《自动控制原理》matlab分析与设计仿真实验报告

自动控制原理MATLAB分析与设计仿真实验报告院系电气工程与信息工程学院班级控制工程基地一班姓名学号自动控制原理MATLAB分析与设计仿真实验任务书一、仿真实验内容及要求1MATLAB软件要求学生通过课余时间自学掌握MATLAB软件的基本数值运算、基本符号运算、基本程序设计方法及常用的图形命令操作；熟悉MATLAB仿真集成环境SIMULINK的使用。2各章节实验内容及要求1）第三章线性系统的时域分析法对教材P13635系统进行动态性能仿真，并与忽略闭环零点的系统动态性能进行比较，分析仿真结果；对教材P13639系统的动态性能及稳态性能通过的仿真进行分析，说明不同控制器的作用；在MATLAB环境下完成英文讲义P153E33。对英文讲义中的循序渐进实例“DISKDRIVEREADSYSTEM”，在时，试采用10AK微分反馈使系统性能满足等设计指标。5,320,5SSTMD2）第四章线性系统的根轨迹法在MATLAB环境下完成英文讲义P157E45；利用MATLAB绘制教材P181453）；在MATLAB环境下选择完成教材第四章习题410或418，并对结果进行分析。3）第五章线性系统的频域分析法利用MATLAB绘制本章作业中任意2个习题的频域特性曲线；4）第六章线性系统的校正利用MATLAB选择设计本章作业中至少2个习题的控制器，并利用系统的单位阶跃响应说明所设计控制器的功能。对英文讲义中的循序渐进实例“DISKDRIVEREADSYSTEM”，试采用PD控制使系统的性能满足给定的设计指标。MSTS150,5）第七章线性离散系统的分析与校正利用MATLAB完成教材P383720的最小拍系统设计及验证。利用MATLAB完成教材P385725的控制器的设计及验证。对英文讲义中的循序渐进实例“DISKDRIVEREADSYSTEM”进行验证，计算DZ4000时系统的动态性能指标，说明其原因。二、仿真实验时间安排及相关事宜1依据课程教学大纲要求，仿真实验共6学时，教师可随课程进度安排上机时间，学生须在实验之前做好相应的准备，以确保在有限的机时内完成仿真实验要求的内容；2实验完成后按规定完成相关的仿真实验报告；3仿真实验报告请参照有关样本制作并打印装订。自动化系自动控制原理课程组35单位反馈系统的开环传递函数为该系统0416SG的阶跃响应曲线如下图所示，其中虚线表示忽略闭环零点时的阶跃响应曲线解程序运行结果如下NUMG041DENG1060NUMH1DENH1NUM1,DEN1FEEDBACKNUMG,DENG,NUMH,DENHSYS1TFNUM1,DEN1NUM21DEN2111IGNOREZISYS2TFNUM2,DEN2T000511FIGURE1STEPSYS1,THOLDONSTEPSYS2,TGRIDFIGURE2STEPSYS1,R,SYS2,B,THOLDONPLOT011,10351035,CHOLDONPLOT011,09650965,CGRIDXLABELTYLABELCTTITLE阶跃响应STEPRESPONSETIMESECONDSAMPLITUDE0123456789101100204060811214SYSTEMSYS1RISETIMESECONDS146SYSTEMSYS2RISETIMESECONDS164SYSTEMSYS1PEAKAMPLITUDE118OVERSHOOT18ATTIMESECONDS315SYSTEMSYS2PEAKAMPLITUDE116OVERSHOOT163ATTIMESECONDS365SYSTEMSYS1SETTLINGTIMESECONDS774SYSTEMSYS2SETTLINGTIMESECONDS808SYSTEMSYS2FINALVALUE1响响响响TSECONDSCT0123456789101100204060811214SYSTEMSYS1RISETIMESECONDS146SYSTEMSYS2RISETIMESECONDS164SYSTEMSYS1PEAKAMPLITUDE118OVERSHOOT18ATTIMESECONDS315SYSTEMSYS2PEAKAMPLITUDE116OVERSHOOT163ATTIMESECONDS365SYSTEMSYS1SETTLINGTIMESECONDS774SYSTEMSYS2SETTLINGTIMESECONDS808SYSTEMSYS2FINALVALUE10123456789100020406081121401234567891000204060811214系统参数上升时间调节时间峰值时间峰值超调量有闭环零点（实线）19477430911818无闭环零点（虚线）24277436111616由上图及表格可以看出，闭环零点的存在可以在一定程度上减小系统的响应时间，但是同时也增大了超调量，所以，在选择系统的时候应该同时考虑减小响应时间和减小超调量。并在一定程度上使二者达到平衡，以满足设计需求。39测速反馈校正系统控制系统，比例微分校正系统要求（1）取T10，T201；2）取T101，T20；试分析在不同控制器下的系统的调节时间，超调量，速度误差。