转子系统固有频率的传递矩阵计算方法及其MATLAB实现
文章介绍了计算多自由度转子系统固有频率的传递矩阵法，以及用于实现该算法的Prohl法和Riccati 法的推导过程。利用Matlab 强大的绘图计算功能和改进的Riccati 传递矩阵法所具有的良好的数值稳定性，避免了传统的Prohl 传递矩阵法在计算过程中的丢根现象，提高了整个转子系统分析运算的精度。并用Matlab 对各算法的数值稳定性进行了分析。190其中112,21,2对应于(3)式的矩阵各项。将式(6)展开,得:}+1=11M}+12引入如下的 Riccal变换式中[]就是ca传递矩阵,它是一个2×2阶的待定矩阵,把式(8)代人式(7)式中得这就是 Riccait递推公式。由起始截面的边界条件(门1=0,(e小)≠0固有初始条件[S]=[0]。代人式(9)就可依次递推[S,[,.S对末端截面N+1有:由边界条件{门}x1-{0},{e≠0故得(10)式有解的条件是:+和PωM/法一样,在感兴趣的范围内按一定的步长选定试算频率计算出剩余量S-值,就可以画出剩余量随a变化的曲线,曲线与横坐标交点所对应的转速就是转子的各界临界转速。在PmM的传递矩阵法中,是用r阶的矩阵递推来求剩余量△(o2)。在Bceb的传递矩阵法中是用r/2阶的矩阵国递推来求剩余量S×+1,由于与的递推式中含有逆矩阵,使得剩余量曲线经常会出现异号无穷型奇点。因而在常见的转子动力系统中,剩余量曲线的根和奇点的位置十分接近。在实际转子系统中,临界转速值与奇点值间的间隔可能少于10/m,因此这种方法的丢根现象不可避免。参考PnoM方法中剩余量△(a2)无奇点的事实,可以对 riccati方法中的剩余量加以改造。由式(10)得+1n{%+12]1{}依次类推{}[]+∏[2+21{12在满足相同边界条件时应有△1=[]L21320064事实上(12)式就是(5)式,只是在数值计算中,它们是按不同的方法递推而得到的。因此在数值上它们的精度也不同。当PmM法出现数值不稳定时,(13)式所示的剩余量仍然保持相当的精度。由于剩余量(o2)随0变化的曲线不存在奇点,因此以作剩余量的曲线也不存在奇点。由于(12)式中un+ux]在进行S的递推过程中都已求得,所以在计算时也不会增加太多的工作量,但却可以克服丟根的缺点。事实上(13)式是把(11)式的异号无穷型奇点变为同号无穷型奇点,这样只有当跨过一个真正的根时才变号。枚除了两个临界转速值非常接近的情况,即当两临界转速的差小于所选步长时,一般不会发生漏根。三利用MmMh编制PmM/法、Bicn法及改进的kKRiccati法的程序对各算法结果进行分析。运用算例:如图转子系统简化模型,其数据如下1转子系统简化模型2.94t=588t(=236)1.3m(=1,2,,6)29592×10(kN·m)(i=1,2,)6)支承简化为如图模型相应参数为1.9600×106kN.m-1;2.7048×10kN·m=3.5771(=1,2)编制Maab程序运行待如下表所示的各阶频率。从表1可以看出在 Protel法的计算结果中,小于1058239rad/s固有频率共计算出了7个, Ricca算法计算出了13个固有频率,而改进了的ieai算法在消除奇点干扰后可以计算出17个固有频率。从而明显的看出改进的Racm法可以很好的避免计算过程中的丢根,在数值上具有很好的稳定性。计算细果慧裝protel算法(rads)Riccati算法(rads)改进的 Riccati算法(rad/s190.812100.815208249197.895197.895445924208.245208.24522.9655646.410445.9256832.610458.175458.1751058.239539925539925580.l659646.415574.265759.225580.165832.615646.415987.0057150451058.23583261516987.0051058.235利用a的绘图功能我们可以直观的从图中分析岀各算法的漏根现黎如图2、图3、图4所示:1912P法计算恩有单率输出固像1eg法计算回有率出四像t”改进计算有率始步入从图2、图3、图4可以看出在530到580的频率区间上,前两条曲线与0轴只有一个交点即所求固有频率为539925a/s的点,第三条曲线在相同的区间上与0轴的交点为三个,显然改进的 mccall方法找回了漏掉的根550.225ad/s和574265rad/s。利用 Matlab程序绘图我们还可以绘出改进的 Riccati方法把异号无穷型奇点转化成了同号的无穷型奇点的情况,如图5、图6所示。从图中区间987ras到1090rad/s的曲线可以明显的看出图5曲线以0轴为对称轴倒置后即得到图6在此区间的曲线线形,从而改进了 Riccati算法,在曲线中,只有在跨过个真正的根时剩余量才变号。所以除了两个临界转速之差小于所选步长的情况除外,一般改进后的riccati算法不会发生丢根c算利0改进的热计算有明p1m0p三41000100在计算多自由度转子系统固有频率的传递矩阵法中,我们可以利用 Matlab编程实现Ph/法、 riccati法以及改进的Riea法对于系统固有频率的计算,利用Maab的绘图功能对各算法的结果进行直观的分析,从而明显的看出各算法的漏根情况。本文对于计算复杂的多自由度系统固有频率具有参考意义,也可用于复杂系统低阶固有频率的粗算。同时 Matlab的矩阵运算功能在传递矩阵法中也得到了充分的利用(Electromechanical Engineering Dept, Sichuan University of Science Engineering, Zigong 643000, China)This article introduced the transfer matrix method about the natural frequency calculation of themuulti- degrees freedom rotor system, as well as inferential reasoning process about Prohl law and thericcatilayUSing formidable cartography and computation function of the Matlab as well as the good value stability aboutimproved riccati law it avoided the losing of the natural frequency and enhanced the precision ofentire rotorsystem further analyze. The value stability of various algorithms areanalyzed with Matlab in the paper toorotor system; natural frequency; transfer matrix method; Matlab
- 2020-12-04下载
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ST FOC 5.0说明书 快速入门 SDK v5.0.pdf
