Model Parameter Identification with SPICE OPUS a Comparison of Direct Search and Elitistic

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韧性断裂准则的参数标定方法及其适用性研究

韧性断裂准则的参数标定方法及其适用性研究摘要在工业生产过程中，材料由于承受大应力和大变形而产生起裂，因此通过数值模拟方法预测材料在成形过程中的起裂位置、起裂时刻以及裂纹扩展的方式越来越受到人们的重视。

数值模拟结果的准确性依赖于所选取的韧性断裂准则。

由于可移植性好，很多韧性断裂准则都已经被植入各主流的商业有限元软件中，使用者通过输入模型参数即可使用。

而一般的韧性断裂准则往往存在众多参数，不同的参数所得到的模拟结果截然不同。

模型参数确定需要通过一系列的不同应力状态的试验结果得到，但是所需要的应力状态变量在试验过程中并不是一个定值，因此有学者引入了平均值的计算方法来便于进行参数的标定。

不过目前还没有人评估过，该计算方法确定的参数是否会对韧性断裂准则的使用引入新的误差。

因此研究韧性断裂准则的参数标定方法及其适用性对于有限元数值模拟的应用具有重要意义。

为了评估使用平均值变量带来的误差，本文引入一系列的宽应力三轴度的试验，并提取了试验模拟的初始起裂点的断裂相关状态变量，如应力三轴度、罗德参数和等效断裂应变。

在此基础上，计算了初始起裂点的平均应力三轴度和平均罗德参数，并利用L-H韧性断裂准则来评估使用平均值变量带来的误差，同时引入了一个相对误差公式来标定该误差。

通过比较每组试验计算的累积损伤值和临界阈值，得到了使用平均值变量所引入的相对误差。

研究发现，在压缩试验中，该相对误差值较大。

且对于不同的试验，参数值C1和C2对引入相对误差值的影响也是不尽相同的。

因此为了深入探究平均值变量引入的误差受到哪些因素的影响，针对韧性断裂准则中存在的变量，如参数值C1和C2、应力三轴度与等效应变的函数类型以及被积函数类型，建立了一系列的以不同应力三轴度与等效应变的函数类型为基础的研究。

应力三轴度与等效应变的函数对引入相对误差的影响，即分段函数的指数a、应力三轴度截距值以及等效应变分段值对引入相对误差的影响。

研究发现，参数C2、应力三轴度与等效应变函数的指数a和应力三轴度截距值，会对相对误差的增加产生较大影响。

永磁直驱风电系统建模及其机电暂态模型参数辨识

永磁直驱风电系统建模及其机电暂态模型参数辨识程玮;陈宏伟;石庆均【摘要】Aiming at the characters of direct-driven wind-power system with permanent magnet synchronous generator (PMSG) based on back-to-back pulse width modulation(PWM) converter, the wind turbine, the control strategies of turbine-side converter and grid-side con verter were analyzed. PMSG detail model using Matlah/Simulink was established. Based on this, electromechanical transient model for di rect-driven wind-turbine generator was constructed according to 3 orders synchronous generator model. Particle swarm optimization ( PSO) al gorithm was used to identify the parameter for the mathematical model. The simulation results show that the detail model can reflect direct- driven wind-power system' s operation as wind speed changing, while it can track the maximum power point. The electromechanical transient model coincides with the detail model well. It reflects the active and reactive power of the direct-driven wind-power system when grid voltage is changed. The parameter identification using PSO is effective. The results indicate that the detail model can be used to refine power output control strategy, the electromechanical transient model can be used to study direct-driven wind-power system interacted with the grid.%针对基于双脉宽调制(PWM)变换器的永磁直驱风电系统的运行特性,分析了风力机特性、电机侧变换器和电网侧变换器的控制策略,利用Matla/Simulink建立了反映电力电子开关动作的永磁直驱风电系统详细模型,并在此基础上根据同步电机3阶暂态模型,建立了直驱风机的机电暂态数学模型,采用粒子群算法(PSO)对模型进行了参数辨识.仿真结果表明,该详细模型能够描述永磁直驱风电系统对不同风速的响应,实现风能的最大功率跟踪；机电暂态数学模型与详细模型特性接近,能够从总体上反映永磁直驱风电系统对端电压变化的有功、无功响应,PS0参数辨识有效.研究结果表明,所建立的详细模型能够用于控制方式的研究以改善输出特性,机电暂态模型能够用于研究电网与永磁直驱风电系统的相互影响.【期刊名称】《机电工程》【年(卷),期】2012(029)007【总页数】4页(P817-820)【关键词】双脉宽调制变换器;机电暂态;参数辨识;粒子群算法【作者】程玮;陈宏伟;石庆均【作者单位】浙江大学电气工程学院,浙江杭州310027;浙江大学电气工程学院,浙江杭州310027;浙江大学电气工程学院,浙江杭州310027【正文语种】中文【中图分类】TM6140 引言当前，变速恒频(variable-speed constant-frequency，VSCF)风力发电系统已被广泛应用，其特点是通过先进的变速和变桨技术，在风速变化时调节发电机转速处于相应的最佳值从而最大限度地捕获风能，提高了风力发电的效率，且低风速情况下风机转速下降，从而大大降低了系统的机械应力和装置成本。

六自由度工业机器人标定

摘要运动学标定是提高机器人精度的关键技术，也是机器人学的重要内容，在机器人空前发展的今天有十分重要的理论和现实意义。

机器人运动学标定以运动学建模为基础，几何误差参数辨识为目的，为机器人的误差补偿提供依据。

现今机器人厂家生产的机器人其重复定位精度比较高，而绝对定位精度却很低。

伴随着机器人越来越广泛的运用，提高机器人绝对定位精度已成为其中一关键技术问题。

本文采用一种运动学标定方法，应用先进的激光跟踪测量系统和基于模型的参数辨识方法识别出一种 6R机器人模型的准确参数，提高了该机器人的绝对定位精度。

针对工业机器人标定问题，首先结合机器人的实际机构特点，运用 D-H 方法建立了机器人的连杆坐标系，在此基础上进行了机器人运动学正逆解和雅可比矩阵的详细推导及求解，并运用 Matlab 语言进行运动学模型的编程求解，通过与机器人控制器中位姿数据对比，验证了所建立的连杆坐标系统的正确性。

针对工业机器人的机构特点，分析了影响机器人末端绝对定位精度的误差来源，采用修正的运动学连杆参数模型，基于微分变换法推导了用于机器人标定的误差模型，并基于 Matlab 软件系统编制了机器人运动学误差模型的最小二乘算法，通过对误差模型进行模拟求解，验证了机器人标定误差模型的可行性。

关键词：工业机器人; 运动学; 定位精度; 标定; 误差模型 ;连杆参数。

AbstractKinematic calibration is the key technology to improve the accuracy of robot, is also the important content of robotics, an unprecedented development in robot today have very important theoretical and practical significance. The robot kinematics calibration modeling based on kinematics, geometric error parameter identification for the purpose, to provide basis for error compensation of robot. The robot manufacturers robot its repetitive positioning precision is higher, but the absolute positioning accuracy is very low. With the use of robots are more and more widely, improving the robot absolute positioning accuracy has become a key technology problem which. This paper uses a kinematic calibration method, the application of advanced laser tracking measurement system based on parameter identification method and identification model of accurate parameters of a 6R robot model, improves the accuracy of the robot absolute positioning. Aiming at the industrial robot calibration, the actual mechanism firstly with the robot, the robot is established by D-H method of pole coordinates, based on the detailed derivation and solution of robot kinematics and Jacobi matrix, programming and kinematics model using Matlab language, with the attitude data comparison of robot controller, verified the correctness of the established link coordinate system. According to the mechanism of industrial robot, analyzes the impact of absolute location error precision of the robot, the kinematics model, based on differential transform method is derived for the error model calibration of robots, and based on the Matlab software system of least square algorithm for robot kinematics error model, through the simulation to solve the error model, validation the feasibility of robot calibration error model.Keywords: industrial robot; kinematics; positioning accuracy; calibration; error model; link parameters.目录摘要 (1)Abstract (II)第一章绪论 (1)1.1引言 (1)1.2工业机器人运动学标定技术的背景和意义 (1)1.3机器人标定技术的研究现状 (3)第二章机器人运动学 (5)2.1 机器人运动学模型的建立 (5)2.2正向运动学求解 (9)2.3逆向运动学求解 (10)2.4 微分运动学模型 (13)2.5 本章小结 (17)第三章 SR06 型机器人的标定技术 (17)3.1 标定用运动学模型的建立 (18)3.1.1 直线的无极点表示法 (19)3.1.2 CPC 模型的建立 (20)3.2 机器人的标定方法 (24)3.2.1 几何误差的来源 (24)3.2.2 连杆参数的线性求解方法 (25)3.3 本章小结 (30)第四章标定实验及结论 (31)4.1 原始数据采集 (32)4.2 数据处理 (33)4.2.1 齐次坐标变换矩阵与绕任意轴的旋转矩阵之间的关系334.2.2 方程RA Rx= RxRb的求解 (36)4.3 标定结果 ............................ 错误！未定义书签。

基于MATLAB与PSIM软件光伏故障联合仿真平台设计

姜萍等:基于MATLAB与PSIM软件光伏故障联合仿真平台设计120《激光杂志》2021年第42卷第2期LASER JOURNAL(Vol.42,No.2,2021)•光通信与网络•基于MATLAB与PSIM软件光伏故障联合仿真平台设计姜萍,代金超河北大学电子信息工程学院，河北保定071002摘要：太阳能光伏阵列的故障分析是提高其效率、安全可靠性和适用性的一项重要工作。

为进一步提高故障光伏系统的建模准确性，简化操作步骤，提出了一种新型联合仿真模型的方法。

以辐照度和温度作为外界环境参数输入，结合MATLAB和PSIM软件各自的优势，实现模型的参数辨识，实时数据交互通讯。

通过输入仿真故障类型M值来实现随机阴影等参数的相应改变，得到每种异常工作状态下对应的电压、电流等数据特征值。

最后经过结果对比，仿真精度能始终控制在5%以内，实验结果证实了所搭建模型的准确性及有效性。

关键词：光伏阵列；故障分析；联合仿真；参数辨识；数据交互中图分类号:TN315文献标识码：A doi：10.14016/ki.jgzz.2021.02.120Design of photovoltaic fault joint simulation platform based onMATLAB and PSIMJIANG Ping,DAI JinchaoSchool of Electronic Information Engineering,Hebei University,Baoding071002,ChinaAbstract:Fault analysis of solar photovoltaic array is an important work to improve its efficiency,safety,reliability and applicability.To improve the modelling accuracy of the fault photovoltaic system and simplify the operation steps,a new joint simulation model method is proposed.Taking irradiance and temperature as the input of external environment parameters,combined with MATLAB and PSIM software z s advantages,the model parameter identification and real-time data communication were realised.By inputting m value of simulation fault type to realise the corresponding change of parameters such as random shadow,the corresponding data eigenvalues of voltage and current under each abnomial working state are obtained.Finally,by comparing the results,the simulation accuracy can always be controlled within5%.The experimental results confirm the accuracy and effectiveness of the model.Key words:photovoltaic array；fault analysis；joint simulation；parameter identification；data interaction1引言近几年来，世界各国逐渐意识到能源危机对本国的影响日益增大,而太阳能作为最有代表性的新型能源,凭借其可再生、高效、无污染的特点，很早进入了人们的视野并引起了广泛关注，而其中的太阳能用于发电最为常见。