解MATLAB程序如下，NUM110DEN11210SYS1TFNUM1,DEN1NUM2110DEN21210SYS2TFNUM2,DEN2NUM010DEN01110SYS0TFNUM0,DEN0T000057FIGURE1STEPSYS0,THOLDONSTEPSYS1,THOLDONSTEPSYS2,TGRIDFIGURE2STEPSYS0,R,SYS1,B,SYS2,K,THOLDONPLOT011,10351035,CHOLDONPLOT011,09650965,CGRIDXLABELTYLABELCTTITLE阶跃响应不同控制器下的单位阶跃响应曲线如下图所示，其中红色实线为没有任何改善的系统的阶跃响应，黑色点线为比例微分校正系统的单位阶跃响应曲线，蓝色虚线为测速反馈校正系统的阶跃响应。STEPRESPONSETIMESECONDSAMPLITUDE01234567002040608112141618SYSTEMSYS2PEAKAMPLITUDE137OVERSHOOT371ATTIMESECONDS094SYSTEMSYS1RISETIMESECONDS0425SYSTEMSYS2SETTLINGTIMESECONDS344SYSTEMSYS2FINALVALUE1SYSTEMSYS1SETTLINGTIMESECONDS354SYSTEMSYS0PEAKAMPLITUDE16OVERSHOOT605ATTIMESECONDS101SYSTEMSYS1PEAKAMPLITUDE135OVERSHOOT351ATTIMESECONDS104响响响响TSECONDSCT01234567002040608112141618SYSTEMSYS0PEAKAMPLITUDE16OVERSHOOT605ATTIMESECONDS101SYSTEMSYS2PEAKAMPLITUDE137OVERSHOOT371ATTIMESECONDS094SYSTEMSYS1PEAKAMPLITUDE135OVERSHOOT351ATTIMESECONDS104SYSTEMSYS2RISETIMESECONDS0392SYSTEMSYS1RISETIMESECONDS0425SYSTEMSYS0RISETIMESECONDS0367SYSTEMSYS2SETTLINGTIMESECONDS344SYSTEMSYS1SETTLINGTIMESECONDS354SYSTEMSYS0FINALVALUE1SYSTEMSYS2FINALVALUE10010203040506070809100204060811214TIMESECONDSDATATIMESERIESPLOT1S20TRANSFERFCN55000S1000TRANSFERFCN41S20TRANSFERFCN31S20TRANSFERFCN25000S1000TRANSFERFCN15000S1000TRANSFERFCNSTEP3STEP2STEP1STEPSCOPE1SINTEGRATOR21SINTEGRATOR11SINTEGRATOR1GAIN6KGAIN5KGAIN40GAIN3KGAIN2KGAIN1KGAIN结果分析系统参数上升时间调节时间峰值时间峰值超调量测速反馈校正系统（蓝色虚线）063126110513535比例微分反馈校正系统（黑色点线）055434409413737据上图及表格可知，测速反馈校正系统的阶跃响应中（虚线），其峰值为135，峰值时间TP105，比例微分校正系统中（点线），其峰值为137，峰值时间TP094，对比以上两个曲线可明显看出，测速校正控制器可以明显降低系统的峰值及超调量，但是会增加系统的调节时间；而比例微分控制器能缩短系统的调节时间，但是会增加系统的超调量，所以针对不同的系统要求应采用不同的控制器，使系统满足设计需求。E33系统的开环传递函数为2605138GSSDETERMINETHEPOLESANDZEROSOFTHETRANSFERFUNCTIONUSEAUNITSTEPINPUT,RS1S,ANDOBTAINTHEPARTIALFRACTIONEXPANSIONFORCSANDTHESTEADYSTATEVALUEPLOTCTANDDISCUSSTHEEFFECTOFTHEREALANDCOMPLEXPOLESOFTHETRANSFERFUNCTION解MATLAB程序文本如下NUMG6205DENG11312810NUMH1DENH1NUM,DENFEEDBACKNUMG,DENG,NUMH,DENHSYSTFNUM,DENPROOTSDENZROOTSNUMT0000053FIGURE1STEPSYS,TGRIDXLABELTYLABELCTTITLE阶跃响应FIGURE2RLOCUSSYSFIGURE3PZMAPSYSXLABELJYLABEL1TITLE零极点分布图GRID；响响响响TSECONDSCT005115225300204060811214SYSTEMSYSRISETIMESECONDS0405SYSTEMSYSSETTLINGTIMESECONDS0802SYSTEMSYSPEAKAMPLITUDE1OVERSHOOT0000455ATTIMESECONDS211SYSTEMSYSFINALVALUE1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS12502001501005