臺灣博碩士論文加值系統

摘　要
本文針對傳統可變結構控制 (Variable Structure Control，簡稱VSC)之滑動(sliding)模式下會發生高速顫動(chattering)現象，將使系統產生不想要的高頻成分，甚至造成系統不穩定，提出模糊推論積分型滑動模式之小腦模型控制器 (Fuzzy based Integral Sliding Mode Using Cerebellar Model Articulation Controller，簡稱CFISMC)。滑動模式控制器具有系統參數變動及雜訊干擾之不敏性，擁有強健性控制，積分器可有效消除系統穩態誤差，並能夠提升系統控制穩定度，由模糊控制加入可簡化設計系統的複雜性，控制法則簡單，易於實現並利用狀態點與滑動面之距離，進行適應性控制增益之動態調整，使狀態點能快速到達滑動面並降低超越量，以提昇系統之暫態響應品質，並引用小腦模型控制器加入，可輔助積分型滑動模式控制器之系統架構，小腦模型控制器(CMAC)，是應用查表方式之類神經網路，對非線性系統具備優越之快速學習收斂速度及類化（generalization）能力，以補償積分型滑動模式控制器，因系統控制器設計之限制而使系統控制效能品質不理想。此外亦希望經由小腦模型輔助控制器的加入，能夠縮短系統上昇時間並簡化系統設計之目的，以減少暫態響應時間並使系統快速到達穩定狀態。最後並將本研究之架構模擬於球體平衡桿系統(Ball-on-Beam Balancing)控制與雙倒單擺系統(Tandem Pendulum)控制，以驗證其控制效能。
關鍵字：可變結構控制，滑動模式，模糊推論，強健性，不敏性，小腦模型控制器，類化能力。

Abstract
The sliding mode causes high speed chattering phenomenon in the traditional Variable Structure Control (VSC), and produces unwanted high frequency in the system and even creates instability. This paper proposes Fuzzy based Integral Sliding Mode Using Cerebellar Model Articulation Controller, abbreviated as FCISMC. The integral controller effectively clears up errors in the system stability, and the sliding mode controller has invariable property with variation in the system parameters and interfering surface noise, thus excelling in robust control. By adding the fuzzy logic controller, it simplifies system difficulty in design. Fuzzy logic control rules are simple to make and easy to implement. We can regulate the control gain by the distance between state point and sliding surface. In this way, the state point can reach the sliding surface rapidly and reduce the overshoot. The transient response of the system will then be improved. By adding the Cerebellar model articulation controller, it aids the system structure of the integral sliding mode controller. Also, with the surpassing nonlinear learning ability of Cerebellar Model Articulation Controller (CMAC) and its sample generalization ability, it is hoped to compensate the poor control efficiency caused by design limitation in the conventional ISMC. Besides, adding the CMAC shortens the design procedure and reduces the difficulties in design. This cuts down the temporary state respond time and enables the system to reach its stable state. Finally, one experiment for the integral sliding mode with CMAC is simulated with the Ball-on-Beam Balancing control system and the Tandem Pendulum control system to demonstrate the improvement in its control performance.
Keywords：Integral Sliding Mode, Sliding mode, robust, invariance property, Cerebellar Model Articulation Controller, generalization

