分數階控制系統仿真研究畢業(yè)論文

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

2、其性質，分數階控制系統的求解：包括數值解法和解析解法，并給出了仿真實例，最后對分數階控制系統的進行了仿真分析，并給出了仿真實例。關鍵詞分數階微積分，分數階控制系統，分數階控制器，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分數階微積分的應用發(fā)展....

9、.....................................................................................21.3本文研究內容.............................................................................................................32數學理論基礎........

10、.......................................................................................................32.1數學基本函數...........................................................................................................

11、..42.2分數階微積分的定義................................................................................................82.3分數階微積分的性質..............................................................................................11

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

13、2.6本章小結...................................................................................................................173分數階控制系統的求解.....................................................................................

14、........183.1分數階微分方程......................................................................................................183.2分數階微分方程的數值解法.................................................................................

15、..203.3分數階微分方程的解析解法...................................................................................253.4本章小結.............................................................................................................

16、.....314分數階控制系統的仿真..............................................................................................324.1整數階控制系統仿真實例.......................................................................................324.2

17、分數階控制系統仿真實例.......................................................................................364.3本章小結.................................................................................................................

18、.445結論.............................................................................................................................45致謝.....................................................................................

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

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