非最小相位系统的极点配置设计

哈尔滨理工大学学士学位论文-I-非最小相位系统的极点配置设计摘要具有非最小相位环节的系统称为非最小相位系统，非最小相位环节会对控制系统的稳定性和其他性能指标产生不利的、有时是非常严重的影响，因此对非最小相位系统的研究具有十分重要的理论意义和实际工程应用价值。极点配置方法是一种有效的设计控制器的方法，特别适用于非最小相位系统的设计。但对于具有不稳定极点的非最小相位系统，这种方法鲁棒性较差，其应用也受到限制。本文对常规极点配置方法进行了改进，应用了一种新的极点配置方法。指出非最小相位系统不符合Bode的幅-相定理，带宽不能反映系统的动态特性，故不宜再用带宽来作为设计指标，而应该采用穿越频率作为性能指标，应小于非最小相位的零点。对不稳定非最小相位系统,提出了一种新的极点配置方法,将极点配置问题转换为正实性问题,用线性矩阵不等式求解控制器,并指出将是鲁棒性设计时的极限值。本文将非最小相位环节与系统的其余部分结合在一起进行讨论，将对象分为稳定的和不稳定对象，并给出鲁棒性设计的范围。首先，建立倒立摆系统的数学模型。倒立摆系统稳定效果非常明了，可以通过摆动角度、位移和稳定时间直接度量，控制好坏一目了然。理论是工程的先导，倒立摆的研究具有重要的工程背景。然后，推导小车倒立摆归一化模型，确定小车倒摆系统无量纲处理后的传递函数。由于其是有一个不稳定零点和一个不稳定极点，是非最小相位系统里最经典，又较为简单的例子，所以用研究不稳定非最小相位系统最为合适。最后，设计非最小相位控制器。先后设计非最小相位零点a=1.414，a=3.317，a=7.14时对应的Nyquist的图线，并给出本文结论。关键词非最小相位；倒立摆；鲁棒性；极点配置哈尔滨理工大学学士学位论文-II-PoleplacementdesignofnonminimumphasesystemsAbstractSystemwithnonminimumphasesystemarecallednonminimumphasesystem,nonminimumphasesystemwillhaveonthestabilityofthecontrolsystemandotherperformanceindicatorsofadverse,sometimesveryseriousimpact,soithasveryimportanttheorysignificanceandpracticalapplicationvalueforthestudyofnonminimumphasesystems.Thepoleplacementmethodisaneffectivemethodtodesignthecontroller,thedesignisparticularlyapplicabletononminimumphasesystems.Butfornonminimumphasesystemswithunstablepoles,thismethodhaspoorrobustness,itsapplicationisrestricted.Thispaperimprovestheconventionalpoleplacementmethod,usinganewmethodofpoleplacement.PointsoutthatthenonminimumphasesystemdoesnotmeettheBodeamplitudephasetheorem,bandwidthcannotreflectthedynamiccharacteristicsofthesystem,soitshouldnotbereusedbandwidthasadesignindex,andshouldusethecrossoverfrequencyastheperformanceindex,shouldbelessthanthenonminimumphasezeros.Onunstablenonminimumphasesystem,proposesanewmethodofpoleplacement,convertingthepoleassignmentproblemforpositiverealness,controllerforsolvinglinearmatrixinequalities,andthatwillbethelimitvalueoftherobustdesign.Therestofthenonminimumphasesystemandsystemintegrationindiscussionstogether,willbedividedintostableandunstableobject,andgivesthedesignofrobustrange.Firstofall,toestablishthemathematicalmodelofinvertedpendulumsystem.Invertedpendulumeffectonthestabilityofsystemisveryclear,theswingangle,displacementandstabilityofdirectmeasurementoftime,thecontroleffectisstickoutamile.Theoryisthepilotproject,theresearchoftheinvertedpendulumhasimportantengineeringbackground.Then,thenormalizedmodelofinvertedpendulumsystem,determinethecartand哈尔滨理工大学学士学位论文-III-invertedpendulumsystemdimensionlesstransferfunctionaftertreatment.Becauseitisanunstablezerosandanunstablepole,isthemostclassicnonminimumphasesystem,andthemoresimpleexample,sothestudyonunstablenonminimumphasesystemisthemostappropriate.Finally,thedesignofnonminimumphasecontroller.Hasthedesignofnonminimumphasezerosofa=1.414,a=3.317,correspondingtothegrapha=7.14,andgivestheconclusionofthispaper.Keywordsnon-minimumphase;invertedpendulum;robustness;poleassignment哈尔滨理工大学学士学位论文目录摘要.................................................................................................................................IAbstract.........................................................................................................................II第1章绪论..................................................................................................................11.1课题背景.........................................................................................................11.2国内外现状.....................................................................................................11.3问题的提出及研究的意义.............................................................................21.4非最小相位系统概述.....................................................................................21.5论文内容.........................................................................................................3第2章被控对象机理模型的建立..............................................................................42.1引言.................................................................................................................42.2倒立摆系统研究现状.....................................................................................42.3倒立摆数学模型的建立.................................................................................52.4倒立摆的归一化模型.....................................................................................72.5本章小结.........................................................................................................7第3章控制器求解的预备知识..................................................................................93.1一种新的极点配置方法.................................................................................93.2LMI及其在控制理论中的应用...................................................................153.2.1LMI问题的求解.................................................................................183.3本章小结.......................................................................................................19第4章非最小相位系统的鲁棒性设计极限............................................................204.1非最小相位系统的设计特点............