臺灣博碩士論文加值系統

由於倒單擺系統(Inverted pendulum system)是屬於非線性，單輸入多輸出之系統，且具有非極小相位與不穩定之特性，因此常被學者與研究人員用來檢驗控制器的性能。本文提出利用PID控制器應用於單軸式倒單擺系統平衡控制，並加入Ziegler–Nichols參數調整法與基因演算法來求取近似最佳PID參數解，避免以往由專家系統設計、費時嘗試錯誤或主觀經驗法來設計控制器參數，達到智慧型搜尋最佳化參數且省時省力設計控制器之目標。在模擬和實驗中，提出簡單的PID控制器架構，並應用Ziegler–Nichols參數調整法與基因演算法搜尋調整PID控制器相關參數，設計出完善的系統PID控制器，成功地讓單軸式倒單擺系統之單擺垂直向上穩定控制。此外，在經過各控制器的控制性能之比較與分析後，發現上述兩種方法設計的控制器中控制性能表現比較良好的為基因演算法PID控制器。最後，經由單軸式倒單擺平台實驗證明了基因演算法PID控制器於倒單擺控制系統是可行的。

Since the inverted pendulum is a non-linear, single input multi-output system with the characteristics of non-minimum phase and instability, it is widely used by scholars and researchers for verifying the performance of various controllers.This paper proposes the use of PID controller is applied to single-axis inverted pendulum control system balance and add parameters to adjust the Ziegler-Nichols method and genetic algorithm to compute approximate solutions of optimal PID parameters to avoid ever by an expert system design, time-consuming trial and error or subjective experience method to design the controller parameters to achieve the goal of intelligent search optimization parameters and time-saving controller design.In the simulation and experiment, proposed a simple PID controller architecture and applied Ziegler-Nichols method and genetic algorithm parameter tuning PID controller to adjust the search parameters, to design a perfect system PID controller, succeeded in getting the formula down uniaxial pendulum stability control system vertically upwards.Moreover, after a comparison and analysis on the control performance of each controller, found that the above two methods designed to control the performance of the controller is relatively good genetic algorithm PID controller. Finally, through a single-axis platform inverted pendulum experiment proves the genetic algorithm PID controller in inverted pendulum control system is feasible.

中文摘要.......................................................................................I
英文摘要.......................................................................................II
誌謝..........................................................................................III
目錄..........................................................................................IV
表目錄.........................................................................................VI
圖目錄.........................................................................................VII
第一章 緒論.....................................................................................1
1-1 研究動機....................................................................................1
1-2 文獻回顧....................................................................................2
1-3 研究目的....................................................................................4
1-4 論文架構....................................................................................5
第二章 理論.....................................................................................6
2-1 倒單擺系統的數學模型推導......................................................................6
2-1-1 模型建立與系統之參數........................................................................6
2-1-2 牛頓力學之數學推導..........................................................................7
2-2 PID控制器的基礎理論..........................................................................10
2-3 PID控制器的特性分析..........................................................................12
2-3-1 比例控制.................................................................................12
2-3-2 積分控制.................................................................................12
2-3-3 微分控制…................................................................................13
2-3-4 比例-積分-微分控制........................................................................13
2-4 Ziegler–Nichols參數調整法..................................................................14
2-5 基因演算法理論..............................................................................16
2-5-1 編碼，解碼...............................................................................17
2-5-2 適合度函數...............................................................................19
2-5-3 原始族群.................................................................................20
2-5-4 停止條件.................................................................................20
2-6 基因演算法運算因子...........................................................................21
2-6-1 選擇與複製...............................................................................21
2-6-2 交配....................................................................................22
2-6-3 突變....................................................................................26
2-7 基因演算法之特性…...........................................................................29
2-8 基因演算法流程….............................................................................29
2-8-1 基因演算範例..............................................................................30
第三章 模擬與實驗................................................................................35
3-1 單軸式倒單擺平衡控制系統......................................................................35
3-2 系統說明...................................................................................40
3-3 模擬流程...................................................................................43
3-3-1 倒單擺控制系統............................................................................43
3-3-2 倒單擺系統分析............................................................................44
3-3-3 設計控制器參數............................................................................46
3-3-4 定義適應函數.............................................................................47
3-3-5 PID控制系統建構..........................................................................48
3-3-6 應用Ziegler–Nichols參數調整法............................................................49
3-3-7 基因演算法設計PID控制器....................................................................52
3-4 單軸式倒單擺實驗步驟.........................................................................58
3-4-1 倒單擺PID控制系統方塊圖....................................................................59
3-4-2 單軸式倒單擺平衡控制實驗....................................................................61
第四章 結果與討論...............................................................................63
4-1 單軸式倒單擺平衡控制實驗結果與分析..............................................................63
4-2 討論.......................................................................................70
第五章 結論與未來展望.............................................................................73
5-1 結論.......................................................................................73
5-2 未來展望...................................................................................74
參考文獻.......................................................................................75

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