分數(shù)階控制系統(tǒng)仿真研究畢業(yè)論文

1、I摘要分數(shù)階微積分是整數(shù)階微積分的一種推廣，即是將階次推廣到實數(shù)范圍內(nèi)，其誕生于300多年前，發(fā)展到現(xiàn)在，分數(shù)階微積分已經(jīng)應用于許多的領域，并逐漸發(fā)展成為一個非常熱門的研究方向。分數(shù)階控制系統(tǒng)即用分數(shù)階微分方程而非整數(shù)階微分方程來表述的系統(tǒng)，與整數(shù)階微分方程表述的系統(tǒng)相比，分數(shù)階控制系統(tǒng)可以在本質(zhì)上反映實際系統(tǒng)的真實變化過程，所以與利用整數(shù)階控制系統(tǒng)模型相比利用分數(shù)階控制系統(tǒng)模型可以比較全面清晰地分析系統(tǒng)。本文給出了分數(shù)階微積分的定義及

2、其性質(zhì)，分數(shù)階控制系統(tǒng)的求解：包括數(shù)值解法和解析解法，并給出了仿真實例，最后對分數(shù)階控制系統(tǒng)的進行了仿真分析，并給出了仿真實例。關鍵詞分數(shù)階微積分，分數(shù)階控制系統(tǒng)，分數(shù)階控制器，仿真AbatractFractionalcalculusisageneralizationofthefractionalcalculus.ThatisdegreederwillbeextendedWithinthescopeofrealNumbers.Itwas

3、inventedmethan300yearsagonowFractionalcalculushasbeenusedinmanyfieldsgraduallydevelopedintoaveryhotresearchdirection.Fractionaldercontrolsystemwithfractionalderdifferentialequationratherthanintegerderdifferentialequation

4、todescribethesystem.ComparedwithIntegerderdifferentialequationtodescribethesystemThefractionaldercontrolsystemcanreflecttheRealchangeoftheactualsysteminessenceSocomparedwithusingintegerdercontrolsystemmodelusingfractiona

5、ldercontrolsystemmodelcananalysissystemmecomprehensiveclearly.InthispaperwegivethedefinitionoffractionalcalculustheirpropertiesSolutionofthefractionaldercontrolsystem:Includingthenumericalsolutionanalyticsolutiongivethes

6、imulation.Finallyanalysisthefractionaldercontrolsystemgivethesimulation.KeywdsfractionalcalculusfractionaldercontrollersystemIII目錄摘要........................................................................................

7、............................................IAbatract............................................................................................................................I1緒論.......................................

8、.........................................................................................11.1課題的背景和意義....................................................................................................11.2分數(shù)階微積分的應用發(fā)展....

9、.....................................................................................21.3本文研究內(nèi)容.............................................................................................................32數(shù)學理論基礎........

10、.......................................................................................................32.1數(shù)學基本函數(shù)...........................................................................................................

11、..42.2分數(shù)階微積分的定義................................................................................................82.3分數(shù)階微積分的性質(zhì)..............................................................................................11

12、2.4拉普拉斯變換..........................................................................................................122.5分數(shù)階微積分的仿真實例.......................................................................................13

13、2.6本章小結(jié)...................................................................................................................173分數(shù)階控制系統(tǒng)的求解.....................................................................................

14、........183.1分數(shù)階微分方程......................................................................................................183.2分數(shù)階微分方程的數(shù)值解法.................................................................................

15、..203.3分數(shù)階微分方程的解析解法...................................................................................253.4本章小結(jié).............................................................................................................

16、.....314分數(shù)階控制系統(tǒng)的仿真..............................................................................................324.1整數(shù)階控制系統(tǒng)仿真實例.......................................................................................324.2

17、分數(shù)階控制系統(tǒng)仿真實例.......................................................................................364.3本章小結(jié).................................................................................................................

18、.445結(jié)論.............................................................................................................................45致謝.....................................................................................

19、............................................46參考文獻.........................................................................................................................46附錄1外文資料翻譯......................................

20、..............................................................47A1.1譯文：分數(shù)階控制系統(tǒng)的頻域穩(wěn)定性條件........................................................47A1.2原文：FrequencyDomainStabilityCriteriafFractionalderControlSystems.........