臺灣博碩士論文加值系統

小腦模型控制器(CMAC)為類神經網路的一支系，構造簡單與演算法撰寫容易是此控制器的特色之一。但本研究發現，當使用簡單迭代法進行演算時，CMAC的誤差曲線會呈現巨幅地振盪然後收歛，此種情形於實際的控制應用裡是不被允許的，因此本研究提出加權因子的概念，改進了控制器在收歛曲線中所發生之振盪現象。
整合加權因子與小腦模型控制器，將此新的控制器命名為「加權因子小腦模型控制器」(WCMAC)。為測試其實用性，本論文之研究範圍包括WCMAC的原理分析、函數學習性能測試和實際控制測試，茲概述如下：
在WCMAC的原理分析裡，本研究採用條件數為測度依據，以實驗說明加權因子的施用能改善CMAC之關聯矩陣，使迭代運算次數明顯地減少。
就函數學習性能測試裡，以Sayil於2002年所整理之資料為依據，分別對連續型函數與非連續型函數進行學習記錄，其中配合殘差理論，發現WCMAC在此項測驗中，就學習的精度而言，WCMAC的性能測試明顯地不遜於他種演算法。
最後的實際控制測試，採用球-桿平衡系統為實驗對象，此為典型控制實驗室裡的測試工具，為一非最小相位系統。本論文以二次型最佳化控制理論設計一主控制器，然後施加WCMAC作為輔助控制器，實驗發現WCMAC能提高響應品質並且不會有學習發散的現象。

The Cerebellar Mode Articulation Controller (CMAC), one kind of Neural Network, is well known of its simple architecture and easily developed algorithm. We found that the curve of error is oscillational, and its situation is not acceptable for real time control, but after the heavy oscillation, it goes steady for some time when CMAC applied simple iterative algorithm. The concept of weighted factor is hereby proposed in order to improve the curve of error in a smoother converging curve.
This paper presents a novel WCMAC, weighted CMAC, to discuss whether or not that it can be suitably applied in the future. The following discussions are focuses on the 1) theory of WCMAC, 2) its learning ability for specific mathematical function and 3) experiment with WCMAC on Ball on Beam Control System.
Firstly, the numbers of iterative applied by WCMAC can be reduced after concluding the result of experiment that is based on the criteria of mathematical condition number.
Secondly, the responses of the WCMAC, when integrated with principle of residual are accurate as well as the other algorithms of CMAC based on the learning specific mathematical function that was adapted from the table from Sayil in 2002.
Finally, this study chooses the Ball on Bean System, a well-known nonminimum phase system, as a tester. We designed a main controller using theory of quadratic optimal control for the purpose of implementing WCMAC as an auxiliary controller. The responses of results found that the control system worked well with WCMAC applied.

總目錄
中文摘要 I
英文摘要 II
總目錄 III
圖目錄 VI
表目錄 X
第一章 緒 論 1
1.1 研究背景與動機 1
1.2 研究目的 5
1.3 研究範圍與限制 5
1.4 研究方法 5
1.5 研究步驟 6
第二章 小腦模型控制器 8
2.1 有關小腦模型控制器的相關研究 8
2.1.1 CMAC的優點 9
2.1.2 CMAC的缺點 10
2.1.3 CMAC對記憶體需求之改善 11
2.1.4 CMAC學習速度的改善 12
2.1.5 CMAC學習精度的改善 12
2.1.6 CMAC 的應用例子 13
2.1.7 具微分特性的CMAC 13
2.2 小腦模型控制器的基本架構 14
2.3 小腦模型控制器的記憶體分割方式 16
2.3.1 一維小腦模型控制器記憶體的分割方式 17
2.3.2 二維小腦模型控制器記憶體的分割方式 19
2.4 小腦模型控制器之數學表示法 21
2.5 小腦模型控制器之學習與回想演算法 22
第三章 加權因子小腦模型控制器之設計 24
3.1 WCMAC之架構 24
3.1.1 記憶體加權因子 24
3.2 WCMAC特性之探討 26
3.2.1 WCMAC條件數之探討 26
3.2.2 WCMAC索引矩陣之範數探討 28
3.3 WCMAC與傳統CMAC對函數學習之比較 29
3.4 加入殘差理論的WCMAC學習架構 31
第四章 球-桿平衡系統之模擬與實驗 34
4.1 球-桿平衡系統之簡介 34
4.1.1 球-桿平衡系統之機構單元 36
4.1.2 球-桿平衡系統之電器單元 37
4.1.3 球-桿平衡系統之介面單元 38
4.2 球-桿平衡系統之系統之數學模型 39
4.2.1 連續時間之數學模型 39
4.2.2 非線性模型之狀態空間描述 41
4.2.3 非線性模型之線性化 42
4.2.4 間時系統之數學模型 43
4.3 間時加權因子小腦模型控制器之實驗與設計 46
4.3.1 二次型最佳控制器 47
4.3.1.1 前言 47
4.3.1.2 輸出完全可控制 49
4.3.1.3 輸入完全可觀測 51
4.3.1.4 二次型最佳控器之設計 53
4.3.1.5 降階狀態估測器之設計 61
4.3.1.6 控制器穩定度之測試 68
4.3.2 間時加權因子小腦模型控制器之設計 71
4.3.2.1 控制器參數設定 71
4.3.2.2 控制器之學習演算法 72
4.3.2.3 控制器之回想演算法 72
4.4 控制實驗與設計 73
4.5 結果與討論 75
第五章 研究結論與建議 101
5.1 研究結論 101
5.2 研究建議 102
參考文獻 103
作者簡介 106
附錄 107

參考文獻
英文部份
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中文部份
[34] 張冠文, ”模糊推論積分型滑動模式之小腦模型控制器設計”,國立台灣師範大學工業教育研究所碩士論文，2002。
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