基于参数在线辨识的高速永磁电机无差拍电流预测控制

第27卷㊀第9期2023年9月㊀电㊀机㊀与㊀控㊀制㊀学㊀报Electri c ㊀Machines ㊀and ㊀Control㊀Vol.27No.9Sep.2023㊀㊀㊀㊀㊀㊀基于参数在线辨识的高速永磁电机无差拍电流预测控制刘刚1,㊀张婧1,2,㊀郑世强1,2,㊀毛琨1,2(1.北京航空航天大学惯性技术重点实验室,北京100191;2.北京航空航天大学宁波创新研究院,浙江宁波315800)摘㊀要:针对无传感器表贴式永磁同步电机高速运行过程中电气参数摄动影响电流环性能和转子位置估计精度的问题,提出一种基于参数辨识的无传感器高速永磁电机无差拍电流预测控制方法㊂首先,为了提升电流环控制器的动态性能,结合永磁电机控制系统的特点,采用无差拍电流预测控制并进行模型参数敏感性分析㊂其次,针对多参数在线辨识存在的欠秩问题,提出在3种不同时间尺度下,采用基于神经元迭代求解的总体最小二乘法在线分步辨识电机定子电感㊁电阻和永磁体磁链㊂最后将辨识结果用于更新无差拍电流预测控制器及滑模观测器参数㊂实验结果表明,基于参数辨识的无传感器高速永磁电机无差拍电流预测控制方法能有效提高电流环控制器稳态性能及转子位置估计精度㊂关键词:高速永磁同步电机;无差拍电流预测控制;无传感器控制;多参数在线辨识;总体最小二乘算法;神经元DOI :10.15938/j.emc.2023.09.011中图分类号:TM341文献标志码:A文章编号:1007-449X(2023)09-0098-11㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀收稿日期:2022-02-13基金项目:国家自然科学基金(61822302)作者简介:刘㊀刚(1970 ),男,博士,教授,博士生导师,研究方向为航天器惯性执行机构技术㊁磁悬浮高速永磁电机技术;张㊀婧(1997 ),女,博士研究生,研究方向为高速永磁同步电机控制㊁原子磁强计控制;郑世强(1981 ),男,博士,教授,博士生导师,研究方向为航天器惯性执行机构技术㊁磁悬浮高速永磁电机技术;毛㊀琨(1988 ),男,博士,助理研究员,研究方向为电机控制㊂通信作者:毛㊀琨Deadbeat predictive current control of high speed permanent magnet motor based on online parameter identificationLIU Gang 1,㊀ZHANG Jing 1,2,㊀ZHENG Shiqiang 1,2,㊀MAO Kun 1,2(1.Science and Technology on Inertial Laboratory,Beihang University,Beijing 100191,China;2.Ningbo Innovation Research Institute,Beihang University,Ningbo 315800,China)Abstract :During the high-speed operation of sensorless surface-mounted permanent magnet synchronous motor (SPMSM),the perturbation of electrical parameters affects the performance of current loop and the accuracy of rotor position estimation.Therefore,a deadbeat predictive current control (DPCC)method for sensorless high speed permanent magnet motor based on parameter identification was proposed.First-ly,combined with the characteristics of permanent magnet motor control system,DPCC was adopted to improve the dynamic performance of the current loop controller.Besides,the parameter sensitivity of DPCC was analyzed.Secondly,in order to solve the rank deficient problem,a total least square (TLS)method based on neuron iterative solution was used to identify the inductance,resistance and permanent magnet flux linkage on-line and step by step.Finally,the identification results were used to update theparameters of deadbeat predictive current controller and sliding mode observer.The experimental resultsshow that DPCC method of sensorless high-speed permanent magnet motor based on parameter identifica-tion can effectively improve the steady state performance of current loop controller and the accuracy of ro-tor position estimation.Keywords:high speed permanent magnet synchronous motor;deadbeat predictive current control;sen-sorless control;multi parameter online identification;total least squares algorithm;neuron0㊀引㊀言随着稀土永磁材料的开发,基于矢量控制技术的永磁同步电机(permanent magnet synchronous mo-tor,PMSM)以其优良的性能广泛应用于工业伺服驱动㊁电动汽车㊁新能源发电等领域[1]㊂永磁同步电机的高精度控制需要准确的转子位置信息和速度信息,但机械式传感器的使用具有安装维护困难㊁成本高㊁极高转速下响应速度有限等问题,因此,基于观测器的无传感器控制在高速永磁同步电机中得到了极大的发展[2],其中,滑模观测器(sliding mode ob-server,SMO)以计算简单㊁对外部扰动鲁棒性强等优势备受关注[3]㊂永磁同步电机矢量控制一般为电流速度双闭环结构,电流环的动态和稳态特性是影响系统整体性能的关键因素,目前常见的电流环控制策略有滞环控制㊁比例积分(proportional integral,PI)控制和预测控制[4]㊂滞环控制具有电流响应速度快㊁鲁棒性强㊁易于计算等优点,但开关频率易受负载影响且电流纹波大[5]㊂相比之下,PI控制电流纹波小,可以有效降低稳态误差且开关频率固定,但数字控制的固有滞后特性会限制系统响应速度的提升,难以获取最优电流环带宽响应[6]㊂而基于离散模型的预测控制显示出良好的动态性能,能够在当前控制周期预测出下一周期的控制指令,提升系统带宽[7]㊂预测控制通过系统模型来预测状态变量的未来行为,直接预测控制和无差拍预测控制是研究较为广泛的两种预测控制方法[8]㊂其中,直接电流预测控制通过最小化表示系统期望行为的成本函数来定义控制动作,电流动态响应最快,但开关频率可变,产生的电流纹波也最大[9]㊂无差拍预测控制具有固定的开关频率和良好的动态性能,无需开关状态评估和成本函数计算,计算负担大大降低[10-11]㊂但无差拍预测控制是基于离散模型的控制方法,需要准确电机模型参数和电机运行状态,而实际电机高速运行时,受温度升高㊁磁饱和等因素影响不可避免地会造成定子电阻㊁定子电感㊁永磁体磁链发生变化[12]㊂一方面,电机参数失配会导致电流谐波㊁电流跟踪偏差等问题,影响系统电流环的控制性能[13],另一方面,转子磁极位置估计的准确性决定PMSM无传感器控制系统的性能,电机参数失配会降低转子位置估计精度[14]㊂目前解决无差拍电流预测控制电流跟踪误差问题的常见方法有扰动观测器和参数辨识,为同时解决由于电机参数失配造成的电流跟踪误差和转子位置观测误差,对永磁同步电机进行多参数在线辨识并依次更新滑模观测器与无差拍电流预测控制器参数,是提高电流环控制性能和转子位置估计精度的重要策略[15]㊂参数辨识是解决电机模型参数偏离原始设计值问题的一个重要手段,目前较为成熟的在线辨识方法有递推最小二乘法(recursive least squares,RLS)㊁模型参考自适应法㊁扩展卡尔曼滤波法等[16]㊂针对上述表贴式永磁同步电机无差拍电流预测控制器的参数不匹配问题,文献[17]提出一种基于模型参考自适应系统参数辨识的无差拍电流预测控制方法,解决磁链和电感参数不匹配的问题,然而未考虑定子电阻的识别,且寻找使辨识参数收敛的自适应律较为困难㊂文献[18]提出了一种改进的具有参数识别的PMSM无差拍电流预测控制方法,通过电流注入扰动观测器重构特征向量辨识定子电阻和定子电感,减小了计算负担却未考虑磁链参数的影响㊂上述方法只辨识了部分电气参数,不满足多参数在线辨识的要求㊂针对基于反电势法进行转子位置估计易受参数摄动影响的问题,文献[19]运用扩展卡尔曼滤波器在线辨识内置式永磁电机的转子磁链和交轴电感,但未辨识电阻参数㊂文献[20]将电阻㊁电感辨识策略集成到位置观测器中,在αβ轴上施加高频正弦电压以识别d㊁q轴电感,在α轴上注入直流电压以识别电阻㊂对于表贴式永磁同步电机,文献[21]通过向d轴注入电流脉冲获取参数辨识所需数据,可以估计逆变器非线性引起的电阻误差㊁电感误差及99第9期刘㊀刚等:基于参数在线辨识的高速永磁电机无差拍电流预测控制永磁体磁链,但需要求解一个多元非线性回归问题㊂上述方法采用分时分步手段解决多参数在线辨识欠秩问题,但只考虑观测误差而未考虑到系数矩阵误差,忽略了参数之间的耦合影响㊂在实际应用中系数矩阵误差普遍存在,采用总体最小二乘法(total least squares,TLS)进行参数辨识可以同时考虑系数矩阵误差和观测误差,得到更精确的参数估计值,但直接求解TLS问题计算复杂,目前可以通过兴奋和抑制性神经元学习方法(excitatory and inhibitory learning,EXIN)进行在线迭代求取[22]㊂在TLS EX-IN辨识电机本体参数的基础上,利用辨识结果更新电流环预测控制器和转子位置观测器参数,降低电机参数失配的影响㊂针对表贴式永磁同步电机参数不匹配导致的电流跟踪偏差及转子位置观测误差,本文提出一种基于多参数在线辨识的无传感器高速永磁电机无差拍电流预测控制方法㊂首先推导出永磁同步电机的无差拍电流预测方程和基于反电势法的滑模观测器转子位置估计方程,分析电机模型参数误差引起的电流跟踪静差和转子位置估计偏差问题㊂为提高系统鲁棒性和稳态精度,采用基于TLS EXIN神经元求解的总体最小二乘法对电感㊁电阻及磁链参数分步辨识,在解决多参数在线辨识秩亏问题的同时,考虑观测误差和系数矩阵误差㊂根据辨识结果实时更新无差拍电流预测控制器和转子位置观测器参数㊂最后基于高速电机系统进行实验验证,结果表明本文所述方法能有效增强系统的鲁棒性,优化系统动态特性并提升系统控制精度㊂1㊀无差拍电流预测控制1.1㊀电流预测模型本文以表贴式永磁同步电机为研究对象,为简化分析,假设三相PMSM为理想电机,在忽略电机的铁心饱和,不计电机涡流和磁滞损耗,转子上无阻尼绕组且相绕组中感应电动势波形为正弦波的前提下,PMSM在同步旋转坐标系下的电压方程为:u d=Ri d+L d d i dd t-ωe L q i q;u q=Ri q+L q d i qd t+ωe L d i d+ωeψf㊂üþýïïïï(1)式中:u d㊁u q分别是定子电压的d㊁q轴分量;i d㊁i q分别是定子电流的d㊁q轴分量;L d㊁L q分别是d㊁q轴电感分量;R是定子电阻;ψf是转子永磁体磁链;ωe是转子电角速度㊂选定子电流为状态变量,对表贴式永磁同步电机有L d=L q=L,由式(1)可得PMSM的状态方程为:d i dd t=-R L i d+1L u d+ωe i q;d i qd t=-R L i q+1L u q-ωe i d-1Lωeψf㊂üþýïïïï(2)使用前向差分对电流状态方程离散化,采样周期为T,得到永磁同步电机电流预测模型为:i d(k+1)=(1-TR L)i d(k)+T L u d(k)+Tωe(k)i q(k);i q(k+1)=(1-TR L)i q(k)+T L u q(k)-Tωe(k)i d(k)-T Lψfωe(k)㊂üþýïïïïïïïï(3)1.2㊀无差拍电流预测控制原理无差拍电流预测控制的结构框图如图1所示,将电流指令值i∗(k+1)作为下一周期的电流预测值,与电机当前运行状态下的电流采样值i(k)一起代入式(3),计算使电机实际电流精确跟随指令值所需的电压矢量u(k),通过空间矢量脉冲宽度调制,生成所需要的开关信号作用于逆变器㊂速度外环仍采用经典的PI控制,所以无差拍预测控制系统依旧是双闭环系统,且与传统矢量控制结构接近,易在原有控制基础上实现㊂图1㊀PMSM无差拍电流预测控制结构框图Fig.1㊀Structure block diagram of PMSM deadbeat predictive current control根据式(3),无差拍电流预测控制的输出电压矢量方程表示如下:001电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀u d (k )=L i ∗d (k +1)-i d (k )T +Ri d (k )-Lωe (k )i q (k );u q (k )=L i ∗q (k +1)-i q(k )T+Ri q (k )+Lωe (k )i d (k )+ωe (k )ψf ㊂üþýïïïïïïïï(4)其中:R ㊁L ㊁ψf 分别代表电机电阻㊁电感和磁链参数;ωe (k )为k 时刻电角速度;i d (k )㊁i q (k )分别为k 时刻定子电流采样值的d㊁q 轴分量;i ∗d (k +1)和i ∗q (k +1)分别为k +1时刻d㊁q 轴的参考电流值,由于采样周期足够小,使用k 时刻参考电流值i ∗d(k )㊁i ∗q (k )代替㊂在2个连续的控制周期中,控制器在第1个控制周期根据当前电机的运行状态,使用控制器电机模型参数,计算出下一控制周期需要作用的电压矢量,其过程可以用式(4)表示㊂在第2个控制周期中,上一时刻计算得到的电压矢量作用于实际的电机模型,产生新的d㊁q 轴电流,其过程如下:i d (k +1)=(1-TR 0L 0)i d (k )+TL 0u d (k )+Tωe (k )i q (k );i q (k +1)=(1-TR 0L 0)i q (k )+TL 0u q (k )-Tωe (k )i d (k )-TL 0ψf0ωe (k )㊂üþýïïïïïïïïï(5)其中R 0㊁L 0㊁ψf0分别代表电机实际电阻㊁电感和磁链参数㊂将式(4)代入式(5),得到控制器电机模型参数偏离原始设计值时电流响应与给定的关系为:i d (k +1)=L L 0i ∗d (k +1)+-ΔLL 0i d(k )+ΔR L 0Ti d (k )+-ΔLL 0Tωe (k )i q (k );i q (k +1)=L L 0i ∗q (k +1)+-ΔLL 0i q (k )+ΔR L 0Ti q (k )+ΔL L 0Tωe (k )i d (k )+T L 0ωe(k )ψf ㊂üþýïïïïïïïïïïïï(6)式中ΔL ㊁ΔR ㊁Δψf 分别为控制器电机模型参数与实际参数的差值,ΔL =L -L 0,ΔR =R -R 0,ψf =ψf -ψf0㊂1.3㊀无差拍电流预测控制参数敏感性分析无差拍预测控制是一种基于电机模型的预测控制方法,这意味着无差拍预测控制器具有参数敏感性,预测模型的精度将直接影响控制性能㊂1.3.1㊀稳定性分析为讨论模型电感参数对控制器稳定性的影响,将式(6)转换到z 域㊂采用i d =0控制方式,考虑采样周期T 