【正文】 The firstorder linear inverted pendulum is a typical “fast, multivariable, nonlinear, unstable system”, for an inverted pendulum system stability research in theory and method has the profound significance. For an inverted pendulum can boil down to the research on nonlinear, multivariable, unstable system research. In application, an inverted pendulum is widely used in control theory, aerospace control and other fields, in the field of automation has important value. This paper is to establish a mathematical model of the inverted pendulum, and using the double closedloop control system, through the inverted pendulum double closedloop control mathematical model analysis, a fuzzy control method is applied to an inverted pendulum control, Wherein, the inner control of the inverted pendulum swing angle, the outer loop controls the position of inverted pendulum. Fuzzy controller design including the membership function and fuzzy control rule, fuzzy solution, finally using the Matlab software simulation. The fuzzy control method is applied to an inverted pendulum control system, fuzzy control can play in the control of nonlinear system, plex object systems control advantages, simplify the design, improve the stability of system. Key words: Inverted pendulum,Mathematical model,Fuzzy control,Matlab 本科畢業(yè)設計 (論文 ) 目錄 III 目 錄 摘 要 ............................................................................................................................... I Abstract............................................................................................................................. II 1 緒 論 .............................................................................................................................1 一階倒立擺系統(tǒng)研究的意義 .............................................................................1 一階倒立擺系統(tǒng)在國內(nèi)外研究綜述 .................................................................1 本論文的研究內(nèi)容和所用方法 .........................................................................2 2 一階倒立擺數(shù)學模型的建立與控制系統(tǒng) ...................................................................3 一階倒立擺的數(shù)學模型 .....................................................................................3 一階倒立擺系統(tǒng)的動力學分析 ...............................................................4 系統(tǒng)微分方程的線性化 ...........................................................................5 系統(tǒng)微分方程狀態(tài)空間表示 ...................................................................6 一階倒立擺定性分析 .........................................................................................7 系統(tǒng)的穩(wěn)定性、能控性和能觀測性判據(jù) ...............................................7 基于狀態(tài)方程的系統(tǒng)定性分析 ...............................................................8 一階倒立擺控制系統(tǒng) ....................................................................................... 11 一階倒立擺控制系統(tǒng)硬件 ..................................................................... 11 一階倒立擺系統(tǒng)總體控制框圖 ............................................................. 11 3 模糊控制的基本原理 .................................................................................................15 模糊控制理論的基本概念 ...............................................................................15 模糊邏輯操作 .........................................................................................16 模糊規(guī)則與模糊推理 .............................................................................16 模糊控制系統(tǒng) ...................................................................................................16 模糊控制系統(tǒng)的組成 .............................................................................17 模糊控制系統(tǒng)的特點 .............................................................................18 模糊控制器 .......................................................................................................18 模糊控制器的組成 .................................................................................18 模糊控制器的結構 .................................................................................19 4 雙閉環(huán)模糊控制系統(tǒng)設計 .........................................................................................21 建立雙閉環(huán)模糊控制系統(tǒng) ...............................................................................21 模糊控制器的設計 ...........................................................................................21 隸屬函數(shù)的確定 .....................................................................................21 本科畢業(yè)設計 (論文 ) 目錄 IV 模糊控制規(guī)則 .........................................................................................23 輸出向量的 解模糊 .................................................................................24 建立模糊控制查詢表 .............................................................................25 5 一階倒立擺系統(tǒng)仿真及其分析 .................................................................................28 MATLAB 及其模糊工具箱的介紹 ...................................................................28 MATLAB 的主要特點 ....................................................................................28 MATLAB 的基本組成 .............................................................................29 一階倒立擺模糊控制系統(tǒng)仿真實驗 ...............................................................30 利用 GUI 編輯 FIS 結構文件，即設計模糊控制器 ............................30 建立一階倒立擺模糊控制系統(tǒng)的仿真模型圖 .....................................33 6 結論與展望 .................................................................................................................38 參考文獻 .........................................................................................................................39 致 謝 .............................................................................................................................40 系統(tǒng)總體框圖 ......................................................................