直线一级倒立摆的PID和LQR控制及其仿真

华北电力大学毕业设计（论文）I摘要倒立摆系统是一个典型的快速、多变量、非线性、不稳定系统，许多抽象的控制理论概念都可以通过倒立摆实验直观的表现出来。因此，倒立摆系统经常被用来检验控制策略的实际效果。应用上，倒立摆广泛应用于航空航天控制、机器人、杂技顶杆表演等领域，研究倒立摆的精确控制对工业复杂对象的控制也有着重要的工程应用价值。本文以固高公司直线一级倒立摆为研究对象，对直线一级倒立摆模型进行了建模，控制算法的仿真对比，并得出了相应结论。文中介绍了倒立摆的分类、特性、控制目标、控制方法等以及倒立摆控制研究的发展及其现状。利用Newton力学方法推到了直线一级倒立摆的动力学模型，求出其传递函数及其状态空间方程。在建立了系统模型的基础下，本文还研究了倒立摆系统的控制策略，对直线一级倒立摆首先采用了经典控制算法，设计了常规PID控制器、双闭环PID控制器，并且利用MATALAB/Simulink软件进行仿真，取得了不同的控制效果。然后采用先进的现代控制方法，设计了基于二阶最优控制理论的LQR控制器，借助MATALAB仿真，通过改变LQR模块及状态空间模块中的参数，在仿真调试中，得到最好的控制效果。通过对比PID控制方法和LQR控制方法在仿真中的控制效果，本文得到在条件允许的情况下，现代控制方法比经典控制方法控制效果要好很多。关键词：直线一级倒立摆、控制、PID、LQR、仿真RoyaliceProduce-graduatedsouvenir.NCEPUBYNBGONG华北电力大学毕业设计（论文）IIABSTRACTInvertedpendulumsystemisatypicalfast,multivariable,nonlinear,unstablesystem,andmanyabstractconceptsofcontroltheorycanbeinvertedpendulumthroughthevisualshow.Therefore,theinvertedpendulumsystemisoftenusedtotestthepracticaleffectofcontrolstrategies.Application,theinvertedpendulumcontroliswidelyusedinaerospace,robots,acrobaticperformancesmandrillareasofprecisecontrolofinvertedpendulumcontroloftheindustrialcomplexobjectalsohasimportantengineeringapplications.Inthispaper,solidlineofhigh-levelcompanyastheresearchobjectinvertedpendulumonaninvertedpendulummodeloflinearmodeling,controlalgorithmsimulationcomparison,andconclusionsaredrawn.Thispaperintroducestheclassificationofinvertedpendulum,characteristics,controlobjectives,controlmethodsandthedevelopmentofaninvertedpendulumcontrolandthestatusquo.UsingNewtonmechanicspushedtothelinearinvertedpendulumdynamicmodel,findthetransferfunctionandstatespaceequation.Theestablishmentofasystemmodelbasis,westudytheinvertedpendulumcontrolstrategy,onthefirstlineusesaclassicinvertedpendulumcontrolalgorithm,thedesignofconventionalPIDcontroller,dualloopPIDcontroller,anduseMATALAB/Simulinksimulationsoftware,withvaryingcontrolresults.Thentheuseofadvancedmoderncontrolmethods,designbasedonsecond-orderLQRcontrolleroptimalcontroltheory,withMATALABsimulation,bychangingthestateLQRspacemoduleandthemoduleparametersinthesimulationdebugging,thebestcontroleffect.BycomparingthePIDcontrolmethodandtheLQRcontrolmethodofcontrolinthesimulationresults,thepaperobtainedundertheconditionspermit,themoderncontrolmethodstocontrolthanclassicalcontrolbetterthanmany.KEYWORDS：Linearinvertedpendulum,Control,PID,LQR,simulationRoyaliceProduce-graduatedsouvenir.NCEPUBYNBGONG华北电力大学毕业设计（论文）III目录摘要...........................................................................................................................................IABSTRACT.....................................................................................................................................II第1章：绪论..................................................................................................................................11.1倒立摆简介.........................................................................................................................11.1.1倒立摆分类..............................................................................................................21.1.2倒立摆的特性.........................................................................................................21.1.3倒立摆的控制目标.................................................................................................31.1.4倒立摆的控制方式.................................................................................................31.2倒立摆控制研究的发展及其现状....................................................................................41.3本文的主要内容................................................................................................................7第2章：直线一级倒立摆系统数学模型.......................................................................................82.1直线一级倒立摆系统的物理模型....................................................................................82.2直线一级倒立摆系统的数学模型....................................................................................92.3直线一级倒立摆系统的系统分析..................................................................................122.3.1直线一级倒立摆系统的系统稳定性分析...........................................................122.3.2直线一级倒立摆系统的系统能控性、能观性分析...........................................14第3章：直线一级倒立摆系统的PID控制及仿真.....................................................................163.1PID控制概述....................................................................................................................163.2PID的控制规律、原理....................................................................................................173.3PID参数整定....................................................................................................................173.4直线一级倒立摆双闭环PID控制算法...........................................................................18第4章：直线一级倒立摆系统的线性二次最优控制及仿真.....................................................244.1线性二次最优控制简介..................................................................................................244.2直线一级倒立摆LQR控制算法及仿真...................................................