足够小,可得电流响应i dq 与电流给定i ∗dq 的离散域闭环传递函数为i dq(z )i ∗dq(z )=(L /L 0)zz +(L /L 0-1)㊂(7)由闭环系统稳定性条件,其闭环极点必须位于单位圆内,由此得系统稳定性条件:0<L <2L 0,即控制器模型电感小于两倍电机实际电感,若模型电感大于两倍电机实际电感,闭环极点不再位于单位圆内,导致控制电流出现振荡㊂1.3.2㊀稳态精度分析当预测模型参数与电机实际参数存在偏差时,实际电流值不能跟踪给定电流值,导致电流控制出现静差㊂为分析电气参数不准确对电机电流控制性能的影响,在电机稳定运行时,认为采样周期足够小,有i d (k +1)等于i d (k ),i q (k +1)等于i q (k ),整理式(6)得电机稳定运行时d㊁q 轴给定电流值和实际电流值受参数偏差影响的关系式为:Δi d =-ΔRT L i d (k )+ΔLL Tωe (k )i q (k );Δi q =-ΔRT L i q (k )-ΔLL Tωe (k )i d (k )-ΔψfLTωe (k )㊂üþýïïïïïï(8)其中:d 轴电流偏差Δi d =i ∗d (k +1)-i d (k +1);q 轴电流偏差Δi q =i ∗q (k +1)-i q (k +1)㊂由于采用i d =0控制策略,因此与i q 相比,i d 的作用基本可以忽略,式(8)中起主要作用的是含有电流i q 的项,因此简化为:㊀Δi d =ΔLLTωe (k )i q (k );(9)㊀Δi q =-ΔRTL i q (k )-Δψf LTωe (k )㊂(10)当电机模型参数R 不匹配时,由式(10)可以看出,若电机模型电阻大于实际电阻参数,有Δi q <0,系统稳定后q 轴电流响应i q 大于给定电流i ∗q ;反之,系统稳定后q 轴电流响应小于给定电流㊂101第9期刘㊀刚等:基于参数在线辨识的高速永磁电机无差拍电流预测控制当电机模型参数L 不匹配时,由式(9)可知,若模型电感大于电机实际电感参数,有Δi d >0,系统稳定后会出现d 轴电流响应i d 要小于给定值i ∗d的静态误差;反之,系统稳定后d 轴电流响应要大于给定值㊂当电机模型参数ψf 不匹配时,由式(10)可得,若模型磁链大于实际磁链参数,有Δi q <0,系统稳定后q 轴电流响应i q 大于给定电流i ∗q ;反之,系统稳定后q 轴电流响应小于给定电流㊂2㊀基于滑模观测器转子位置估计表贴式永磁同步电机在两相静止坐标系下的电压方程为u αu βéëêêùûúú=R +p L 0R +p L []i αi βéëêêùûúú+E αE βéëêêùûúú㊂(11)其中:p =d /d t ,为微分算子;u α㊁u β与i α㊁i β分别是定子电压和定子电流;E α㊁E β为扩展反电动势,且满足E αE βéëêêùûúú=ωe ψf -sin θe cos θe éëêêùûúú㊂(12)式中θ为转子角位置㊂由式(12)可以看出,扩展反电动势包含电机转子位置和转速的全部信息,为便于应用滑模观测器估计反电动势,基于PMSM 定子电流方程的滑模观测器设计如下:d d t i ^αi ^βéëêêùûúú=-R L i ^αi ^βéëêêùûúú+1Lu αu βéëêêùûúú-v αv βéëêêùûúú()㊂(13)采用反向差分变换法可得:i ^α(k +1)=Ai ^α(k )+B (u α(k )-v α(k ));i ^β(k +1)=Ai ^β(k )+B (u β(k )-v β(k ))㊂}(14)式中:A =exp(-R /LT );B =(1-A )/R ;i ^α㊁i ^β为定子电流观测值㊂设计滑模控制律为v αv βéëêêùûúú=k sgn(I α)k sgn(I β)éëêêùûúú㊂(15)其中:I α=i ^α-i α㊁I β=i ^β-i β为电流观测误差;sgn()为符号函数;k 为滑模增益,且满足要求:k >max{a ,b },且:a =-R |I α|+E αsgn(I α);b =-R |I β|+E βsgn(I β)㊂}(16)当观测器的状态变量达到滑模面I α=0㊁I β=0后,观测器状态将一直保持在滑模面上,由滑模控制的等效原理,估计的反电势表示为E αE βéëêêùûúú=νανβéëêêùûúúeq =k sgn (I α)eq k sgn (I β)eq éëêêùûúú㊂(17)获取反电动势之后,通过反正切函数或者锁相环即可提取转子位置信息㊂在电机高速运行时,采用滑模观测器实现转子位置估计,此时,式(16)中含有反电动势的项远大于另一项,因此含反电动势的项占据主导地位,由式(12)可知,该项与永磁体磁链有关,若将磁链辨识结果反馈至滑模系数中,可以减小位置估计误差㊂此外,式(14)含有与电阻㊁电感有关的项,若参数存在偏差在一定程度上也会降低位置估计精度,因此实现多参数在线辨识是解决参数不匹配问题㊁提高转子位置估计精度的重要手段㊂3㊀PMSM 多参数在线辨识永磁同步电机参数辨识的本质是利用输入㊁输出数据辨识电机参数㊂目前常用的参数辨识方法是递推最小二乘法,但是这种方法只考虑观测量误差,未考虑系数矩阵误差㊂另外,PMSM 数学模型的状态空间秩为2,要辨识电阻㊁电感和磁链3个参数存在方程欠秩问题,因此提出在3种时间尺度下采用TLS 方法在线分步辨识电气参数㊂3.1㊀TLS 辨识算法在实际应用中,系数矩阵误差普遍存在,通常采用最小二乘法或者RLS 辨识方法只考虑观测量误差,但是忽略了系数矩阵误差,因此得到的参数估计值不再是最优无偏估计,降低了辨识精度和响应速度㊂而TLS 算法不仅考虑到观测量误差,同时考虑了其余算法容易忽略的系数矩阵误差,因此,TLS 在辨识结果的精度方面具有更加优秀的性能,其超调量相对RLS 有所减小,且具有较快的响应速度和收敛速度㊂为提高参数辨识的准确性,选用TLS 辨识算法进行研究㊂对于TLS 回归参数的估计,常用的直接求解方法是奇异值分解,但求解计算复杂度较高,因此采用一种递归的TLS EXIN 神经元算法求解TLS 问题㊂3.2㊀TLS 多参数辨识架构如图2所示为PMSM 多参数辨识整体架构,其中,首先对变化较快的电感参数进行估计,然后估计定子电阻,最后估计变化较慢的磁链,辨识出的电感参数可以用于更新电阻和磁链,而辨识所得电阻参数可以用于更新电感和磁链,基于上述方法的多参201电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀数在线辨识同时考虑了观测量和系数矩阵的误差,在保证辨识精度的同时解决了多参数在线辨识的欠秩问题㊂图2㊀PMSM 多参数辨识整体架构Fig.2㊀Overall architecture of multi parameteridentification of PMSM3.3㊀基于TLS 的多参数在线辨识算法当系数矩阵和观测向量都包含误差时,基于总体最小二乘算法的平差模型要优于普通的最小二乘算法,表示输入输出关系的回归方程可描述为b +E b =(A +E A )x ㊂(18)其中:b 为系统观测值向量;E b 为系统观测误差向量;A 为系数矩阵;E A 为系数误差矩阵;x 为待估计参数向量㊂TLS 问题归结为解决以下优化问题:x ^=argmin A ^,b^[A ;b ]-[A ^;b ^] F ㊂(19)其中㊃ F 表示矩阵的Frobenius 范数㊂TLS EXIN 神经元通过递归方式解决TLS 问题,根据文献[23],通过最小化下式所示成本函数,可以得到TLS 的解,即:E TLS (x )=(Ax -b )T (Ax -b )1+x T x=[A ;b ][x T;-1]T22[x T ;-1]T 22=ðmi =1E (i )(x );(20)ðmi =1E i(x )=(a T i x -b i )21+x T x =ðnj =1(a ij x j-b i )21+x T x=δ21+x T x㊂(21)TLS EXIN 神经元是一个线性单元,具有n 个输入(向量a i ),n 个权重(向量x ),一个输出(标量y i =a T i x -b i )和一个训练误差(标量δ(k )),该方法对应的最速下降离散时间学习律为x (k +1)=x (k )-α(k )γ(k )a i +[α(k )γ2(k )]x (k )㊂(22)其中α(k )为学习率,是一个正常数函数,γ(k )定义为γ(k )=δ(k )1+x T (k )x (k )㊂(23)式中δ(k )是一个时变函数,它依赖于每个采样时间计算的残差,定义为δ(k )=a T (k )x (k )-b (k )1+x T (k )x (k )㊂(24)对式(1)中d 轴电压方程采用后向差分离散化,首先辨识电感参数,整理电感辨识模型为a L (k )x 1=b L (k )㊂(25)其中a L ㊁x 1㊁b L 分别为系数矩阵㊁待辨识参数以及观测值向量,有:b L (k )=i d (k )-i d (k -1)-Tωe (k -1)i q (k -1);a L (k )=u d (k -1)-Ri d (k -1);x 1=T /L ㊂üþýïïïïï(26)其次辨识电阻参数,根据离散化的d 轴电压方程整理辨识模型为a R (k )x 2=b R (k )㊂(27)其中a R ㊁x 2㊁b R 分别为:b R (k )=u d (k -1)+ωe (k -1)i q (k -1)L -[i d (k )-i d (k -1)]L /T ;a R (k )=i d (k -1);x 2=R ㊂üþýïïïïï(28)最后辨识磁链参数,根据离散化的q 轴电压方程整理辨识模型为a ψf (k )x 3=b ψf (k )㊂(29)其中:b ψf (k )=u q (k -1)-[i q (k )-i q (k -1)]L /T -Ri q (k -1)-ωe (k -1)i d (k -1)L ;a ψf (k )=ωe (k -1);x 3=ψf T ㊂üþýïïïïï(30)为保证解的收敛性,应使辨识参数初值x (0)=301第9期刘㊀刚等:基于参数在线辨识的高速永磁电机无差拍电流预测控制0,在辨识电感参数时先假设式(26)所需电阻参数为常数,利用TLS 辨识出电感稳态值后,再依次辨识电阻和磁链,式(28)中所需电感参数采用式(26)辨识结果,式(30)中所需电阻和电感参数采用式(26)和式(28)辨识结果,当本次电机参数辨识结果与上一次参数辨识结果之间的相对误差小于1ɢ,即可认为所辨识参数已经达到精度要求,此时可以停止迭代更新㊂在中高转速阶段,采用基于反电动势的SMO 实现转子位置估计,在启动阶段,电机的初始定位通过给定d 轴电压实现强制定位,并且利用q 轴电压开环拖动转子㊂如图3所示为基于参数辨识的无位置传感器高速永磁电机电流预测控制系统框图,在启动阶段通过电压开环拖动转子,当转速达到600r /min 时,切换到SMO 进行转子位置估计㊂采用三层TLS 算法分别对表贴式永磁同步电机的电感㊁电阻和磁链参数进行在线辨识,并将辨识结果分别反馈到电流环无差拍预测控制器及滑模观测器中,实现电流控制稳态性能和转子位置估计准确性的提高㊂图3㊀基于参数辨识的无传感器PMSM 无差拍电流预测控制系统框图Fig.3㊀Block diagram of PMSM deadbeat predictivecurrent control system without sensor based on parameter identification4㊀实验结果及分析实验平台如图4所示,使用一台600W,1对磁极的表贴式永磁同步电机,控制芯片选用TI 公司的TMS320F28069,实验所用负载类型为叶轮负载,并且在转子轴上加装一个自研的增强型磁编码器以在实验中进行转子位置估计的准确性对比㊂图4㊀实验平台Fig.4㊀Experimental platform实验使用的永磁同步电机参数如表1所示㊂表1所示电机定子电阻初始值和d㊁q 轴电感初始值采用IM3536LCR 测试仪离线测量得到,将LCR 测试仪的探头分别接到电机三相线和中线上,即可获得电机的相电阻和相电感㊂而永磁体磁链初始值则通过反拖电机并根据下式计算获得,反拖转速为100r /min,计算得到磁链值为0.0029Wb:ψf =E p ωe =2E lv 3ωe=106πp K E ㊂(31)其中:E p 是空载相反电势幅值;E lv 是线反电动势有效值;K E 是线反电动势常数;p 是极对数㊂表1㊀永磁同步电机参数Table 1㊀Parameters of permanent magnet synchronousmotor㊀㊀㊀参数数值额定功率P /W 600额定转速ω/(r /min)10000额定转矩T /(N㊃m)0.573直流母线电压U dc /V 28转动惯量J /(kg㊃m 2)0.003定子电阻R /Ω0.022d㊁q 轴定子电感L /mH 0.023永磁体磁链ψf /Wb 0.0029极对数p14.1㊀TLS 与RLS 参数辨识比较实验结果为对比TLS 和RLS 两种算法的参数辨识效果,在电机稳定运行至10000r /min 之后的0.05s 加入辨识算法,如图5所示为采用两种算法的参数辨识结果,表2为采用两种算法的辨识结果及与标称值之间的误差㊂401电㊀机㊀与㊀控㊀制㊀学㊀报㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀第27卷㊀图5㊀TLS与RLS辨识结果对比Fig.5㊀Comparison of TLS and RLS identification results表2㊀电气参数辨识结果对比Table2㊀Comparison of electrical parameter identification results参数标称值TLS辨识值TLS辨识误差RLS辨识值RLS辨识误差电感/mH0.0230.02280.87%0.02267 1.435%电阻/Ω0.0220.021840.727%0.0217 1.364%磁链/Wb0.00290.002890.345%0.00293 1.034%由图5以及表2可以看到,对于电感参数的辨识,RLS算法在辨识开始阶段波动较大,TLS辨识算法的收敛速度明显优于RLS,其辨识误差为0.87%,约为RLS辨识误差的二分之一;对于电阻参数的辨识,基于TLS的辨识算法在响应速度和辨识精度方面要优于RLS,其辨识误差为0.727%,而RLS辨识误差为1.364%;对于磁链参数的辨识,相比RLS算法,基于TLS算法的辨识误差更小,为0.345%㊂通过上述图表分析可以看出,TLS算法在表贴式永磁同步电机参数辨识过程中具有更快的收敛速度和更小的辨识误差㊂4.2㊀加入TLS参数辨识对电流控制性能的影响为验证1.3节中DPCC的参数敏感性,同时对比验证TLS辨识算法的有效性,速度环采用传统的PI控制,电机负载转矩在额定负载0.573N㊃m,转速为额定转速10000r/min㊂在10000r/min工况运行时,设置电机模型参数与本体参数不匹配,并在1.5s分别加入2种辨识算法,将辨识结果反馈至电流预测控制器㊂由于电机本体的参数不能任意修改设置,因此需要改变控制程序中的电阻㊁电感和磁链参数,以实现相应的参数不匹配,从而完成参数敏感性验证,同时通过RLS和TLS两种辨识算法的加入,对比验证TLS算法对提高电流稳态控制性能的有效性㊂图6为TLS与RLS两种算法的控制器电流响应对比,表3为TLS与RLS的dq轴电流响应误差对比㊂表3㊀两种辨识算法dq轴电流响应误差对比Table3㊀Comparison of dq axis current response errors be-tween two identification algorithms参数偏差轴原电流偏差/ATLS电流偏差/ARLS电流偏差/A R0=2R q轴0.9870.3050.607L0=2L d轴0.40780.1230.210ψf0=2ψf q轴 1.420.1420.433由图6结合表3可知,1.5s之前预测控制器参数与电机实际参数之间存在偏差,导致dq轴电流响应存在静差,电流静差情况与1.3节理论分析一致,且磁链偏差对控制电流影响最大,在1.5s时,分别采用TLS和RLS进行参数辨识,并将辨识结果注入无差拍电流预测控制器中,图6(a)㊁(c)㊁(e)为采用TLS的电流响应波形,图6(b)㊁(d)㊁(f)为采用RLS的电流响应波形㊂当实际磁链为给定值两倍时,q轴电流偏差可达1.42A,1.5s加入TLS辨识501第9期刘㊀刚等:基于参数在线辨识的高速永磁电机无差拍电流预测控制。