ST FOC 5.0说明书 配合 开源库 https://download.csdn.net/download/hxinstar/10322042使用UM2374List of tablesList of tablesTable 1. List of acronymsTable 2Document revision history..23UM2374 Rey 13/24List of figuresUM2374List of figuresFigure 1. ST MC Workbench -Icon and installation folder treeFigure 2. ST MC Workbench-GUI expanded top viewFigure 3. ST Motor Profiler-GUI889Figure 5. ST Motor Profiler-SM-PMSM parameters exampleFigure 4. ST Motor Profiler- Hardware setup list examples1011Figure 6. ST Motor Profiler-l-PMSM parameters exampleFigure 7. ST Motor Profiler-Measurement results12Figure 8. ST Motor Profiler-Save window13Figure 9. ST MC Workbench - New Project window14Figure 10. ST MC Workbench -New Project Info window14Figure 11. ST MC Workbench -Project Settings15Figure 12. ST MC Workbench-Project Settings window.15Figure 13. ST MC Workbench -Project generation button16Figure 14. ST MC Workbench -Workspace selectionFigure 15. ST MC Workbench -Project generation build infoFigure19. ST MC Workbench- Use of the motor control and monitoring.∴、∴,"…,,∴…….17Figure 16. IDE-MC Project view example18Figure 17. STMC Workbench-Motor monitoring button.19Figure 18. ST MC Workbench -Motor monitoring GUI204/24UM2374 Rey 1/UM2374General informationGeneral informationThe Mc sDK is used for the development of motor-control applications running on STM3232-bit microcontrollers based on the arm Cortex-M processorTable 1 presents the definition of acronyms that are relevant for a better understanding ofthis documentTable 1. List of acronymsAcronymDescriptionGUIGraphical user interfaceIDEIntegrated development environmentFOCField-oriented controlFWFirmwareMotor controlMC WBMotor control Workbench(STMicroelectronics sw tool)MPMotor Profiler(STMicroelectronics software tool)PMSMPermanent-magnet synchronous motorPWMPulse-width modulationSDKSoftware development kitVCVector controlMore information about ST MC Workbench is provided in the stm32 motor control SDKv5.0toolsusermanual(um2380)availableatwww.st.comarmUM2374 Rey 15/24Motor control ecosystem setupUM23742Motor control ecosystem setupA suitable ST Motor Control ecosystem environment includesA PC running the needed Mc software toolsA third-party IDEa third-party ANSI C-compilerA JTAG/SWD interface for debugging and programmingAn STMicroelectronics application board with one of the STM32 microcontrollerssupported. It drives the power stage and featuresPWM outputs to gate driverADC channels to measure currentsDC bus voltageA three-phase PMsM motol· A power supplyRefer to the STM32 motor control software development kit(Mc sDk data brief(DB3548)atwww.st.comandtothereleasenoteformoredetails2.1Software tool setupThe STMicroelectronics motor-control ecosystem runs on a pc with Windows7The following Pc software tools are correctly installedST MC Workbench (v5.0.0 or later)STM32CubeMX(v4 24.0 or later)ST-LINK/2(v4.0.0 or later)Any supported IDEIAR Embedded Workbench@ for Arm(v7.80.4Keil MDK tools (v5.24.2 or later)Ac6 System Workbench(v2.3.0 or later)(a)Refer to the respective user manuals for proper installation. STMicroelectronics documentsareavailablefromtheinternetsiteatwwwst.comSTM32 motor control SDK v5.0 tools user manual (UM2380STM32 CubeMX for STM32 configuration and initialization c code generation usermanual (UM1718)STM32 ST-LINK utility software description user manual(UM0892)The AC6 tool framework is not supported in SDK v5.0 but in later versions6/24UM2374 Rey 1/UM2374Motor control ecosystem setup22Hardware setupThe connection of the STMicroelectronics application board to the pc requires a USBType-A connector. Refer to the description of the application board for details on the USBcableA dedicated description card is delivered with each STMicroelectronics application board forproper installation For more details, refer to the user manual of the board available atwww.st.comThe selected hardware can be one of the three setups· The complete MC KitOne of the complete inverter boardsAny STM32 evaluation board combined with one of the ST evaluation power stagesthat include the mc connectorUM2374 