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系统辨识大牛Ljung编写的MATLAB系统辨识使用手册，这本书详细地介绍了在MATLAB已经所属simulink环境下，系统辨识工具箱的一些使用办法，是一本非常经典的教材！Revision Historypril 1988First printingJuly 1991Second printingMay1995Third printingNovember 2000 Fourth printingRevised for Version 5.0(Release 12)pril 2001Fifth printingJuly 2002Online onlyRevised for Version 5.0.2 Release 13)June 2004Sixth printingRevised for Version 6.0.1(Release 14)March 2005Online onlyRevised for Version 6.1.1Release 14SP2)September 2005 Seventh printingRevised for Version 6.1.2(Release 14SP3)March 2006Online onlyRevised for Version 6.1.3(Release 2006a)September 2006 Online onlyRevised for Version 6.2 Release 2006b)March 2007Online onlyRevised for Version 7.0 ( Release 2007a)September 2007 Online onlyRevised for Version 7.1 (Release 2007bMarch 2008Online onlyRevised for Version 7.2(Release 2008a)October 2008Online onlyRevised for Version 7.2.1 Release 2008b)March 2009Online onlyRevised for Version 7.3(Release 2009a)September 2009 Online onlyRevised for Version 7.3.1(Release 2009b)March 2010Online onlyRevised for Version 7. 4 (Release 2010a)eptember2010 Online onlyRevised for Version 7.4.1(Release 2010b)pril 2011Online onlRevised for Version 7.4.2(Release 2011a)September 2011 Online onlyRevised for Version 7.4.3(Release 2011b)March 2012Online onlyRevised for Version 8.0( Release 2012aabout the DevelopersAbout the Developersystem Identification Toolbox software is developed in association with thefollowing leading researchers in the system identification fieldLennart Ljung. Professor Lennart Ljung is with the department ofElectrical Engineering at Linkoping University in Sweden. He is a recognizedleader in system identification and has published numerous papers and booksin this areaQinghua Zhang. Dr. Qinghua Zhang is a researcher at Institut Nationalde recherche en Informatique et en Automatique(INria) and at Institut deRecherche en Informatique et systemes Aleatoires (Irisa), both in rennesFrance. He conducts research in the areas of nonlinear system identificationfault diagnosis, and signal processing with applications in the fields of energyautomotive, and biomedical systemsPeter Lindskog. Dr. Peter Lindskog is employed by nira dynamiAB, Sweden. He conducts research in the areas of system identificationsignal processing, and automatic control with a focus on vehicle industryapplicationsAnatoli Juditsky. Professor Anatoli Juditsky is with the laboratoire JeanKuntzmann at the Universite Joseph Fourier, Grenoble, france. He conductsresearch in the areas of nonparametric statistics, system identification, andstochastic optimizationAbout the developersContentsChoosing Your System Identification ApproachLinear model structures1-2What Are Model objects?Model objects represent linear systemsAbout model data1-5Types of Model objectsDynamic System Models1-9Numeric Models1-11umeric Linear Time Invariant (LTD Models1-11Identified LTI modelsIdentified Nonlinear models1-12Nonlinear model structures1-13Recommended Model Estimation Sequence1-14Supported Models for Time- and Frequency-DomainData,,,,,,,1-16Supported Models for Time-Domain Data1-16Supported Models for Frequency-Domain Data1-17See also1-18Supported Continuous-and Discrete-Time Models1-19Model estimation commands1-21Creating Model Structures at the command Line ... 