动力学参数辨识英文

动力学参数辨识英文Dynamics Parameter Identification.Dynamics parameter identification is a crucial processin various engineering applications, ranging from aerospace engineering to civil engineering. It involves theestimation of unknown parameters in dynamic systems basedon experimental data or system observations. These parameters are essential for understanding the behavior of the system and predicting its response to external excitations.The process of dynamics parameter identificationtypically involves several steps, including data collection, model development, parameter estimation, and validation. Each step requires careful consideration and may involve complex mathematical techniques and computational algorithms.1. Data Collection.The first step in dynamics parameter identification is to collect relevant data from the system. This data can be obtained through experiments, simulations, or real-time monitoring of the system's behavior. The quality and quantity of data collected directly impact the accuracy and reliability of the parameter identification results. Therefore, it is crucial to ensure that the data is representative of the system's dynamics and covers a wide range of operating conditions.2. Model Development.Once the data is collected, the next step is to develop a mathematical model that describes the system's dynamics. This model should capture the essential features of the system and be capable of predicting its response to external excitations. The model may be a simple linear model or a complex nonlinear model, depending on the nature of the system and the level of detail required for parameter identification.3. Parameter Estimation.The next step is to estimate the unknown parameters in the developed model using the collected data. This step involves solving a set of equations or optimization problems to find the parameter values that best fit the observed data. Various estimation techniques can be employed, including least squares methods, maximum likelihood estimation, and Bayesian inference. The choice of estimation technique depends on the nature of the model, the type of data available, and the desired accuracy of the parameter estimates.4. Validation.After estimating the parameters, it is crucial to validate the identified model against the original data or additional experimental data. This validation step helps assess the accuracy and reliability of the identified parameters and ensures that the model can indeed predict the system's behavior. If the validation results are satisfactory, the identified parameters can be used forfurther analysis, design, or control of the system.Challenges and Considerations in Dynamics Parameter Identification.Dynamics parameter identification, while a crucial process, also faces several challenges and considerations.1. Noise and Uncertainty.Real-world data often contains noise and uncertainty, which can affect the accuracy of parameter estimation. To address these issues, it is necessary to employ robust estimation techniques that can handle noisy and uncertain data effectively. This may involve the use of regularization techniques, noise models, or advanced optimization algorithms.2. Model Complexity.The complexity of the system model can significantly affect the parameter identification process. Simple modelsmay not capture all the essential features of the system, leading to inaccurate parameter estimates. On the other hand, overly complex models can make the estimation process computationally intractable. Therefore, it is crucial to strike a balance between model complexity and accuracy.3. Experimental Design.The design of experiments for data collection is also crucial for successful parameter identification. The experiments should be designed to excite the system in a way that allows for accurate estimation of the parameters. This may involve careful consideration of the excitation signals, measurement setup, and operating conditions.4. Identification of Multiple Parameters.In some cases, there may be multiple unknown parameters in the system model. Estimating these parameters simultaneously can be a challenging task, as it may require solving highly nonlinear and coupled equations. Advanced estimation techniques, such as multi-objective optimizationor genetic algorithms, may be required to handle such complex estimation problems.Conclusion.Dynamics parameter identification is a fundamental task in engineering analysis and design. It involves estimating unknown parameters in dynamic systems based on experimental data or system observations. The process involves data collection, model development, parameter estimation, and validation. Successful parameter identification requires careful consideration of various challenges and considerations, such as noise and uncertainty, model complexity, experimental design, and identification of multiple parameters. By addressing these challenges and employing appropriate estimation techniques, engineers can obtain accurate and reliable parameter estimates that support effective system analysis, design, and control.。

实践者指南模态试验实用技术

实践者指南模态试验实用技术英文回答：Practitioner's Guide to Practical Techniques for Modal Experimentation.Modal experimentation is a valuable technique used in various fields such as engineering, physics, and biology to study the dynamic characteristics of a system. It involves exciting the system with a known input and measuring the response to determine its modal properties, such as natural frequencies, damping ratios, and mode shapes.In this practitioner's guide, we will discuss some practical techniques for modal experimentation that can be applied in a wide range of applications. These techniques are designed to provide accurate and reliable results while minimizing experimental errors.1. Excitation Methods:There are several methods available for exciting a system during modal experimentation. Some common techniques include impact hammer testing, shaker testing, and acoustic excitation. Each method has its pros and cons, and the choice depends on the specific requirements of the experiment.2. Measurement Techniques:Accurate measurement of the system's response iscrucial for obtaining reliable modal parameters. Various measurement techniques can be used, such as accelerometers, laser vibrometers, and strain gauges. It is important to carefully select the appropriate measurement technique based on the system under study and the desired accuracy.3. Data Acquisition and Analysis:Data acquisition systems play a vital role in modal experimentation. These systems are used to capture the response signals from the sensors and convert them intodigital data for further analysis. Advanced signal processing techniques, such as frequency domain analysis and time-domain analysis, can be employed to extract modal parameters from the acquired data.4. Experimental Setup and Instrumentation:Proper experimental setup and instrumentation are critical for obtaining accurate and repeatable results. This includes ensuring proper sensor placement, minimizing noise and interference, and calibrating the measurement devices. It is also important to consider the environmental conditions and any potential disturbances that may affect the experiment.5. Modal Parameter Identification:The ultimate goal of modal experimentation is to identify the modal parameters of the system, such as natural frequencies, damping ratios, and mode shapes. Various techniques, such as frequency response functions, modal analysis, and curve fitting, can be employed formodal parameter identification. It is essential tocarefully analyze the data and validate the results to ensure their accuracy.In conclusion, modal experimentation is a powerful technique for studying the dynamic characteristics of a system. By following the practical techniques discussed in this guide, practitioners can conduct modal experiments effectively and obtain reliable results. It is important to pay attention to experimental setup, measurement techniques, data acquisition, and analysis to ensure accurate modal parameter identification.中文回答：实践者指南，模态试验实用技术。

