本論文中，以視覺伺服(visual servo)的觀念， 結合數位訊號處理器(Digital Signal Processor, DSP)的基礎，完成了一套視覺伺服球與板控制系統。整體系統架構包含了機械結構、馬達致動器、影像感測器、控制器部份，以及配合自行設計的週邊介面電路與軟體程式。球與板系統是一個高度非線性的系統，由於系統存在有離心力項，相對階數(relative degreee)沒有被適當定義(not well defined)，使系統易跳動而不穩定。本論文先使用解耦合的方式將系統解耦合成兩個獨立的球與桿系統，再利用倒階(backstepping)控制方法與近似回授線性化(approximate feedback linearization)控制方法設計控制器。倒階控制為利用遞迴程序重複選用Lyapunov function來判斷穩定性的一種回授控制設計方法；近似回授線性化為利用李氏微分(Lie derivative)進行狀態變換，將一些非線性項視為極小的擾動，進而捨棄之，將原非線性的系統轉換近似成線性的輸入-輸出系統(approximate input-output system)。由模擬與實驗結果得知，近似回授線性化控制器與倒階控制器性能相仿，但近似回授線性化之控制法則的複雜度較低，使得控制器進行參數調整時更能觀察出各個控制參數的特性，增加控制器在實作上的可行性與便利性。而兩者皆可在限制的條件下解決穩定化(stabilization)、追蹤(tracking)以及強健性(robustness)的問題，減少離心力項對系統的影響，使系統達到漸近穩定。

In this thesis, a visual-servo and digital signal processor based ball and plate system is constructed. This system consists of a mechanism, two motor actuators, an image sensor, a DSP-based control card, the relevant peripheral interface circuits, and the software programs. The ball and plate system is a highly nonlinear system. Due to existence of the centrifugal force, the system relative degree is not well defined. Moreover, the centrifugal force provides a strong positive feedback and easily leads to the peaking phenomenon. In this thesis, the decoupling method is used to obtain two independent ball and beam systems. The backstepping control techniques and approximate feedback linearization are then used to design the controllers. Backstepping control design is a recursive procedure that interlaces the choice of a Lyapunov function to discriminate stability with design of feedback control. The approximate feedback linearization technique regards some nonlinear terms as very small disturbances and neglects them. The original nonlinear system is then tranformed into an approximate input-output system. It is shown that approximate feedback linearization not only reaches the excellent performance, but also has less complexity in controller design and implementation. So that we can re-tune each parameter of the controller much easier. It is greatly helpful when we proceed the experiments. Both of the controllers can achieve stabilization, tracking and robust control under restrictive conditions. Moreover, they can reduce the effect of centrifugal force on the system, and make the system reach asymptotic stability.

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
圖表目錄 IX
第一章 緒論 1-1
1-1 研究背景 1-1
1-2 研究動機及目的 1-1
1-3 研究步驟 1-2
1-4 相關文獻探討 1-5
1-5 實驗室相關成果 1-7
1-6 論文結構 1-8
第二章 相機模型與相機參數估測 2-1
2-1 前言 2-1
2-2 數位影像處理簡介 2-1
2-3 針孔成像模型 2-7
2-4 相機內部參數 2-9
2-5 相機規格介紹 2-15
2-6 相機內部參數估測 2-17
2-7 資料位元不足 2-20
2-8 球與板系統之影像視差補償 2-22
第三章 影像處理演算法 3-1
3-1 前言 3-1
3-2 物體偵測流程規劃 3-1
3-2-1 影像二值化 3-1
3-2-2 影像相減法 3-3
3-2-3 影像雜訊 3-6
3-2-3-1 影像濾波器 3-7
3-2-3-2 中值濾波器 3-10
3-3 物體在影像平面上的座標之計算 3-11
3-4 影像處理流程規劃 3-13
第四章 永磁式直流馬達和球與板系統數學模型 4-1
4-1 前言 4-1
4-2 永磁式直流馬達數學模型之建立 4-1
4-3 永磁式直流馬達參數識別 4-4
4-4 球與板系統數學模型之建立 4-12
4-5 利用MATLAB/Simulink驗證數學模型 4-19
4-6 球與板系統之解耦合數學模型 4-23
第五章 球與板系統控制器設計 5-1
5-1 前言 5-1
5-2 球與板系統之LQR平衡控制器設計 5-1
5-3 球與板系統之倒階控制器設計 5-6
5-3-1 倒階控制器之概要 5-6
5-3-2 倒階控制器設計步驟 5-7
5-3-3 設計球與板系統的倒階控制器 5-14
5-4 球與板系統之回授線性化控制器設計 5-32
5-4-1 輸入-輸出線性化 5-33
5-4-2 全狀態線性化 5-36
5-5 近似回授線性化控制器設計 5-39
5-6 極點配置法 5-50
第六章 球與板系統模擬結果 6-1
6-1 前言 6-1
6-2 球與板系統之LQR平衡控制器模擬結果 6-1
6-3 球與板系統之倒階控制器模擬結果 6-6
6-4 球與板系統之近似回授線性化控制器模擬結果 6-14
第七章 球與板系統機構與感測器介紹 7-1
7-1 前言 7-1
7-2 球與板系統機構設計與製作 7-2
7-3 馬達角度感測器 7-7
第八章 硬體電路及軟體程式介紹 8-1
8-1 前言 8-1
8-2 周邊硬體電路與規格 8-1
8-2-1 解碼電路設計 8-1
8-2-2 數位/類比轉換電路及馬達驅動電路 8-4
8-2-3 影像同步序向電路 8-8
8-2-4 CMOS影像感測器 8-9
8-2-5 影像感測器傳輸規格 8-13
8-2-6 RS-232通訊傳輸 8-17
8-2-7 外部記憶體 8-22
8-3 系統核心晶片與影像處理系統實現 8-23
8-3-1 TMS320F2812核心簡介 8-23
8-3-1-1 QEP模組簡介 8-24
8-3-1-2 SCI模組介面簡述 8-25
8-3-1-3 USB傳輸模組介面簡述 8-28
8-3-1-4 傳輸資料之封包定義與交握協定 8-29
8-3-2 可程式邏輯陣列(FPGA) 8-31
8-3-2-1 Cyclone EP1C12Q240C8 FPGA 8-32
8-3-2-2 FPGA內部規劃 8-36
8-4 軟體環境介紹 8-44
8-4-1 Code Composer Studio簡介 8-44
8-4-2 Quartus II簡介 8-48
第九章 實驗結果 9-1
9-1 前言 9-1
9-2 微分器之實現 9-3
9-3 球與板系統之實驗結果 9-4
第十章 結論與未來展望 10-1
10-1 結論 10-1
10-2 未來展望 10-1
參考文獻
附錄A 座標軸旋轉定理
附錄B 圖B-1 USB傳輸介面電路
附錄C 動力學簡介
C-1 前言C-1
C-2 本論文所需之動力學觀念C-1
C-2-1 物體的動能C-1
C-2-2 球的轉動動能C-2
C-2-2-1 角位移、角速度C-3
C-2-2-2 轉動慣量C-4
C-2-2-3 角位移、角速度C-5
C-2-3 物體的位能C-6
C-2-4 球與板系統的位能C-6
C-3 Lagrange’s方程式推導C-7
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