1-22about system Identification Toolbox Model Objects ... 1-22When to Construct a Model Structure Independently ofEstimation1-23Commands for Constructing Model Structures1-24Model Properties1-25See als1-27Modeling Multiple-Output Systems ......... 1-28About Modeling multiple-Output Systems1-28Modeling Multiple Outputs Directly1-29Modeling multiple outputs as a Combination ofSingle-Output Models.......1-29Improving Multiple-Output Estimation Results byWeighing Outputs During Estimation ....... 1-30Identified linear Time-Invariant models1-32IDLTI Models1-32Configuration of the Structure of Measured and Noise oRepresentation of the Measured and noise Components foVarious model Types1-33Components ....1-35Imposing Constraints on the Values of ModeParameters1-37Estimation of Linear models1-8Data Import and Processing2「Supported Data ...2-3Ways to Obtain Identification DataWays to Prepare Data for System Identification ... 2-6Requirements on Data SamplingRepresenting Data in MATLAB Workspace·····Time-Domain Data Representation2-9Time-Series Data Representation2-10ContentsFrequency-Domain Data Representation ....... 2-11Importing Data into the Gui2-17Types of Data You Can import into the GUi2-17Importing time-Domain Data into the GUI2-18Importing Frequency-Domain Data into the GUI2-22Importing Data Objects into the GUI ......... 2-30Specifying the data sampling interval2-34Specifying estimation and validation Data2-35Preping data Using Quick StartCreating Data Sets from a Subset of Signal Channelo2-362-37Creating multiexperiment Data Sets in the gUi2-39Managing data in the gui ............. 2-46Representing Time- and Frequency-Domain Data Usingiddata object2-55iddata constructor2-55iddata Properties.........2-58Creating Multiexperiment Data at the Command Line .. 2-61Select Data Channels, I/O Data and Experiments in iddataObjects2-63Increasing Number of Channels or Data Points of iddataObjects2-67Managing iddata Objects2-69Representing Frequency-Response Data Using idfrdObiec2-76idfrd Constructor2-76idfrd Properties2-77Select I/o Channels and Data in idfrd Objects ..... 2-79Adding Input or Output Channels in idfrd Objects2-80Managing idfrd Objects2-83Operations That Create idfrd Objects2-83Analyzing Data quality2-85Is your data ready for modeling?2-85Plotting Data in the guI Versus at the command line2-86How to plot data in the gui2-86How to plot data at the command line2-92How to Analyze Data Using the advice Command2-94Selecting Subsets of Data2-96IXWhy Select Subsets of Data?2-96Extract Subsets of Data Using the GUI2-97Extract Subsets of data at the Command Line2-99Handling Missing Data and outliers2-100Handling missing data2-100Handling outliers2-101Extract and Model Specific Data Segments2-102See also2-103Handling offsets and Trends in Data2-104When to detrend data2-104Alternatives for Detrending Data in GUi or at theCommand-Line2-105Next Steps After detrending2-107How to Detrend Data Using the Gui2-108How to detrend data at the Command line2-109Detrending Steady-State Dat109cending transient Dat2-109See also2-110Resampling Data2-111What Is resampling?...,,.,,,,,,,,,,,.2-111Resampling data without Aliasing Effects2-112See also2-116Resampling data Using the GUi.,,,,2-117Resampling Data at the Command line2-118Filtering Data2-120Supported Filters2-120Choosing to Prefilter Your Data2-120See also2-121How to Filter Data Using the gui2-122Filtering Time-Domain Data in the GuI........ 2-122Content