基于希尔伯特变换结构模态参数识别

基于希尔伯特变换结构模态参数识别范兴超;纪国宜【摘要】应用HHT方法对GARTEUR飞机模型模态参数进行识别，通过采用多通带滤波器对信号进行滤波，较好的解决模态混叠问题，采用NExT法对信号预处理，由EMD分解获得较准确的各阶固有模态函数分量（IMF），在EMD分解中使用镜像延拓方法对极值点进行处理来抑制端点效应，然后将分解得到的IMF分量进行希尔伯特变换并结合ITD法识别出各阶固有频率和阻尼比。

最后对悬臂梁进行数值仿真模拟，并将模态参数识别结果和理论值进行对比，并运用此方法进一步识别GARTEUR飞机模型固有模态参数。

%The HHT method is applied to the modal parameter identification of GARTEUR plane model. The multi-channel filter is applied to process the signal for solving the problem of modal aliasing. Meanwhile, the NExT method is adopted to get more accurate individual-order intrinsic mode functions (IMF) form the EMD decomposition. The mirror continuation method is applied to process extreme value points for suppressing the endpoint effect. Then, the natural frequency of each order and the damping ratio are identified with Hilbert transform and ITD method. The numerical simulation of a cantilever beam is carried out and the simulation results are compared with the theoretical results. Finally, the intrinsic modal parameters of the GARTEUR plane model are recognized with this method.【期刊名称】《噪声与振动控制》【年(卷),期】2014(000)003【总页数】5页(P52-56)【关键词】振动与波;模态参数识别;Hilbert-Huang变换;模态阻尼比;镜像延拓【作者】范兴超;纪国宜【作者单位】南京航空航天大学机械结构力学及控制国家重点实验室，南京210016;南京航空航天大学机械结构力学及控制国家重点实验室，南京 210016【正文语种】中文【中图分类】O241.82Hilbert-Huang变换[1]（HHT）是1998年美国华裔科学家Huang提出的一种新的数据处理方法，该方法已应用到地球物理学领域，并取得较好的效果，其主要是由经验模态分解（Empirical Mode Decomposition）和Hilbert变换（Hilbert Transform）两个部分组成，其主要思想是EMD分解[5]。

机械工程及自动化专业外文翻译--应用坐标测量机的机器人运动学姿态的标定翻译

外文原文：Full-Pose Calibration of a Robot Manipulator Using a Coordinate-Measuring MachineThe work reported in this article addresses the kinematic calibration of a robot manipulator using a coordinate measuring m a c h i n e(C M M)w h i c h i s a b l e t o o b t a i n t h e f u l l p o s e o f t h e e n d-e f f e c t o r.A k i n e m a t i c m o d e l i s d e v e l o p e d f o r t h e manipulator, its relationship to the world coordinate frame and the tool. The derivation of the tool pose from experimental measurements is discussed, as is the identification methodolo gy.A complete simulation of the experiment is performed, allowing the observation strategy to be defined. The experimental work is described together with the parameter identification and accuracy verification. The principal conclusion is that the m et ho d is a ble t o calibrate the robot succes sful ly, with a resulting accuracy approaching that of its repeatability.Keywords: Robot calibration; Coordinate measurement; Parameter identification; Simulation study; Accuracy enhancement 1. IntroductionIt is wel l known tha t robo t manip ula tors t ypical ly ha ve reasonable repeatability (0.3 ram), yet exhibit poor accuracy(10.0m m).T h e p r o c e s s b y w h i c h r o b o t s m a y b e c a l i b r a t e di n o r d e r t o a c h i e v e a c c u r a c i e s a p p r o a c h i n g t h a t o f t h e m a n i p u l a t o r i s a l s o w e l l u n d e r s t o o d .I n t h e c a l i b r a t i o n process, several sequential steps enable the precise kinematic p ar am et er s o f th e m an ip u l ato r to b e ide nti fi ed,l ead ing t o improved accuracy. These steps may be described as follows: 1. A kinematic model of the manipulator and the calibration process itself is developed and is usually accomplished with s t a n d a r d k i n e m a t i c m o d e l l i n g t o o l s.T h e r e s u l t i n g m o d e l i s u s e d t o d e f i n e a n e r r o r q u a n t i t y b a s e d o n a n o m i n a l (m a n u f a c t u r e r's)k i n e m a t i c p a r a m e t e r s e t,a n d a n u n k n o w n, actual parameter set which is to be identified.2. Ex pe ri me n ta l m ea su re m e nts o f th e rob ot po se (p art ial o r complete) are taken in order to obtain data relating to the actual parameter set for the robot.3.The actual kinematic parameters are identified by systematicallyc h a n g i n g t h e n o m i n a l p a r a m e t e r s e t s o a s t o r ed u ce t h e e r r o r q u a n t i t y d ef i n e d i n t h e m o d e l l i ng ph a s e.O n e a p p r o a c h t o a c hi e v i n g t h i s i d e n t i f i c a t i o n i s d e t e r m i n i n g t h e a n a l y t i c a l d i f f e r e n t i a l r e l a t i o n s h i p b e t w e e n t h e p o s e v a r i a b l e s P a n d t h e k i n e m a t i c p a r a m e t e r s K i n t h e f o r m of a Jacobian,and then inverting the equation to calculate the deviation of t h e k i n e m a t i c p a r a m e t e r s f r o m t h e i r n o m i n a l v a l u e sAlternatively, the problem can be viewed as a multidimensional o p t i m i s a t i o n t a s k,i n w h i c h t h e k i n e m a t i c p a r a m e t e r set is changed in order to reduce some defined error function t o z e r o.T h i s i s a s t a n d a r d o p t i m i s a t i o n p r o b l e m a n d m a y be solved using well-known methods.4. The final step involves the incorporation of the identified k i n e m a t i c p a r a m e t e r s i n t h e c o n t r o l l e r o f t h e r o b o t a r m, the details of which are rather specific to the hardware of the system under study.This paper addresses the issue of gathering the experimental d a t a u s e d i n t h e c a l i b r a t i o n p r o c e s s.S e v e r a l m e t h o d s a r e available to perform this task, although they vary in complexity, c o s t a n d t h e t i m e t a k e n t o a c q u i r e t h e d a t a.E x a m p l e s o f s u c h t e c h n i q u e s i n c l u d e t h e u s e o f v i s u a l a n d a u t o m a t i c t h e o d o l i t e s,s e r v o c o n t r o l l e d l a s e r i n t e r f e r o m e t e r s, a c o u s t i c s e n s o r s a n d v i d u a l s e n s o r s .A n i d e a l m e a s u r i n g system would acquire the full pose of the manipulator (position and orientation), because this would incorporate the maximum information for each position of the arm. All of the methods m e n t i o n e d a b o v e u s e o n l y t h e p a r t i a l p o s e,r e q u i r i n g m o r ed a t a t o be t a k e nf o r t h e c a l i b r a t i o n p r o c e s s t o p r o c e e d.2. TheoryIn the method described in this paper, for each position in which the manipulator is placed, the full pose is measured, although several intermediate measurements have to be taken in order to arrive at the pose. The device used for the pose m e a s u r e m e n t i s a c o o r d i n a t e-m e a s u r i n g m a c h i n e(C M M), w h i c h i s a t h r e e-a x i s,p r i s m a t i c m e a s u r i n g s y s t e m w i t h a q u o t e d a c c u r a c y o f0.01r a m.T h e r o b o t m a n i p u l a t o r t o b e c a l i b r a t e d,a P U M A560,i s p l a c e d c l o s e t o t h e C M M,a n d a special end-effector is attached to the flange. Fig. 1 shows the arrangement of the various parts of the system. In this s e c t i o n t h e k i n e m a t i c m o d e l w i l l b e d e v e l o p e d,t h e p o s e estimation algorithms explained, and the parameter identification methodology outlined.2.1 Kinematic ParametersIn this section, the basic kinematic structure of the manipulator will be specified, its relation to a user-defined world coordinatesystem discussed, and the end-point toil modelled. From these m o d e l s,t h e k i n e m a t i c p a r a m e t e r s w h i c h m a y b e i d e n t i f i e d using the proposed technique will be specified, and a method f o r d e t e r m i n i n g t h o s e p a r a m e t e r s d e s c r i b e d. The fundamental modelling tool used to describe the spatial relationship between the various objects and locations in the m a n i p u l a t o r w o r k s p a c e i s t h e D e n a v i t-H a r t e n b e r g m e t h o d ,w i t h m o d i f i c a t i o n s p r o p o s e d b y H a y a t i,M o o r i n g a n d W u t o a c c o u n t f o r d i s p r o p o r t i o n a l m o d e l s w he n tw o co n se cu t iv e jo i n t a x e s ar e nom ina ll y p a r all el. A s s h o w n i n F i g.2,t h i s m e t h o d p l a c e s a c o o r d i n a t e f r a m e o neach object or manipulator link of interest, and the kinematics a r e d e f i n e d b y t h e h o m o g e n e o u s t r a n s f o r m a t i o n r e q u i r e d t o change one coordinate frame into the next. This transformation takes the familiar formT h e a b o v e e q u a t i o n m a y b e i n t e r p r e t e d a s a m e a n s t o t r a n s f o r m f r a m e n-1i n t o f r a m e n b y m e a n s o f f o u r o u t o f t h e f i v e o p e r a t i o n s i n d i c a t e d.I t i s k n o w n t h a t o n l y f o u r transformations are needed to locate a coordinate frame with r es pect to the p revious one. Whe n consecutiv e ax es are not parallel, the value of/3. is defined to be zero, while for the case when consecutive axes are parallel, d. is the variable chosen to be zero.W h e n c o o r d i n a t e f r a m e s a r e p l a c e d i n c o n f o r m a n c e w i t h the modified Denavit-Hartenberg method, the transformations given in the above equation will apply to all transforms of o n e f r a m e i n t o t h e n e x t,a n d t h e s e m a y b e w r i t t e n i n a g e n e r i c m a t r i x f o r m,w h e r e t h e e l e m e n t s o f t h e m a t r i x a r e functions of the kinematic parameters. These parameters are simply the variables of the transformations: the joint angle 0., the common normal offset d., the link length a., the angle o f tw is t a., a nd th e an g l e /3.. Th e mat rix f orm i s u suall y expressed as follows:For a serial linkage, such as a robot manipulator, a coordinate frame is attached to each consecutive link so that both the instantaneous position together with the invariant geometry a r e d e s c r i b e d b y t h e p r e v i o u s m a t r i x t r a n s f o r m a t i o n.'T h etransformation from the base link to the nth link will therefore be given byF i g.3s h o w s t h e P U M A m a n i p u l a t o r w i t h t h e D e n a v i t-H a r t e n b e r g f r a m e s a t t a c h e d t o e a c h l i n k,t o g e t h e r with world coordinate frame and a tool frame. The transformation f r o m t h e w o r l d f r a m e t o t h e b a s e f r a m e o f t h e manipulator needs to be considered carefully, since there are potential parameter dependencies if certain types of transforms a r e c h o s e n.C o n s i d e r F i g.4,w h i c h s h o w s t h e w o r l d f r a m e x w,y,,z,,t h e f r a m e X o,Y o,z0w h i c h i s d e f i n e d b y a D H t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e f i r s t j o i n t a x i s o f t h e m a n i p u l a t o r,f r a m e X b,Y b,Z b,w h i c h i s t h e P U M Amanufacturer's defined base frame, and frame xl, Yl, zl which is the second DH frame of the manipulator. We are interested i n d e t e r m i n i n g t h e m i n i m u m n u m b e r o f p a r a m e t e r s r e q u i r e d to move from the world frame to the frame x~, Yl, z~. There are two transformation paths that will accomplish this goal: P a t h1:A D H t r a n s f o r m f r o m x,,y,,z,,t o x0,Y o,z o i n v o l v i n g f o u r p a r a m e t e r s,f o l l o w e d b y a n o t h e r t r a n s f o r m f r o m x o,Y o,z0t o X b,Y b,Z b w h i c h w i l l i n v o l v e o n l y t w o parameters ~b' and d' in the transformFinally, another DH transform from xb, Yb, Zb to Xt, y~, Z~ w hi ch i nv ol v es f o ur p ar a m ete r s e xc ept t hat A01 a n d 4~' ar e b o t h a b o u t t h e a x i s z o a n d c a n n o t t h e r e f o r e b e i d e n t i f i e d independently, and Adl and d' are both along the axis zo and also cannot be identified independently. It requires, therefore, o nl y ei gh t i nd ep e nd en t k i nem a t ic p arame ter s to g o fr om th e world frame to the first frame of the PUMA using this path. Path 2: As an alternative, a transform may be defined directly from the world frame to the base frame Xb, Yb, Zb. Since this is a frame-to-frame transform it requires six parameters, such as the Euler form:T h e f o l l o w i n g D H t r a n s f o r m f r o m x b,Y b,z b t O X l,Y l,z l would involve four parameters, but A0~ may be resolved into 4~,, 0b, ~, and Ad~ resolved into Pxb, Pyb, Pzb, reducing theparameter count to two. It is seen that this path also requires e i g h t p a r a m e t e r s a s i n p a t h i,b u t a d i f f e r e n t s e t.E i t h e r o f t h e a b o v e m e t h o d s m a y b e u s e d t o m o v e f r o m t h e w o r l d f r a m e t o t h e s e c o n d f r a m e o f t h e P U M A.I n t h i s w o r k,t h e s e c o n d p a t h i s c h o s e n.T h e t o o l t r a n s f o r m i s a n E u l e r t r a n s f o r m w h i c h r e q u i r e s t h e s p e c i f i c a t i o n o f s i x parameters:T he total n umber of paramete rs u sed in the k inem atic model becomes 30, and their nominal values are defined in Table 1.2.2 Identification MethodologyThe kinematic parameter identification will be performed as a multidimensional minimisation process, since this avoids the calculation of the system Jacobian. The process is as follows: 1. Be gi n wi t h a g ue ss s e t of k in em atic par am ete r s, s uch a s the nominal set.2. Select an arbitrary set of joint angles for the PUMA.3. Calculate the pose of the PUMA end-effector.4.M e a s u r e t h e a c t u a l p o s e o f t h e P U M A e n d-e f f e c t o r f o r t he s am e se t o f j oi nt a n g les.In g enera l, th e m e a sur ed an d predicted pose will be different.5. Mo di fy t h e ki n em at ic p ara m e te rs in a n o rd erl y man ner i n o r d e r t o b e s t f i t(i n a l e a s t-s q u a r e s s e n s e)t h e m e a s u r e d pose to the predicted pose.The process is applied not to a single set of joint angles but to a number of joint angles. The total number of joint angles e t s r e q u i r e d,w h i c h a l s o e q u a l s t h e n u m b e r o f p h y s i c a l measurement made, must satisfyK p i s t h e n u m b e r o f k i n e m a t i c p a r a m e t e r s t o b e i d e n t i f i e d N i s t h e n u m b e r o f m e a s u r e m e n t s(p o s e s)t a k e n D r r e p r e s e n t s t h e n u m b e r o f d e g r e e s o f f r e e d o m p r e s e n t i n each measurement.In the system described in this paper, the number of degrees of freedom is given bysince full pose is measured. In practice, many more measurements s h o u l d b e t a k e n t o o f f s e t t h e e f f e c t o f n o i s e i n t h e e xp er im en ta l m ea s ur em en t s. T h e o pt imisa tio n pro c e dur e use d is known as ZXSSO, and is a standard library function in the IMSL package .2.3 Pose MeasurementIt is apparent from the above that a means to determine the f u l l p o s e o f t h e P U M A i s r e q u i r e d i n o r d e r t o p e r f o r m t h e calibration. This method will now be described in detail. The end-effector consists of an arrangement of five precisiontooling b a l l s a s s h o w n i n F i g. 5.C o n s i d e r t h e c o o r d i n a t e s o f the centre of each ball expressed in terms of the tool frame (Fig. 5) and the world coordinate frame, as shown in Fig. 6. T h e r e l a t i o n s h i p b e t w e e n t h e s e c o o r d i n a t e s m a y b e w r i t t e n as:w he re P i' i s t he 4 x 1 c o lum n ve ct or of th e coo r d ina tes o f the ith ball expressed with respect to the world frame, P~ is t he 4 x 1 c o lu mn ve ct or o f t h e c oo rdina tes o f t h e it h bal l expressed with respect to the tool frame, and T is the 4 • 4 h o m o g e n i o u s t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e t o o l frame.The n may be foun d, a n d use d as th e m easure d pose in t he calibration process. It is not quite that simple, however, since it is not possible to invert equation (11) to obtain T. The a bo ve proce ss is performed f or t he four ball s, A, B, C and D, and the positions ordered as:or in the form:S i n c e P',T a n d P a r e a l l n o w s q u a r e,t h e p o s e m a t r i x m a y be obtained by inversion:I n pr ac ti ce it m a y be d i f fic u l t fo r the CM M to a c ces s fou r b a i l s t o d e t e r m i n e P~w h e n t h e P U M A i s p l a c e d i n c e r t a i n configurations. Three balls are actually measured and a fourth ball is fictitiously located according to the vector cross product:R e g a r d i n g t h e d e t e r m i n a t i o n o f t h e c o o r d i n a t e s o f t h ec e n t r e o f a b a l l b a s ed o n me a s u r e d p o i n t s o n i t s s u rf a c e, n o a n a l y t i c a l p r o c e d u r e s a r e a v a i l a b l e.A n o t h e r n u m e r i c a l optimisation scheme was used for this purpose such that the penalty function:w a s m i n i m i s e d,w h e r e(u,v,w)a r e t h e c o o r d i n a t e s o f t h e c e n t r e o f t h e b a l l t o h e d e t e r m i n e d,(x/,y~,z~)a r e t h e coordinates of the ith point on the surface of the ball and r i s th e ba ll di am e te r. I n the t es ts perf orm ed, i t was foun d sufficient to measure only four points (i = 4) on the surface to determine the ball centre.中文译文：应用坐标测量机的机器人运动学姿态的标定这篇文章报到的是用于机器人运动学标定中能获得全部姿态的操作装置——坐标测量机（CMM）。