005010015020015010050050100150200SYSTEMSYSGAIN0POLE435IDAMPING0114OVERSHOOT698FREQUENCYRAD/S352SYSTEMSYSGAIN0183POLE592DAMPING1OVERSHOOT0FREQUENCYRAD/S592SYSTEMSYSGAIN0638POLE241352IDAMPING00684OVERSHOOT806FREQUENCYRAD/S353POLEZEROMAPREALAXISSECONDS1IMAGINARYAXISSECONDS1654321040302010010203040SYSTEMSYSPOLE435IDAMPING0114OVERSHOOT698FREQUENCYRAD/S352SYSTEMSYSPOLE5DAMPING1OVERSHOOT0FREQUENCYRAD/S5SYSTEMSYSPOLE435IDAMPING0114OVERSHOOT698FREQUENCYRAD/S352结果分析由图可知，该系统的上升时间0405，峰值RT时间211，超调量0000448，峰值为1。PT由于闭环极点就是微分方程的特征根，因此它们决定了所描述系统自由运动的模态，而且在零初始响应下也会包含这些自由运动的模态。也就是说，传递函数的极点可以受输入函数的激发，在输出响应中形成自由运动的模态。英文讲义中的循序渐进实例“DISKDRIVEREADSYSTEM”，在时，试采用微分反馈使系统性能满足10AK5,等设计指标。325,10SSTMD解MATLAB程序文本如下GTF500000,11000G1TF1,1200G2SERIESG,G1G3TF0029,1,101234567891002002040608112SYSFEEDBACKG2,1SYS1FEEDBACKG2,G3,1FIGURESTEPSYS,SYS1GRID程序运行结果如下结果分析参数上升时间调节时间峰值时间峰值超调量单位反馈系统（蓝）0068103760159122218微分反馈系统（绿）010402480216102237通过以上图表可以看出给系统外加一个微分反馈（GSSTEPRESPONSETIMESECONDSAMPLITUDE0010203040506070800204060811214SYSTEMSYSRISETIMESECONDS00682SYSTEMSYSSETTLINGTIMESECONDS0376SYSTEMSYSPEAKAMPLITUDE122OVERSHOOT218ATTIMESECONDS0156SYSTEMSYS1SETTLINGTIMESECONDS0248SYSTEMSYS1RISETIMESECONDS0104SYSTEMSYS1PEAKAMPLITUDE102OVERSHOOT238ATTIMESECONDS0219SYSTEMSYS1FINALVALUE1YSTSYSILVL0029S1）可使系统的超调量和调节时间降低，所以在系统中增加微分反馈可以增加系统的稳态性能。E45ACONTROLSYSTERMSHOWNINFIGURE41HASAPLANT1SG1WHENGCSK,SHOWTHATTHESYSTEMISALWAYSUNSTABLEBYSKETCHINGTHEROOTLOCUS2WHEN20SKGC,SKETCHTHEROOTLOCUSANDDETERMINETHERANGEOFKFORWHICHTHESYSTEMISSTABLEDETERMINETHEVALUEOFKANDTHECOMPLEXROOTSWHENTWOLIEONTHEJWAXIS解MATLAB程序文本如下GTF1,110FIGURE1RLOCUSGNUM12DEN120GCTFNUM,DENSYSPARALLELGC,GFIGURE2RLOCUSSYS0200204060811208060402002040608ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS10200204060811208060402002040608SYSTEMGGAIN000071POLE0000711DAMPING1OVERSHOOT0FREQUENCYRAD/S0000711SYSTEMGGAIN0POLE1DAMPING1OVERSHOOT0FREQUENCYRAD/S1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS12520151050525215105005115225SYSTEMSYSGAIN0000659POLE20DAMPING1OVERSHOOT0FREQUENCYRAD/S20SYSTEMSYSGAININFPOLE323DAMPING1OVERSHOOT0FREQUENCYRAD/S323SYSTEMSYSGAININFPOLE111223IDAMPING0448OVERSHOOT482FREQUENCYRAD/S249SYSTEMSYSGAIN784POLE111222IDAMPING0447OVERSHOOT480FREQUENCYRAD/S248SYSTEMSYSGAIN0136POLE0841DAMPING1OVERSHOOT0FREQUENCYRAD/S0841SYSTEMSYSGAIN0POLE0DAMPING1OVERSHOOT0FREQUENCYRAD/S02520151050525215105005115225ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1结果分析在第一小题的根轨迹图中可以看出，系统的闭环极点都位于S平面的有半平面，所以系统不稳定。