臺灣博碩士論文加值系統

倒單擺系統為一種構造簡單、響應快速、不穩定之非線性系統，故學術領域常用來驗證各種先進的控制理論。在本論文中探討以線性馬達為致動器，並以不同之控制器法則，達到倒單擺之平衡控制。本論文先以Euler-Lagrange方法對倒單擺系統建立動態數學模型，再依此模型設計LQR (Linear Quadratic Regulator)控制器、傳統順滑模態控制器以及二階順滑模態控制器，接著利用MATLAB/Simulink軟體進行模擬，最後將各自模擬結果互相比較。在實作上，本系統使用德州儀器公司(Texas Instruments, TI)所生產的數位訊號處理器TMS320F28335做為控制核心以實現倒單擺之平衡控制的目的。藉由模擬與實作結果得知，二階順滑模態控制具有較佳的性能及強健性。

The inverted pendulum system is a simple, fast, unstable and nonlinear system. It is commonly used as a testbed for studying many advanced control theory. This thesis considers the problems of controlling an inverted pendulum actuated by a linear motor. Different control schemes are used to design the stabilizing controllers. In this thesis, the Euler-Lagrange method is used to derive the dynamic model of the inverted pendulum system. The LQR (Linear Quadratic Regulator) control law, first-order sliding mode control law and second order sliding mode control law are then designed to achieve balance control of this system. The MATLAB/Simulink software is used to conduct the simulation. In the experiments, control laws are implemented through a digital signal processor (TMS320F28335) produced by Texas Instruments. The effectiveness of the control schemes are verified and validated through experimental and simulation studies. It is shown that second-order sliding mode control has better performance and robustness.

摘要 Ⅰ
Abstract Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
圖表目錄 Ⅷ
第一章 緒論
1-1研究背景及動機 1-1
1-2研究目的 1-1
1-3 研究步驟 1-2
1-4 相關文獻探討 1-4
1-5 論文結構 1-4
第二章 倒單擺與線性馬達數學模型
2-1前言 2-1
2-2一節倒單擺系統數學模型之建立 2-1
2-3二節倒單擺系統數學模型之建立 2-9
2-4線性馬達數學模型 2-17
2-5線性馬達參數 2-18
第三章 傳統順滑模態控制理論之探討
3-1 前言 3-1
3-2 順滑模態之介紹 3-1
3-3 順滑條件與迫近條件之探討 3-2
3-4 傳統順滑模態控制器之設計方法 3-4
3-5滑動層的考量 3-7
3-6 非線性機電系統之順滑模態控制設計方法 3-8
第四章 二階順滑模態控制理論之探討
4-1 前言 4-1
4-2 一階與二階順滑模態控制理論比較 4-2
4-3二階順滑模態控制設計方法 4-2
4-3-1 螺旋控制器 4-4
4-3-1-1 穩定度分析 4-5
4-3-1-2 有限時間內收斂分析 4-18
4-3-2 次最佳化控制器 4-20
4-3-2-1 穩定度分析 4-21
4-3-2-2 有限時間內收斂分析 4-30
4-3-3 超螺旋控制器 4-32
4-3-3-1 穩定度及有限時間內收斂分析 4-33
第五章 平衡控制器設計與模擬結果
5-1 前言 5-1
5-2 完整模型與近似模型 5-2
5-3 一節倒單擺系統LQR平衡控制器設計 5-4
5-4 一節倒單擺系統LQR平衡控制模擬結果 5-9
5-5 一節倒單擺系統一階順滑模態平衡控制器設計 5-10
5-6 一節倒單擺系統一階順滑模態平衡控制模擬結果 5-17
5-7 一節倒單擺系統二階順滑模態平衡控制器設計 5-18
5-8 一節倒單擺系統二階順滑模態平衡控制模擬結果 5-20
5-9 二節倒單擺系統LQR平衡控制器設計 5-24
5-10二節倒單擺系統LQR平衡控制模擬結果 5-29
5-11二節倒單擺系統傳統順滑模態平衡控制器設計 5-31
5-12二節倒單擺系統傳統順滑模態平衡控制模擬結果 5-33
5-13二節倒單擺系統二階順滑模態平衡控制器設計 5-35
5-14二節倒單擺系統二階順滑模態平衡控制模擬結果 5-36
5-15模擬響應之性能比較 5-38
第六章 倒單擺系統機構設計
6-1前言 6-1
6-2倒單擺長度與穩定度分析 6-1
6-3整體機構之設計 6-4
第七章 系統控制核心晶片與周邊電路介紹
7-1前言 7-1
7-2控制核心晶片與模組 7-2
7-2-1 數位訊號處理器TMS320F28335 7-2
7-2-2 正交編碼脈衝(Quadrature Encoder Pulse, QEP)介面 7-3
7-2-3 脈衝寬度調製(Pulse Width Modulation, PWM)介面 7-4
7-2-4 通用型輸入/輸出(General Purpose I/O, GPIO)介面 7-4
7-2-5 PWM電壓位準提升與隔離電路 7-5
7-3馬達變頻驅動模組 7-5
7-4回授感測電路模組 7-6
7-4-1 電流感測電路 7-6
7-4-2 電壓感測電路 7-7
第八章 平衡控制實作結果
8-1前言 8-1
8-2系統整體架構 8-1
8-3 系統程式流程及整體控制系統架設 8-1
8-4 控制器平衡實作結果 8-4
第九章 結論與未來展望
9-1結論 9-1
9-2未來展望 9-1
參考文獻 Ref-1
附錄A APP-1

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