基于变频器的异步电机离线参数辨识

基于变频器的异步电机离线参数辨识段亮;莫锦秋;曹家勇【摘要】分析了基于变频器控制的异步电机参数辨识方案.对传统测定子电阻的直流试验方法进行改进,提出了一种消除功率开关器件压降影响的定子电阻辨识方法.通过向电机施加单相电压信号,得到了电机参数的计算公式.针对单相试验中电机定子电流准幅值和相位的对电机参数精确估计的需求,提出了一种基于离散傅里叶变换测量电机定子电流幅值与初始相位的方法,所述算法考虑到由于非同步测量误差以及频谱泄漏和栅栏效应引起的离散傅里叶变换计算误差的修正问题.MATLAB/Simulink仿真结果证实了所提方法的有效性.%A motor parameter identification method to asynchronous motor controlled by frequency converter was proposed. First, an improved method was proposed to identify the stator resister, compared with the traditional DC test new method could eliminate the influence of voltage drop caused by power switching device. Second, the calculate formula of motor' s parameter could be deduced by excite a single-phase signal to motor. Since the accurate value of motor stator current's amplitude and initial phase obtained through single-phase test was essential, a method based on DFT theory was proposed to calculate those values. Considering the errors caused by asynchronous measurement and DFT calculation process, an improved method based on DFT theory to calculate the stator current' s amplitude and initial phase was proposed. To confirm the validity of this method, a simulation model was built on the MATLAB/ Simulink environment and the result proved the effectiveness of this method.【期刊名称】《电机与控制应用》【年(卷),期】2011(038)007【总页数】6页(P38-43)【关键词】异步电机;电机参数;离线辨识;离散傅里叶变换【作者】段亮;莫锦秋;曹家勇【作者单位】上海交通大学机械与动力学院,上海200240;上海交通大学机械与动力学院,上海200240;上海交通大学机械与动力学院,上海200240【正文语种】中文【中图分类】TM921.51;TM3430 引言工业应用中对高性能交流调速系统的需求，使得矢量控制、直接转矩控制等一些高性能的调速理论越来越广泛地应用于实际调速系统之中。

211003044_涡轮增压器超高速轴承一转子动力学建模及模态参数识别

Dynamic Modeling and Modal Parameter Identification ofUltra-high Speed Bearing-Rotor of Turbocharger *Ping Gong 1Zhen-hui Hu 2Qing-shan Zhang 2Ri-xiu Men 3Shi-yuan Pei 2,*(1.China Aviation Development Harbin Bearing Limited Company;2.Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System,Xi’an Jiaotong University;3.National key Laboratory of High Turbocharging Technologyfor Diesel Engine,North China Engine Research Institute)Abstract：Aiming at the problems of traditional turbocharger ultra-high speed bearing-rotor system,such as low accuracy of dynamic modeling,difficult identification of modal parameters and so on,the dynamic model and differential equation of motion of turbocharger are established based on Timoshenko beam theory.The modal parameters of turbocharger under different excitation positions and with or without pre-tightening force are identified by hammering test.And the theoretical and experimental results are compared and verified.The results show that when the excitation turbocharger is in different positions,the excitation modes of the system are different.The pretightening force has an important influence on the dynamic analysis results of the rotor,and increasing the pretightening force can significantly improve the rotor stiffness.The established dynamic model and modal identification method have certain accuracy and applicability,which can provide theoretical and experimental basis for subsequent turbocharger structure optimization design and modal parameter identification.Keywords:Timoshenko Beam Finite Element Theory;Dynamic Modeling;Turbocharger;Modal Test;Frequency Response Function摘要：针对传统涡轮增压器超高速轴承-转子系统动力学建模精度不高、模态参数不易识别等问题，基于Timoshenko 梁理论建立了涡轮增压器动力学模型及运动微分方程，利用锤击法试验对增压器不同激励位置、有无预紧力等工况下的模态参数进行了识别，并将理论与试验分析结果进行了对比验证。

下肢外骨骼机器人系统参数辨识与控制器设计

摘　要外骨骼是一种能够穿戴于人体外侧并协助人体行走的机械装置,可以帮助患者、老人、残疾人正常行走，有效提高其生活质量，因此对用于康复医疗的下肢外骨骼机器人的研究具有重要的现实意义和应用价值。

本文为开发一套下肢外骨骼机器人系统，涉及到机器人平台、系统参数辨识、人机运动控制的设计和实现，并利用该机器人平台开展相关健康人实验，为相关康复工程领域的关键问题研究奠定了基础。

首先搭建一套下肢外骨骼机器人平台。

主要工作有以下几点：1、首先在结构上通过设计可拉伸内凹连杆和腿部贴片以适应不同腿长人员穿戴的舒适性，使人机一体重心更偏向于中心，并根据腿部运动的极限位置设计可调安全限位模块，最后为充分检测人机之间耦合力和同步性，设计采用三维力传感器和姿态传感器测量人机之间各个维度耦合力矩和姿态误差。