Rey 17/24Getting StartedUM23743Getting StartedWarning: Check that the board is correctly configured for the motorcontrol application and supplied with the expected inputvoltageNoteRefer to the user manual of the related hardware to setup the correct configuration, voltagerange, serial communication capabilities, and programming/debugging interface3.1Hardware connectionConnect a uSb cable between the pc and the stmicroelectronics application board andthe JTAG/SWD programming cable if it is different from the USB cable3.2Motor profilingLaunch the ST MC Workbench software tool either byclicking on its iconrunning it directly from the installation folder treeBoth ways of launching the ST MC Workbench are illustrated in Figure 1Figure 1. ST MC Workbench- Icon and installation folder treeI STMicroelectrorics感FOC SDKLv.3.0MotorControlv500WorkBenchST Motor Control Workbenchd ST Motor profileren the st motor profiler tool either byUsing its dedicated button in the St Mc Workbench GUl as illustrated in Figure 2Running it directly from the installation folder tree as illustrated in Figure 1Figure 2. ST MC Workbench-GUl expanded top viewFile Tools Help Documet ta ionNew ProjectLoad Project4 About HelpMotor ProfilRcGert ProJEcts己tdbrsDRpower board8/24UM2374 Rey 1/UM2374Getting StartedClick on the Select Boards button to display the list of supported boards as shown onFigure 3 and select the STMicroelectronics application board setup. Figure 4 on page 10presents examples from this listNoteThe ST Motor Profiler tool may be used only with ST hardware in the list of supportedsetups.Figure 3. ST Motor Profiler-GUI2 ST Motor Profile.l:e augmentedMotor ProfilersPole pairsPe row to detecbeed and Current /mitsMaκSpet1600FPMn7 Select Board∧pk02530pkMagnetic: SM-PMSN○-NSMMechanIcal mode lO CenElectrical modelOW000UM2374 Rey 19/24Getting StartedUM2374Figure 4. ST Motor Profiler-Hardware setup list examplesE ST Motor ProfiY Hideabsolete boarde arch Control board by narSe arch power boac bv nareControl boardower BoardxCancelHide boards with warningNUCLEO-F302R8X-NUCLEO-HMOTM1 3shNUCLEO-F302R8X-NUCLEO-HMOBM1 3shT2F302R8T6L6230PDSTM32F302R8T6STL22ON6FT●Acf8m:m3SELNRV2 Emiol connectorC Product Web PageG Product Web PageC Product Web PageC Product Web PageNUCLEO-F303RESTEVAL-IPMO5F 3ShNUCLEO.F303RESTEVAL-IPM108 3sh●Aiv命Ativ● Ac livSn Ngor ombreI connectorST-LINKV2C Product Web PageC Product Web PageC Product Web PageC Product Web PageClick on the sTmicroelectronics hardware setup to select it and configure the st motorProfiler toolAs an example, Figure 4 shows the selection of the P-NUCLEO-IHM001 motor controlNucleo pack with NucLEo-F302R8 and X-NUCLEO-IHMO7M1After hardware setup selection, fill in the parameter fields with the motor informationThe number of pole pairs of the motor(mandatory fieldThe Max Speed of the motor(optional field)by default, the st Motor Profiler tool searches for the maximum allowed speedmatching the motor and the hardware setup usedThe Max Current allowed by the motor(optional field)By default, it is the maximum peak current deliverable by the hardware setupThe nominal dC bus voltage used by the hardware setup(optional field)By default, it is the power supply stage as either the bus voltage for low voltageapplications(DC voltage), or the RMs value for high voltage application(Ac voltage)The magnetic built-in type(mandatory field)By default, the SM-PMSM is selectedThe Ld/Lq ratio(mandatory field only when l-PMSM built-in is selected as shown inFigure 6 on page 1110/24UM2374 Rey 1/
- 2020-11-29下载
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