總 目 錄
中文摘要………………………………………………………………...I
英文摘要………………………………………………………………..II
總目錄……………………………………………………………….…III
圖目錄………………………………………………………………….VI
表目錄………………………………………………………………...VII
第一章 緒論…………………………………………………………….1
1.1研究背景與動機………………………………………….2
1.2研究目的………………………………………………….….3
1.3研究範圍與限制………………………….…………………..….4
1.4研究方法…………………….…………..……………………….5
1.5研究步驟………………………………………………….….6
第二章 文 獻 探 討 ……………………..………………………….8
2.1滑動模式控制理論…… ………..…………………………….8
2.1.1滑動模式控制系統理論背景.…………….……..…..…….8
2.1.2滑動模式控制………….………………………..………..12
2.1.3積分型滑動模式控制器…….…….……………………15
2.1.4 積分型滑動模式控制器之數位模擬與分析…..….……19
2.2模糊理論………………………..…..…………………………23
2.2.1 模糊理論之背景……………………………………….23
2.2.2 模糊集合…………………………………………..……23
2.2.3 模糊控制……………..………….…….….…….……….25
2.2.4 模糊滑動模式………………..…………….…..….…….28
2.2.5 模糊滑動模式控制器設計………………...….………...29
2.2.6 模糊滑動模式控制器之數位模擬與分析…………….32
2.3小腦模型控制器之理論背景………………………..……….36
2.3.1 小腦模型控制器基本架構……………………………...36
2.3.2 小腦模型控制器記憶體分割………….….…….……….37
2.3.3 小腦模型控制器數學表示法…………….…….……….39
2.3.4 小腦模型控制器學習演算法…………….…….……….39
第三章 模糊推論積分型滑動模式之小腦模型控制器設計…………41
3.1 積分型滑動模式控制器設計…………..…...……………….41
3.2 小腦模型控制器設計……………………………….….……43
3.2.1 小腦模型記憶體分割方式……………………….…….44
3.2.2 小腦模型數學演算法…………..………………………45
3.3 模糊控制器設計……….……………………………………46
3.4 控制器的架構設計……….…………………………………51
第四章數位模擬結果與討論…………………….…………..………54
4.1 球體平衡桿控制系統模擬結果…………………………….54
4.2 雙倒單擺控制系統模擬結果……………………….….……72
第五章研究結論與建議…………………….…………..………95
5.1 研究結論……………………………..…...……………….95
5.2 研究建議…………………………………………..……….96
參考文獻………………………………………………………………97
作者簡介……………………………………………..…………….100
圖 目 錄
圖1-1 研究步驟流程圖……………………………………………….6
圖2-1 滑動模式控制之二階線性系統方塊圖….…………………….8
圖2-2 相位平面圖…………………………………………...9
圖2-3 相位平面圖……………………..…..…………………9
圖2-4 滑動線在漸進線下方之相位平面圖………………………...10
圖2-5 滑動線在漸進線上方之相位平面圖………………………...11
圖2-6 相位平面圖…..……………………….…………..…………...12
圖2-7 狀態點到達滑動線相位平面圖 …..….…………..………....13
圖2-8 積分型滑動模式控制器方塊圖…….…..……………..……...15
圖2-9 ISMC各狀態變數時間響應圖……………………………21
圖2-10 ISMC控制律時間響應圖……………………………………21
圖2-11 ISMC時間響應圖……………..…….………….……………21
圖2-12 ISMC之時間響應圖…….………..…………….……………22
圖2-13 模糊控制器之方塊圖………………....……………………..26
圖2-14 模糊化之滑動線……………………………………………..28
圖2-15 模糊滑動模式之方塊圖………………………………….….29
圖2-16 FSMC滑動函數 歸屬函數圖……………..……………..….30
圖2-17 FSMC滑動函數變化量 歸屬函數……………………..….30
圖2-18 FSMC輸出變數 歸屬函數圖………………..…………….30
圖2-19 FSMC兩輸入與一個輸出模糊控制器之立體圖…… …….32
圖2-20 FSMC各狀態變數時間響應圖………………….……….….33
圖2-21 FSMC滑動線時間響應圖……………………….…………33
圖2-22 FSMC控制律時間響應圖…………………………………...34
圖2-23 FSMC相位平面圖………………………..………………..34
圖2-24 小腦模型基本學習架構圖.….…………...……………….36
圖2-25 二維小腦模型記憶體等量分割.……………………………37
圖3-1 全狀態變數回授積分型滑動模式控制器方塊圖…………..41
圖3-2 模糊控制器架構圖 …………………………………………46
圖3-3 滑動函數 歸屬函數圖………………………………………47
圖3-4 滑動函數變化量 歸屬函數圖……………………………….48
圖3-5 輸出變數 歸屬函數圖…………………………………….48
圖3-6 兩輸入與一個輸出模糊控制器之立體圖 ………………….49
圖3-7 CFISMC方塊圖……………………………………………51
圖4-1 球體平衡桿系統參考輸入振幅0.2之步階函數……………55
圖4-2 球體平衡桿系統參考輸入振幅 週期25秒之方波函數…55
圖4-3 球體平衡桿系統參考輸入振幅 週期48秒之正弦波函數55
圖4-4 雙倒單擺系統參考輸入振幅0.2之步階函數….……………74
圖4-5 雙倒單擺系統參考輸入振幅 週期30秒之方波函數……74
圖4-6 雙倒單擺系統參考輸入振幅 週期58秒之正弦波函數…74
表 目 錄
表2-1 FSMC模糊推論控制規則表………………..………………...31
表2-2 量化層與超立方塊之關係…………….…….……..…….…….38
表3-1 狀態變數與記憶體之間索引指標建立表………………...….45
表3-2 CFISMC模糊推論控制規則表…………………………...…..50
表4-1 球體平衡桿系統之各控制器的到達模式控制律……....…..55
表4-2 球體平衡桿控制系統各控制器差異性………………....…..72
表4-3 雙倒單擺系統之各控制器的到達模式控制律….……....…..74
表4-4 雙倒單擺控制系統各控制器差異性…………….……....…..94

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