2、其次根据下肢外骨骼系统应用场景设计测控系统。

其中电路系统的设计需要考虑电机驱动系统负载功率，硬件接口转换等。

其次为提高算法开发效率，针对下肢外骨骼机器人系统设计了一套基于MATLAB和LabVIEW联合开发软件平台，软件平台可自动将算法编译成控制器可识别的动态链接库并直接调用。

其次进行下肢外骨骼机器人系统建模与参数辨识。

对下肢外骨骼系统参数进行辨识是其运用的关键，根据其物理结构和运动特性对其采用拉格朗日动力学建模和人机接触力建模。

利用Bspline设计好的激励轨迹可减少回归矩阵病态，有效提高系统参数辨识结果的精度。

本文将采用一种基于生物地理学的学习粒子群优化(BLPSO)的启发式算法用于激励轨迹优化和系统参数识别，通过改善搜索策略，BLPSO不仅可以避免系统参数收敛到局部最小值，同时也可以提高系统参数的辨识精度。

然后为下肢外骨骼机器人设计控制器。

外骨骼机器人是一套高度非线性系统，结合系统辨识的模型参数并针对“机主人辅”控制方式设计了一套具有人机耦合力和运动摩擦力补偿的反步控制算法，通过稳定性分析证明了控制器的稳定性，该控制器相比与无模型控制(比如PID)，具有更多设计上的灵活性。

带可变遗忘因子递推最小二乘法的超级电容模组等效模型参数辨识方法

2021年3月电工技术学报Vol.36 No. 5 第36卷第5期TRANSACTIONS OF CHINA ELECTROTECHNICAL SOCIETY Mar. 2021 DOI：10.19595/ki.1000-6753.tces.200023带可变遗忘因子递推最小二乘法的超级电容模组等效模型参数辨识方法谢文超1赵延明1,2方紫微1刘树立1（1. 湖南科技大学信息与电气工程学院湘潭 4112012. 风电机组运行数据挖掘与利用技术湖南省工程研究中心（湖南科技大学）湘潭 411201）摘要为了准确地辨识风力发电机变桨系统后备电源中超级电容模组等效模型的参数，解决由于“数据饱和”现象所产生增益下降过快的缺点，建立超级电容模组三分支等效电路模型，提出一种带可变遗忘因子的递推最小二乘法（RLS）的超级电容模组等效电路模型参数辨识方法，然后建立超级电容模组多方法参数辨识的Simulink仿真模型，并进行仿真与分析。

结果表明：该方法充电后静态阶段的综合误差为0.19%，比电路分析法的综合误差降低了 6.92%，比分段优化法的综合误差降低了0.09%。

整个充放电过程的综合误差为1.22%，比电路分析法降低了9.5%，比分段优化法降低了1.6%。

带可变遗忘因子的RLS法比电路分析法和分段优化法拥有更高的辨识精度。

关键词：超级电容模组等效模型参数辨识可变遗忘因子中图分类号：TM53Variable Forgetting Factor Recursive Least Squales Based Parameter Identification Method for the Equivalent Circuit Model ofthe Supercapacitor Cell ModuleXie Wenchao1 Zhao Yanming1,2 Fang Ziwei1 Liu Shuli1（1. School of Information and Electrical Engineering Hunan University of Science and TechnologyXiangtan 411201 China2. School of Engineering Research Center of Hunan Province for the Mining and Utilization of WindTurbines Operation Data Hunan University of Science and Technology Xiangtan 411201 China）Abstract In order to accurately identify the parameters of the equivalent model of supercapacitor cell module in the backup power supply of the pitch system of megawatt wind turbine and to solve the problem that the gain decreases too fast due to the data saturation phenomenon, the three-branch equivalent circuit model for the supercapacitor cell module was established, and a parameter identification method of the equivalent circuit model of supercapacitor cell module based on variable forgetting factor recursive least squares(RLS) was proposed in this paper. Then, the Simulink simulation model was also established for the multi-method parameter identification of supercapacitor cell module, and the simulation and analysis were performed. The comprehensive error in the static self-discharge phase of this new method is 0.19%, which is 6.92% and 0.09% lower than circuit analysis method and segmentation optimization method, respectively. Its comprehensive error in the whole process is 1.22%, which is reduced by 9.5% and 1.6% compared with circuit analysis method and segmentation国家重点研发计划（2016YFF0203400）和湖南省研究生创新项目（CX2018B670）资助。

基于轮胎六分力测试的PAC2002轮胎模型参数辨识方法研究

（3）算法设计
图 3 侧偏力辨识结果
图 4 纵向力辨识结果
图 2 辨识流程图
图 5 复合工况侧偏力辨识结果
63
汽车实用技术
作为对比，同时采用传统的单一辨识算法，例如遗传算法对轮胎模型参数进行参数辨识，侧偏力、纵向力、回正力矩参数的辨识误差如表 7 所示。可以看出通过新型辨识方法得到的辨识结果比传统算法得到的结果更可靠，其误差更低。
10.16638/ki.1671-7988.2018.15.023
基于轮胎六分力测试的 PAC2002 轮胎模型参数辨识方法研究
程泽木 1，姜俊昭 2，蔡金文 2，卢剑伟 2*
（1.安徽江淮汽车集团股份有限公司，安徽合肥 230091；2.合肥工业大学汽车与交通工程学院，安徽合肥 230009）
滑移率是否超过系统设定的滑移率门限值，若低于滑移率门 3 结束语
限值λmax，则电磁阀转到减压状态，由于制动压力下降，车轮减速度也会变小，直至（-a）信号出现。在后续的保压状态下，由于车轮惯性作用，车轮加速度增加直至超过门限值（+a）（该门限值用于判断低附着系数路面），随后制动压力一直保持不变。只有在加速度超过较高的门限值（+A）（表明是高附着系数路面），制动压力再次增加，当车轮加速度再次回到（+A）时，电磁阀进入保压状态，车轮加速度逐渐回落到（+a）值，由于此时在滑移率附着系数曲线峰值附近，制
表 7 不同算法的辨识误差对比
全局最优，防止了局部收敛等问题的出现。同时，该方法综合利用了多种算法的优点，较好地解决了复杂工况下非线性轮胎模型参数辨识精度与效率无法统一的问题。
参考文献
[1] 胥永宫.轿车轮胎操纵稳定性匹配研究［D］.长春:吉林大学,2011.

电机参数辨识-matlab官网教程

Creating a High-Fidelity Model of an Electric Motor for Control System Design and VerificationBy Brad Hieb, MathWorksAn accurate plant model is the linchpin of control system development using Model-Based Design. With a well-constructed plant model,engineers can verify the functionality of their control system, conduct closed-loop model-in-the-loop tests, tune gains via simulation,optimize the design, and run what-if analyses that would be difficult or risky to do on the actual plant.Despite these advantages, engineers are sometimes reluctant to commit the time and resources required to create and validate a plant model. Concerns include how much time it will take to run a simulation, how much domain and tool knowledge will be required to build and validate the model, and what type of equipment will be needed to acquire hardware test data for building and validating the model.This article describes a workflow for creating a permanent magnet synchronous machine (PMSM) plant model using MATLAB ®and Simulink ®and commonly available lab equipment. The workflow involves three steps:▪Execute tests▪Identify model parameters from test data▪Verify parameters via simulationWe used the plant model to build and tune a closed-loop PMSM control system model. We ran step response and coast-down tests using the controller model in simulation and on hardware using an xPC Target™ turnkey real-time testing system. We found close agreement between the simulation and hardware results, with normalized root mean square deviation (NRMSD) below 2% for key signals such asrotor velocity and motor phase currents (Figure 1).Figure 1. Comparison of simulation results (blue) with hardware results (red) for rotor velocity (left) and phase current (right).The Plant Model and Its ParametersThe PMSM plant model, developed with SimPowerSystems™, includes the motor and a load—in this example, an acrylic disc. The model has nine parameters that define its behavior: one (disc inertia) associated with the load and eight associated with the motor (Figure 2).See more articles and subscribe at /newsletters .Figure 2. Simulink model of a PMSM.We conducted five tests to characterize these parameters: the bifilar pendulum test, the back EMF test, the friction test, the coast-down test, and the DC voltage step test (Table 1). In this article, we will focus on the coast-down test and the DC voltage step tests. These tests demonstrate progressively more sophisticated methods of parameter identification, and illustrate extracting parameter values via curve fitting and parameter estimation, respectively.Test Parameters Identified Identification MethodBifilar pendulum test Disk inertia (H d)CalculationCalculationBack EMF test Number of poles (P)Flux linkage constant (A pm)Torque constant (Kt)Curve fittingFriction test Viscous damping coefficient (b)Coulomb friction (J0)Coast-down test Rotor inertia (H)Curve fittingParameter estimationDC voltage step test Resistance (R)Inductance (L)Table 1. Model parameters and the tests conducted to characterize them.For each test, we describe the test setup and then explain how we conducted the test, acquired the data, extracted the parameter value, and verified it.Characterizing Rotor Inertia with the Coast-Down TestTo characterize the rotor inertia (H) we spin the rotor up to an initial speed (ωr0) and measure the rotational speed (ω) as the rotor coasts to a stop. Using this measured result, the rotor inertia can be identified by curve fitting the equation for ωr to the measured rotational speed during the period of time when the motor is coasting to a stop.The differential equation [1] describes the mechanical behavior of the motor. The coast-down test is set up so that the load torque (T load) is always 0. Once the motor is up to an initial, steady-state speed, the motor is turned off, so that the electromagnetic driving torque(T em) is also 0. Under these conditions the solution to [1] is given by the equation for ωr[2], whereωr is the rotational speed of the rotor shaftωr0is the initial rotational speed of the rotor shaftJ0and b are the Coulomb friction and viscous damping coefficient, respectively, characterized from aseparate friction testT em is the electromagnetic driving torque (0 during this test)T load is the load torque (0 during this test)Conducting the Test and Acquiring the DataIn the lab we created an open-loop Simulink test model to drive the motor to an initial speed of 150 radians per second, at which time the motor drive was turned off and the rotor coasted to a stop. Throughout the test the model captured the output of the rotational speed sensor. Using Simulink Coder™ and xPC Target, we deployed this model to an xPC Target turnkey real-time system. We executed the model using xPC Target, and imported the rotor speed data into MATLAB for analysis.Extracting and Verifying the Parameter ValuesAfter running the tests, we plotted the measured speed data in MATLAB and used Curve Fitting Toolbox™ to fit equation [2] for the rotor angular velocity (ωr) to the measured speed data while the rotor was coasting to a halt. Using the value of H from the curve fit, we evaluated equation [2] from the point at which the motor started coasting and plotted the results with the original test data (Figure 3). As Figure 3 shows, equation [2] with the value of H from the curve fit closely predicts the motor speed during the coast-down test.Figure 3. Plot of rotor velocity during the coast-down test. Blue = hardware test results; red = curve fitting results.We used a model to verify our parameter identification result. Using the rotor inertia value obtained from the coast-down test(3.2177e-06 Kg m^2 in our PMSM model), we ran a simulation of the coast-down test in Simulink. We then compared and plotted the simulated results with the measured results (Figure 4). The results matched closely, with a normalized root mean square deviation (NRMSD) of about 2%.Figure 4. Comparison of measured rotor velocity (red) and simulated rotor velocity (blue).Characterizing Resistance and Inductance with the DC Voltage Step TestIn the DC voltage step test a DC voltage is applied across the motor phase A and phase B connections and the resulting current is measured. Electrically, under these conditions, a three-phase PMSM behaves like a circuit with two series resistors and two seriesinductors (Figure 5).Figure 5. Equivalent electrical circuit for DC step test.The measured current (i) is used to find the resistance and inductance parameter values. During the test the rotor is held motionless to avoid complicating the analysis with back EMF waveforms, which tend to oppose the current flow. To avoid burning out the motor with the rotor motionless, a current limiting resistor (R limit) is added and a step pulse rather than a steady DC voltage is used.Conducting the Test and Acquiring the DataWe again used xPC Target and an xPC Target turnkey real-time system to conduct the test. In Simulink we developed a model that produced a series of 24-volt pulses roughly 2.5 milliseconds in duration. We deployed this model to our xPC Target system using Simulink Coder, and applied the voltage pulse across the phase A and phase B terminals of the PMSM. We measured the applied voltage and the current flowing through the motor using an oscilloscope, and using Instrument Control Toolbox™ we read the measured data into MATLAB, where we plotted the results (Figure 6).Figure 6. Voltage (top) and current (bottom) for a pulse in the DC voltage step test.Extracting and Verifying the Parameter ValuesExtracting the phase resistance from the measured data required only the application of Ohm’s law (R = V/I) using the steady-state values for voltage and current. For the PMSM we calculated the resistance as 23.26 volts / 2.01 amps = 11.60 ohms. By subtracting 10 ohms (the value of the current limiting resistor), and dividing the result by 2 to account for the two-phase resistances in series, we calculated the motor phase resistance to be 0.8 ohms.Characterizing the inductance required a more sophisticated approach. At first glance, it looks as if we could have used curve fitting, as we did when characterizing the rotor inertia. However, due to the internal resistance of the DC supply, the measured DC voltage decays from an initial value of 24 volts at the start of the test, when the current into the circuit is 0, to a steady-state value of 23.26 volts after the current is flowing in the circuit. Because the input voltage is not a pure step signal, the results from curve fitting the solution to the series RL circuit equation would not be accurate.To overcome this difficulty we opted for a more robust approach using parameter estimation and Simulink Design Optimization™. The advantage of this approach is that it requires neither a pure step input nor curve fitting.We modeled the motor’s equivalent series RL circuit with Simulink and Simscape™ (Figure 7). Simulink Design Optimization applied the measured voltage as an input to the model, and with the value of the limiting resistor (R limit) and the motor phase resistance (R_hat)already known, estimated the value of the inductance (L_hat) to make the current predicted by the model match the measured current data as closely as possible.Figure 7. Simscape model of the motor’s equivalent circuit.To verify the values that we had obtained for phase resistance (0.8 ohms) and inductance (1.15 millihenries), we plugged the values into our PMSM model and stimulated the model with the same input that we used to stimulate the actual motor. We compared the simulation results with our measured results (Figure 8). The results matched closely, with an NRMSD of about 3%.Figure 8. Comparison of measured results (blue) with simulation results (red) for voltage (top) and current (bottom).Using the Plant Model to Design the ControllerAfter identifying and verifying all key parameters, our PMSM plant model was ready to use in the development of the motor controller. We used Simulink Design Optimization to tune the proportional and integral gains of the controller’s outer loop, the velocity regulator. We ran closed-loop simulations to verify the functionality of the controller model, and used Simulink Coder to generate code from the model, which we deployed to an xPC Target turnkey real-time target machine.As a final controller verification step, we ran step response and coast-down simulations in Simulink and hardware tests using the deployed controller code on an xPC Target turnkey real-time system. We compared simulation and hardware test results for rotorvelocity and phase current, and once again found close agreement between the model and the hardware, with NRMSD below 2% in bothcases (Figure 9).Figure 9. Comparison of simulation results (blue) with hardware results (red) for rotor velocity (left) and phase current (right).SummaryDevelopment of the PMSM plant model highlighted two parameter identification tests. Data was acquired via a sensor for thecoast-down test, and with Instrument Control Toolbox via an oscilloscope for the DC voltage step test. We extracted data via curve fitting for the coast-down test and parameter estimation for the DC voltage step test. We verified all parameter values by comparing simulation results against measured test data, which enabled us to produce a plant model that we could trust as we developed and tuned the controller.All this work can be done early in the development process, well before embedded code is generated for the control system, enabling engineers to find and eliminate problems with the requirements and the design before hardware testing begins. These benefits typically far outweigh the costs associated with creating the plant model, particularly if the model can be reused on other projects.We would like to acknowledge the contribution of Professor Heath Hofmann of the University of Michigan, who recommended test procedures for characterizing a PMSM and allowed us to use his lab facilities for the initial phase of this project.Products Used▪MATLAB ▪Simulink ▪Curve Fitting Toolbox ▪Instrument Control Toolbox ▪SimPowerSystems ▪Simscape ▪Simulink Coder ▪Simulink Design Optimization ▪xPC Target Learn More ▪Webinar: A Simulink Real-Time Testing Solution for Power Electronics and Motor Control (45:08)▪Webinar: Embedded Code Generation for AC Motors (50:56)▪Video: Parameterizing and Verifying a Permanent Magnet Synchronous Motor Model (37:16)See more articles and subscribe at /newsletters .Published 201392130v00。

