畢業(yè)論文----分?jǐn)?shù)階控制系統(tǒng)仿真研究

1、I摘要分?jǐn)?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(shí)數(shù)范圍內(nèi)，其誕生于300多年前，發(fā)展到現(xiàn)在，分?jǐn)?shù)階微積分已經(jīng)應(yīng)用于許多的領(lǐng)域，并逐漸發(fā)展成為一個(gè)非常熱門的研究方向。分?jǐn)?shù)階控制系統(tǒng)即用分?jǐn)?shù)階微分方程而非整數(shù)階微分方程來(lái)表述的系統(tǒng)，與整數(shù)階微分方程表述的系統(tǒng)相比，分?jǐn)?shù)階控制系統(tǒng)可以在本質(zhì)上反映實(shí)際系統(tǒng)的真實(shí)變化過(guò)程，所以與利用整數(shù)階控制系統(tǒng)模型相比利用分?jǐn)?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?jǐn)?shù)階微積分的定義及

2、其性質(zhì)，分?jǐn)?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(shí)例，最后對(duì)分?jǐn)?shù)階控制系統(tǒng)的進(jìn)行了仿真分析，并給出了仿真實(shí)例。關(guān)鍵詞分?jǐn)?shù)階微積分，分?jǐn)?shù)階控制系統(tǒng)，分?jǐn)?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?jǐn)?shù)階微積分的應(yīng)用發(fā)展....

9、.....................................................................................21.3本文研究?jī)?nèi)容.............................................................................................................32數(shù)學(xué)理論基礎(chǔ)........

10、.......................................................................................................32.1數(shù)學(xué)基本函數(shù)...........................................................................................................

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

12、2.4拉普拉斯變換..........................................................................................................122.5分?jǐn)?shù)階微積分的仿真實(shí)例.......................................................................................13

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

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

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

16、.....314分?jǐn)?shù)階控制系統(tǒng)的仿真..............................................................................................324.1整數(shù)階控制系統(tǒng)仿真實(shí)例.......................................................................................324.2

17、分?jǐn)?shù)階控制系統(tǒng)仿真實(shí)例.......................................................................................364.3本章小結(jié).................................................................................................................

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

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

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