling and control of uncertain or nonlinear systems. NN technique has been applied in the modeling and control of SRM ever since 1990s. There has been quite a lot of school in the research of NN technology, and multi-layer feed-forward NN is one of the most fruitful and the most widely used techniques. However, there have still been some problems in NN research: the NN structure can not be derived analytically; there’s no particular learning algorithm for dynamic identification and control; it’s hard to apply the empirical knowledge in the initialization and training of the networks.
Considering the potential application of SRM in aerospace, this dissertation carries out the research work on the Modelica-based nonlinear modeling of SRM, the application and control analysis of SRM in aerospace, and it’s also aimed to improve or present solutions to some key technical problems in the NN control of SRM. The following are the achievements that are fulfilled in this dissertation:
(1) Based on the analysis of the magnetic field characteristics, an improved nonlinear analytical model of SRM is presented. The original static magnetic characteristics data are derived from FEM and the model is verified through comparison with FEM,statically and dynamically. The model is proved to be satisfactory in accuracy and it also ensures rapid calculation due to its analyticity. Further on, this dissertation derives a BP neural network (NN) model of SRM. The structure of the network is based on gold section method in order for a balance between accuracy and complexity. Compared to the analytical model, the BP NN model of SRM is more accurate. However, the model is much more complex for calculation.
(2) A comparatively complete SRM system model library is developed on Modelica/Dymola. For dynamic simulation of a complex physical system, the calculation is very intense. Therefore, models for sub-systems should be rapidly computable besides precise in accuracy. Thus, the nonlinear analytical model of SRM is chosen for the SRM Modelica model. The model library is parameterized, generic and conveniently expandable. It can be used as an independent modeling software package for the CAE analysis of SRM design alone, and it can also serve the whole aircraft power system model library to assemble a system-level model for system-level simulation analysis.
(3) A BP NN PID controller is developed for the adaptive speed control of SRM. The interest of the dissertation is to explore on the utilization of the prior empirical knowledge as guidance in the initializing and the training of the neural networks. It’s aimed to make the networks less sensitive on the initial weights and biases. Two proposed algorithms are compared. Simulation results show that the two proposed algorithms are much less sensitive on the initial weights. Learning algorithms of feed-forward NN for control applications are further discussed. This dissertation explores to involve the variation of the inputs into the adjusting of the weights. Subsequently, two algorithms, namely Dynamic Levenberg-Marquardt (DLM) and Dynamic Gradient Method (DGM), are presented. The purpose is to accelerate the training of the networks, and to improve the output accuracy after training as well, and also to solve problems caused by the transformation from static-space modeling to dynamic-time modeling.
(5) In the end, this paper analyzes SRM’s aerospace applications and the respective control. Aerospace applications characterize wide-speed operation. Therefore, selective operating points’analysis, which is mostly used in previous research papers, is not enough to evaluate the SRM’s global performance. System-level models of Switched reluctance generator (SRG) coupled with an aircraft engine are constructed on Modelica/Dymola. Dynamic simulation results verify the control methods. The example also verifies the validation of the idea of system-level simulation with multi-field coupling, and thus makes a way to the predictive design of the aircraft power system.
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