cadence运算放大器的仿真详细讲解了对运放放大器各个性能的仿真分析

整理出了如下几个计算六轴机械臂正解和逆解的关键点：01_机器人坐标系和关节的说明02_算法坐标系的建立03_D-H参数表的建立04_FK（正解）算法05_Matlab辅助计算FK（正解）06_IK（逆解）算法07_Matlab辅助计算IK（逆解）文档中针对FK以及IK算法的推导均有详细的推导过程。希望各位能根据推导过程写出自己的代码。图1针对机器人的关节坐标系,我们还需要规定各个关节的转动方向,如下图所示,我们依次描叙了各个关节的正负方向。在关节坐标系下,机器人各个关节的转动方向,必须和下图相符图22.机器人直角坐标系目前所说的直角坐标系是机器人的工具坐标系,如下图所示,因为该机器人没有安装执行末端,所以,工具坐标系原点在第六轴末端法兰中心处,红色箭头是Ⅹ轴,蓝色箭头是乙轴,根据右手定则确定Y轴方向@图3基坐标系所在的位置是定义机器人基座的位置,如上图所示,坐标系原点在第一关节的中心处,红色箭头所示为Ⅹ轴,蓝色箭头所示为乙轴,根据右手定则,即可确定Y轴的方向。具体如上图旁边那个坐标系所示。当我们说六轴机械臂位姿时,说的是六轴机械臂末端的位姿,该位姿包括六个参数,分别为Ⅹ YZABC。六轴机械臂未端的位姿是以基坐标系作为参考坐标系的:笛卡尔坐标系的Ⅹ轴,Ⅹ轴距离Y:笛卡尔坐标系的Y轴,Y轴距离Z:笛卡尔坐标系的Z轴,z轴距离A:XY-Z固定角坐标系下的偏转角B:X-Y-Z固定角坐标系下的俯仰角C:XY-Z固定角坐标系下的回转角ZA2呈Ax图如上图所示,A对应第一个坐标系中的γ,B对应第二个坐标系中的β,C对应第三个坐标系中的Q。为什么我们需要花费专门的一节来讲解六轴机器人的坐标系和关节?因为我们后续要学习的FK和就是以这个为基础的。FK是已知六轴机械臂在关节坐标系下各个关节转动的角度,然后求解直角坐标系下的Ⅹ YZABOK是已知六轴杋械臂在直角坐标系下的 XYZABO,然后求解关节坐标系下各个关节转动的角度二.算法坐标系的建立为了得出D-H参数表,我们首先需要针对六轴机器人的各个关节建立坐标系,在固定的坐标系下,才能最终得出连杆之间的变换关系,从而建立D-H参数表。82个2算法坐标系确定的通用方法如下1)坐标系的Z轴,与各个关节的旋转中心轴线重合2)坐标系的X轴,与沿着相邻两个z轴的公垂线重合3〕坐标系的Y轴,可以通过右手定则来确定当相邻两个z轴相交时,确定坐标系的方法如下1)坐标系的Y轴,沿着第一个Z轴与下一个z轴相交的延长线为Y轴2)坐标系的Ⅹ轴,通过右手定则确定当相邻两个Z轴平行时,确定坐标系的方法如下1)坐标系Ⅹ轴,相邻两个乙轴平行,做两个乙轴的公垂线,相交于下一个z轴为Ⅹ轴,方向为第一个Z轴到下一个Z轴的方向2)坐标系Y轴,通过右手定则确定三.D-H参数表的建立D-H参数表,实际上是相邻各个关节坐标的变换关系表,根据之前针对各个关节所建立的丛标系,按照如下四条变换规则,即可得到D-H参数表。变换规则1)绕Z轴,旋转9n+1n与Xn+1平行(方向一致))沿Zn轴,平移与Xn+1共线3)沿Xn轴,平移aAn与Xn+1原点重4)将Zn绕Xn+1轴,旋转αn+1Zn与Zn+1共线建立D-H参数表的详细步骤第一步,从第一关节到第二关节之间的变换绕z轴,旋转0度,让X0与X1平行且方向一致沿z轴,平移242,让Ⅺ0与X1共线沿Ⅺ轴,平移0,Ⅺ与X1原点重合将石绕X1轴,旋转90度,Z0与z1共线第二步,从第二关节到第三关节之前的交化绕z1轴,旋转90度,让X1与X2平行且方向一致沿Z1轴,平移0,让X1与X2共线沿X1轴,平移225,X1与X2原点重合将Z1绕X2轴,旋转0度,Z1与Z2共线第三步:从第三关节到第四关节之间的交换绕z2轴,旋转0度,让X2与X3平行且方向一致沿Z2轴,平移0,让Ⅹ2与X3共线沿X2轴,平移0,X2与X3原点重合将Z2绕X3轴,旋转90度,Z2与z3共线第四步:从第四关节到第五关节之间的变换绕z3轴,旋转0度让X3与X4平行且方向一致沿3轴,平移22886,让X3与X4共线沿3轴,平移0,X3与X4原点重合将Z3绕X1轴,旋转90度,Z3与Z1共线第五步:从第五关节到第六关节之间的变换绕Z4轴,旋转90度,让X4与X5平行且方向一致沿Z4轴,平移0,让X4与X共线沿X轴,平移0,X1与K5原点重合将Z4绕X5轴,旋转90度,Z4与z共线第六步:从第六关节到未端之间的变换绕z轴,旋转0度,让X5与X6平行且方向一致沿z轴,平移-50,让X5与X6共线沿X轴,平移0,X5与K6原点重合将z绕X轴,旋转0度,Z5与z6共线根据上图所示机械臂的尺寸参数以及以上六个步骤的变换,D-H参数表如下所示420901-202253-4228.864-5900900-500四.正解(FK)算法根据连杆变换规贝T=R(Z, B1*T(Z, di)*T(X, ai)*R(X, ai)6;00因为R(Z06:00100000aT(Z,a1)=00001000011000T(xa10100001d0001000 caROX. a)= osa oa;0001根据以上矩阵变换,可以得到如下连杆变换的通用矩阵如下Bi -se, ca s0,sa, a,c61s0 ce:cad sa asa0 saca d00根据以上连杆变换的通用矩阵和之前的D-H参数表,可以得到如下δ个连杆变换矩阵e10s61^0S0 0T6100102420001s20-22S620225c62000001620s60b203001000040s日4000c0 0010228.860001s50c650C650s650000006-s6006000C001-40FK算法需要解决的问题是:已知各个关节的转动角度,需要求出末端的位姿。已知:(61,2,θ3,θ4,θs,θ6求解:(X,Y,乙,A,B,C)计算公式如下所示13机器末端的位姿矩阵为72272313273300011722723py07*1T2T*37*4T5Tp000在以上的推导过程中,、T、2、37、4、7分别为相对于01、02、63、64、6s、的已知量。由此可以求解出位置变量(pPP)以及姿态变量a1T2723五. Matlab辅助计算正解(FK)根据上一章,我们有如下结论10s10100102420001s2-c620-225s6CS20225C60010

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