基于遗传算法和人工神经网络的冷水机组模型参数辨识及误差补偿方法

第42卷第3期2021年6月Vol.42,No.3June,2021基于遗传算法和人工神经网络的冷水机组模型参数辨识及误差补偿方法文章编号：0253-4339(2021)03-0093-07doi：10.3969/j.issn.0253-4339.2021.03.093基于遗传算法和人工神经网络的冷水机组模型参数辨识及误差补偿方法张丽珠1章超波1陈琦2赵阳1(1浙江大学制冷与低温研究所杭州310027；2浙江省能源集团有限公司杭州310007)摘要DOE-2模型被广泛应用于冷水机组仿真建模,如何根据有限传感器实测数据对某特定冷水机组DOE-2模型的参数进行可靠地辨识，并补偿模型误差，对于节能运行等场景具有重要意义。

在实践中由于传感器不足且数据质量不高等问题,DOE-2模型参数的可靠辨识较为困难。

因此，本文提岀一种基于外部知识库的遗传算法和一种基于人工神经网络的方法分别对DOE-2模型进行参数辨识和误差补偿。

结果表明:基于外部知识库的遗传算法可以有效降低DOE-2模型参数辨识时间，并显著提升DOE-2模型预测精度。

误差补偿后的DOE-2模型的预测精度显著高于未作补偿的DOE-2模型，前者在预测冷冻水岀口温度时的MAE、RMSE、MAPE和CV-RMSE分别降低36.49%,46.OO%、33.16%和45.73%,R2提高25.75%。

关键词冷水机组建模;遗传算法;参数辨识;人工神经网络;误差补偿中图分类号:TU831.4;TP183文献标识码：AGenetic-Algorithm-Based Parameter Identification and Artificial-Neural-Network-Based Error Compensation for Chiller ModelZhang Lizhu1Zhang Chaobo1Chen Qi2Zhao Yang1(1.Institute of Refrigeration and Cryogenics,Zhejiang University,Hangzhou,310027,China; 2.Zhejiang Energy Group Co.,Ltd.,Hangzhou,310007,China)Abstract Accurate chiller models are important for the energy conservation of chillers.The DOE-2model is the most common chiller model.Parameter identification and error compensation are crucial for the development of an accurate DOE-2model.However,the parameter identification of a DOE-2model of an actual chiller is usually challenging because chillers are usually equipped with limited sensors and the quality of actual data is usually low.To address the above issues,a genetic algorithm based on an external knowledge base for parameter identification and artificial-neural-network-based(ANN-based)error compensation method are proposed.The results show that the proposed genetic algorithm can significantly reduce the computation load of parameter identification of the DOE-2model.It can also significantly improve the accuracy of the DOE-2model.Moreover,the accuracy of the DOE-2model with the ANN-based error compensation is significantly higher than that of the DOE-2model without error compensation.The MAE,RMSE,MAPE,and CV-RMSE of the model with error compensation in predicting the chilled water outlet temperature were reduced by36.49%,46.00%,33.16%,and45.73%,respectively,while R2of the model with error compensation was increased by25.75%.Keywords chiller modeling;genetic algorithm;parameter identification;artificial neural network;error compensation作为中央空调系统的重要组成部分，冷水机组能耗约占中央空调系统的40%~50%[1]。

考虑非理想噪声干扰的直升机飞行动力学模型辨识方法

考虑非理想噪声干扰的直升机飞行动力学模型辨识方法周攀;吴伟【摘要】利用MATLAB/SIMULINK平台搭建了直升机仿真实验系统,并以UH-60直升机为对象实现了考虑非理想噪声干扰的仿真飞行实验.建立了非理想噪声数学模型并基于增广最小二乘法设计了一套同时考虑模型参数和噪声参数的综合辨识算法,在此基础上,利用仿真实验数据实现了UH-60直升机纵向飞行动力学模型的辨识与验证.最后,通过与普通最小二乘法的对比验证了本文方法的优越性.【期刊名称】《南京航空航天大学学报》【年(卷),期】2016(048)002【总页数】6页(P224-229)【关键词】直升机;飞行动力学;系统辨识;非理想噪声【作者】周攀;吴伟【作者单位】南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016;南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016【正文语种】中文【中图分类】V212.4直升机相对于固定翼飞机具有垂直升降,全地形作战，近地飞行的独特优势，它的这些特点使之成为一种“万用”的交通工具[1-2]。

但是，由于旋翼气动特性与机身结构的复杂性，直升机又具有振动大、噪声水平高等缺点，这无疑对直升机飞行动力学的建模带来了很大的困难。

系统辨识的建模方法为提高直升机飞行动力学模型的精度提供了有效的技术手段[3]，这种方法是根据飞行试验得到的输入输出数据建立系统的数学模型，其特点是不需要知道对象详细的物理细节。

从20世纪50年代开始，飞行器飞行动力学就开始使用系统辨识的方法进行数学建模，然而，直到20世纪60年代末70年代初，系统辨识方法才开始在直升机飞行动力学建模中得到应用[4]。

文献[5]将成功应用在固定翼飞机上的最小二乘法、输出误差法和极大似然法进行改造，并对MK-50海王直升机展开了相关的辨识工作，研究结果表明，经过适当改造的算法可适用于直升机飞行动力学的辨识。

文献[6]中提出了一种高效批量的子空间辨识算法并对V-22直升机的结构进行了辨识。

汽油机进气道油膜动力学模型参数辨识

汽油机进气道油膜动力学模型参数辨识郑太雄;周可君;李永福;李宣政【摘要】为了更加精确地辨识汽油机进气道油膜模型参数,从而更加精确地控制空燃比,在油膜动力学模型的基础上,考虑模型误差和随机误差,建立了油膜辨识方程.根据递推最小二乘算法得到油膜参数估计的加权矩阵表达式,利用马尔可夫估计得到该加权矩阵,进而得到油膜参数的最优估计.应用GT-power建立了发动机模型,在转速1 000 ～3 500 r/min、节气门开度5％～75％变化时,分别利用提出的算法和最小二乘法对油膜参数进行了辨识,并与标定值进行了比较.结果表明,燃油沉积系数X在同一转速时,随着节气门开度的增大而减小,在同一节气门开度时,随着转速的增加而减小;油膜质量蒸发时间常数τ在同一转速时,随着节气门开度的增大而增加;在同一节气门开度时,随着转速的增加而减小.通过误差分析,表明所提出的方法比最小二乘算法的辨识结果精度更高.【期刊名称】《农业机械学报》【年(卷),期】2015(046)004【总页数】6页(P296-301)【关键词】发动机;油膜模型;参数辨识;递推最小二乘算法;马尔可夫估计【作者】郑太雄;周可君;李永福;李宣政【作者单位】重庆邮电大学先进制造学院,重庆400065;重庆邮电大学自动化学院,重庆400065;重庆邮电大学自动化学院,重庆400065;重庆邮电大学自动化学院,重庆400065【正文语种】中文【中图分类】TK417发动机空燃比的精确控制对汽车节油及减少污染物排放至关重要。

发动机处于稳态工况时，空燃比的精确控制容易实现，但是当发动机处于瞬态工况时，由于油膜动态效应的存在，空燃比控制会出现偏差[1]。

因此准确获知瞬态工况进气道油膜参数是精确控制汽油机过渡工况空燃比的关键[2-3]。

对油膜现象的研究，Jognen等[4]和Almkvist[5]最早进行了进气道附壁油膜实验测量，对附壁油膜的形成、流动及蒸发机理进行了理论研究，使人们对进气道油膜的机理有了非常直接的认识。