一类非线性系统的稳定性分析和控制研究

安徽工业大学毕业设计（论文）说明书共Ⅲ页第I页┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊摘要由于非线性系统的复杂性和理论研究的相对落后，人们对非线性系统的研究方兴未艾。展望未来，将传统的控制理论和方法与现代先进控制理论和方法相结合，形成新的理论和方法，将是非线性系统研究的重要方向和出路。本论文首先介绍了非线性系统的研究现状以及非线性系统的特征。然后针对单摆系统，分别运用Lyapunov稳定性理论、LaSalle不变原理以及局部线性化法对单摆系统的稳定性进行分析。第三章，首先通过对状态反馈与输出反馈的概念进行简单的介绍，然后通过线性化积分控制和反馈线性化的方法分别设计了单摆系统的反馈控制律，最后再通过对Lyapunov函数设计的一个附加控制分量实现系统的稳定。关键词：单摆系统；稳定性；Lyapunov稳定性理论；LaSalle不变原理；反馈控制；线性化安徽工业大学毕业设计（论文）说明书共Ⅲ页第II页┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊AbstractBecauseofthecomplexityofnonlinearsystemandcomparativelybackwardnessoftheoryresearches,theresearchesofthenonlinearsystemareontherise,It’sourexpectationthatthecombinationoftraditionalandmodernadvancedcontroltheoryandmethods,whichformsanewtheoryandmethods,isanimportantdirectionandoutletofnonlinearsystemresearches.Thispaperfirstintroducesthecurrentresearchandthecharacteristicsofnonlinearsystemsofnonlinearsystems.TheselectedsystemmodelispendulumsystemandthroughLyapunovstabilitytheoryandLaSalle'sinvarianceprinciple,aswellaslocallinearizationmethodtoanalyzethestabilityofthependulumsystem.Inthethirdchaper,Firstasimpleintroductiontotheconceptofthestatefeedbackandoutputfeedback,designafeedbackcontrollawofthependulumsystemandthenthroughthelinearizedintegralcontrolandfeedbacklinearizationmethod.Finally,anadditionalcontrolcomponentofthedesignoftheLyapunovfunctionthestabilityofthesystem.Keywords:Pendulumsystem;Stability;Lyapunovstabilitytheory;LaSalle'sinvarianceprinciple;Feedbackcontrol;Linearization安徽工业大学毕业设计（论文）说明书共Ⅲ页第III页┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊目录摘要...................................................................................................................................IAbstract................................................................................................................................II目录................................................................................................................................III第一章绪论.......................................................................................................................11.1课题背景与研究意义..............................................................................................11.2非线性系统的研究现状..........................................................................................11.3非线性系统的特征.................................................................................................31.4相关数学基础..........................................................................................................41.4.1相关数学概念和定义..................................................................................41.4.2相关数学定理..............................................................................................51.5论文的结构..............................................................................................................6第二章单摆系统的稳定性分析.......................................................................................72.1单摆系统的数学模型..............................................................................................72.2单摆系统的平衡点.................................................................................................82.3Lyapunov稳定性理论.............................................................................................92.4LaSalle不变原理分析单摆系统的稳定性...........................................................122.5局部线性化法分析单摆系统的稳定性...............................................................142.6本章小结...............................................................................................................17第三章单摆系统的反馈控制...........................................................................................173.1状态反馈与输出反馈............................................................................................183.2通过线性化实现稳定............................................................................................203.3线性化积分控制....................................................................................................233.4反馈线性化...........................................................................................................273.5跟踪控制...............................................................................................................293.6Lyapunov再设计..................................................................................................323.7本章小结...............................................................................................................35第四章总结.......................................................................................................................35参考文献.............................................................................................................................37致谢.................................................................................................................................36安徽工业大学毕业设计（论文）说明书共38页第1页┊┊┊┊┊┊┊┊┊┊┊┊┊装┊┊┊┊┊订┊┊┊┊┊线┊┊┊┊┊┊┊┊┊┊┊┊┊第一章绪论1.1课题背景与研究意义非线性系统广泛存在于人类生产过程中，所谓线性系统，只是这些非线性系统在某些条件下的良好近似，随着生产和科学技术的发展，对控制系统的性能和精度的要求越来越高，建立在线性化基础上的分