453概略绘出的根轨迹图。13523KGSSJSJ解MATLAB程序文本如下运行结果如下图所示GZPK,013532I32I,1RLOCUSG15105051015105051015ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS115105051015105051015SYSTEMGGAIN0POLE32IDAMPING0832OVERSHOOT0898FREQUENCYRAD/S361SYSTEMGGAIN144POLE354DAMPING1OVERSHOOT0FREQUENCYRAD/S354SYSTEMGGAIN0POLE32IDAMPING0832OVERSHOOT0898FREQUENCYRAD/S361SYSTEMGGAIN0POLE1DAMPING1OVERSHOOT0FREQUENCYRAD/S1SYSTEMGGAIN0POLE0DAMPING1OVERSHOOT0FREQUENCYRAD/S0410设反馈控制系统中，要求2KGSHS概略绘出系统根轨迹图，并判断闭环系统稳定性；如果改变反馈通路传递函数，使，试判断改变后12S的系统稳定性，研究由于HS的改变所产生的效应。解MATLAB程序文本如下NUM11DEN1171000SYS1TFNUM1,DEN1NUM221SYS2TFNUM2,DEN1FIGURE1RLOCUSSYS1FIGURE2RLOCUSSYS2ITISOBVIOUSLYSHOWTHATWHENWEMULTIPIEDGBYHWHICHEQUALTO12STHESYSTEMCAMETOBEMORESTABLEANDWEALSOKNOWTHATWHEN02275SYS2WILLBESTABLE201510505101515105051015ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1201510505101515105051015SYSTEMSYS1GAIN384POLE495DAMPING1OVERSHOOT0FREQUENCYRAD/S495SYSTEMSYS1GAIN0POLE2DAMPING1OVERSHOOT0FREQUENCYRAD/S2SYSTEMSYS1GAIN0233POLE000910152IDAMPING00599OVERSHOOT121FREQUENCYRAD/S01522520151050510201510505101520ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS1ROOTLOCUSREALAXISSECONDS1IMAGINARYAXISSECONDS12520151050510201510505101520SYSTEMSYS2GAIN0POLE0DAMPING1OVERSHOOT0FREQUENCYRAD/S0SYSTEMSYS2GAIN0393POLE19DAMPING1OVERSHOOT0FREQUENCYRAD/S19SYSTEMSYS2GAIN0POLE5DAMPING1OVERSHOOT0FREQUENCYRAD/S5结果分析当HS1时系统无零点，系统临界稳定的增益为698，此时系统的根轨迹与虚轴的交点为316I；HS12S时，系统加入一个一阶微分环节，此时无论增益如何变化，系统总处于稳定状态，也就是说给系统加入一个一阶微分环节能大幅度提高系统的稳定性。58已知系统的开环传递函数为，2105GSHSS画出系统的概略频率特性曲线。解MATLAB程序文本如下NUM10DENCONV210,1051GTFNUM,DENFIGURE1MARGINGFIGURE2NICHOLSGGRIDFIGURE3NYQUISTGBODEDIAGRAMGM225DBAT0707RAD/S,PM136DEGAT162RAD/SFREQUENCYRAD/S15010050050100SYSTEMGFREQUENCYRAD/S0713MAGNITUDEDB225SYSTEMGFREQUENCYRAD/S17MAGNITUDEDB187MAGNITUDEDB10210110010110236027018090SYSTEMGFREQUENCYRAD/S0715PHASEDEG181SYSTEMGFREQUENCYRAD/S166PHASEDEG317PHASEDEGNICHOLSCHARTOPENLOOPPHASEDEGOPENLOOPGAINDB36031527022518013590450120100806040200204060SYSTEMGGAINMARGINDB225ATFREQUENCYRAD/S0707CLOSEDLOOPSTABLENOSYSTEMGPHASEMARGINDEG136DELAYMARGINSEC241ATFREQUENCYRAD/S162CLOSEDLOOPSTABLENO6DB3DB1DB05DB025DB0DB1DB3DB6DB12DB20DB40DB60DB80DB100DB120DBNYQUISTDIAGRAMREALAXISIMAGINARYAXIS252015105054003002001000100200300400SYSTEMGGAINMARGINDB225ATFREQUENCYRAD/S0707CLOSEDLOOPSTABLENOSYSTEMGPHASEMARGINDEG136DELAYMARGINSEC241ATFREQUENCYRAD/S162CLOSEDLOOPSTABLENOSYSTEMGREAL24IMAG819FREQUENCYRAD/S0116SYSTEMGREAL243IMAG102FREQUENCYRAD/S00944516已知系统开环传递函数1STKSG；K,T0试根据奈氏判据，确定其闭环稳定条件（1）T2时，K值的范围；（2）K10时，T值得范围；（3）K,T的取值范围。解MATLAB程序如下K11T12G1TFK1,CONVCONV1,0,T1,1,1,1G11FEEDBACKG1,1K22T205G2TFK2,CONVCONV1,0,T2,1,1,1G21FEEDBACKG2,1K32T305G3TFK2,CONVCONV1,0,T3,1,1,1G31FEEDBACKG3,1FIGURE1STEPG11GRIDFIGURE2STEPG21GRIDFIGURE3STEPG31GRIDSTEPRESPONSETIMESECONDSAMPLITUDE020406080100120002040608112141618SYSTEMG11PEAKAMPLITUDE17OVERSHOOT70ATTIMESECONDS596SYSTEMG11RISETIMESECONDS204SYSTEMG11SETTLINGTIMESECONDS751SYSTEMG11FINALVALUE1STEPRESPONSETIMESECONDSAMPLITUDE0102030405060002040608112141618SYSTEMG21PEAKAMPLITUDE17OVERSHOOT70ATTIMESECONDS298SYSTEMG21RISETIMESECONDS102SYSTEMG21SETTLINGTIMESECONDS376SYSTEMG21FINALVALUE1STEPRESPONSETIMESECONDSAMPLITUDE0102030405060002040608112141618SYSTEMG31PEAKAMPLITUDE17OVERSHOOT70ATTIMESECONDS298SYSTEMG31RISETIMESECONDS102SYSTEMG31SETTLINGTIMESECONDS376SYSTEMG31FINALVALUE165设单位反馈系统的开环传递函数为，若采1280SG用滞后超前校正装置，对系统进行串联1210SSGC校正，试绘制校正前后的对数幅频渐进特性曲线，并计算校正前后的相角裕度。解（1校正前G0ZPK,005,4FIGUREBODEG0GRID校正前系统的图BODEDIAGRAMFREQUENCYRAD/S40200204060SYSTEMG0PEAKGAINDB418ATFREQUENCYRAD/S1E20SYSTEMG0FREQUENCYRAD/S196MAGNITUDEDB00346MAGNITUDEDB10210110010118013590SYSTEMG0PHASEMARGINDEG142DELAYMARGINSEC0126ATFREQUENCYRAD/S197CLOSEDLOOPSTABLEYESSYSTEMG0FREQUENCYRAD/S049PHASEDEG134PHASEDEG（2）校正后G0ZPK,005,4NUMCONV101,21DENCONV1001,021GCTFNUM,DENGSERIESG0,GCFIGUREBODEGGRID校正后的系统BODEDIAGRAMFREQUENCYRAD/S10050050100150SYSTEMGPEAKGAINDB418ATFREQUENCYRAD/S1E20SYSTEMGFREQUENCYRAD/S0942MAGNITUDEDB152MAGNITUDEDB10410310210110010110218013590SYSTEMGPHASEMARGINDEG745DELAYMARGINSEC163ATFREQUENCYRAD/S0796CLOSEDLOOPSTABLEYESPHASEDEG622已知45SSG要求系统超调量小于20，上升时间小于05S，调节时间小于12S，静态误差系数大于等于10试问采用超前校正网络753148SSGC是否合适解G0ZPK,024045,250GCZPK35,3375,14837GSERIESG0,GCG1FEEDBACKG,1FIGURESTEPG1GRIDSTEPRESPONSETIMESECONDSAMPLITUDE00204060811200204060811214SYSTEMG1RISETIMESECONDS0167SYSTEMG1PEAKAMPLI