臺灣博碩士論文加值系統

平行式雙倒單擺相較於一般傳統的倒單擺，除同樣為非極小相位和不穩定系統外，因單擺長度相異，具不同自然頻率特性，尚須考慮軌道長度限制，在所有倒單擺類型中，控制難度相對較高，且因線性馬達滑軌上摩擦力非均勻分佈，單以狀態回授控制無法達到良好的定位性能。本論文提出一串級控制之架構（Cascade Control），內迴路使用狀態回授穩定系統、外迴路採用模型預測控制（Model Predictive Control）來加強線性馬達之定位控制。除此之外，本研究從機構設計開始，完成平行式雙倒單擺系統的建立並推導出系統之動態模型，提出一平行式雙倒單擺之甩上控制方法，將長短單擺分別甩至上平衡點，最後再利用模型預測控制進行平衡控制與定位控制。模擬與實驗結果和傳統狀態回授控制結果相比，使用模型預測控制能明顯降低定位誤差，克服了使用狀態回授需建立足夠精準摩擦力模型的問題。

The aim of this paper is to apply Model Predictive Control (MPC) to the Parallel-type Double Inverted Pendulum (PDIP). Control of the PDIP is more difficult among the inverted pendulum family. Because the different lengths of the two pendulums give them distinct natural frequencies and the stoke length is limited. Besides, friction is not homogenously distributed on the track. Please bear in mind that one cannot achieve good performance if only state feedback is used. Therefore, we proposed a cascade structure where the inner loop was formed via state feedback and MPC directed the outer loop to enhance position control of the linear motor. In this work, a positive feedback control combined with energy-based control is adopted to swing up the PDIP sequentially, and then is switched to balance control. From simulation and experimental results, the proposed control scheme was successfully applied to the PDIP. Compared with conventional state feedback control, position errors could be reduced by MPC, which overcome the requirement of precise friction model needed in state feedback applications.

摘要 I
Abstract II
致謝 III
目錄 IV
表目錄 VI
圖目錄 VII
符號 IX
第一章 緒論 1
1.1 前言 1
1.2 研究背景與文獻回顧 2
1.2.1 倒單擺文獻回顧 2
1.2.2 模型預測控制文獻回顧 5
1.3 模型預測控制的基本架構與原理 7
1.4 本文架構 10
第二章 平行式雙倒單擺之動態模型 11
2.1 平行式雙倒單擺系統之動位能分析 11
2.2 平行式雙倒單擺之拉格朗日方程與動態模型 13
2.3 非線性狀態空間模型 15
2.3.1 單倒單擺之非線性模型 15
2.3.2 平行式雙倒單擺之非線性模型 16
2.4 非線性模型之線性化 16
2.4.1 單倒單擺狀態空間模型 17
2.4.2 平行式雙倒單擺狀態空間模型 19
第三章 參數估測與控制器設計 22
3.1 參數估測簡介 22
3.1.1 參數估測原理 22
3.1.2 最小平方擬合法 23
3.2 參數模型建立 26
3.2.1 資料估測 27
3.3 甩上控制器－能量控制 29
3.3.1 單倒單擺甩上控制 29
3.3.2 平行式雙倒單擺同時甩上控制 31
3.4 甩上控制器－正回授控制 32
3.5 平衡控制器－狀態回授控制 35
3.6 定位控制器－模型預測控制 38
3.6.1 輸入增量與積分動作 38
3.6.2 預測模型之建立 40
3.6.3 閉迴路算法 44
3.6.4 無拘束模型預測控制 45
3.6.5 拘束模型預測控制 47
3.6.5.1 終端代價函數 50
3.6.5.2 仿代數黎卡提方程 53
3.6.6 模型預測控制實現步驟 54
第四章 模擬與實驗結果 60
4.1 實驗架構與軟硬體簡介 60
4.1.1 軟體部分 62
4.1.2 硬體部分 62
4.2 系統鑑別與驗證 67
4.3 單倒單擺 70
4.3.1 長短桿單倒單擺甩上控制之模擬與實驗 70
4.3.2 長短桿單倒單擺平衡控制之模擬與實驗 76
4.3.3 長短桿單倒單擺定位控制實驗 80
4.4 平行式雙倒單擺 82
4.4.1 平行式雙倒單擺同時甩上之模擬與實驗 82
4.4.2 平行式雙倒單擺分別甩上之模擬與實驗 85
4.4.3 平行式雙倒單擺平衡控制之模擬與實驗 88
4.4.4 平行式雙倒單擺模型預測控制之模擬與實驗 91
4.4.5 平行式雙倒單擺定位控制實驗 94
第五章 結論與建議 99
5.1 結論 99
5.2 建議 100
參考文獻 101
自述 106

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