臺灣博碩士論文加值系統

本文首先利用線性分佈參數模式探討無拘束具有端點負載單桿撓性機械臂在輸入與輸出為非共點安置時的最小相位問題。為克服因關節驅動扭矩與撓性臂端點位置間為非共點所導致之非最小相位在控制方法上的潛在限制，本文藉由重新定義輸出的方法推導出一無限維非共點開路轉移函數，進而找出此非共點開路轉移函數為最小相位且與系統參數無關的一般充要條件以及建立與端點負載質量相關的特殊條件。其次，本文進一步利用轉移函數之極點和零點在虛軸上相互交錯排列的特性，找出前述最小相位非共點開路轉移函數為被動式的充要條件。此外，本文亦利用回授方法使具有最小相位但非被動式之開路轉移函數轉換成被動式閉路轉移函數。進而證明PD控制器即可使定義輸出漸近達到期望值。
另外，本文也首度利用線性分佈參數模式探討受拘束單桿撓性臂端點之接觸力控制問題。為克服因關節扭矩(輸入)與撓性臂端點接觸力(輸出)間為非共點所導致之非最小相位系統在控制方法上的潛在限制，本文利用回授及重新定義輸出的方法推導出一被動式轉移函數。進而證明利用PD控制器即可使接觸力漸近達到期望值。
由於控制器之設計係根據分佈參數模式，因此閉路系統不會發生控制及觀測洩漏問題。此外，只要受控系統維持為被動式，則受PD控制後之閉路系統對系統參數之變異在穩定性上必具有強韌性。而採用無窮乘積表示法之目的則是有利於穩定性分析，且可藉之求出閉路系統所有無窮多個確實(exact)極點與零點。實例之數值模擬驗證了本文所提出方法的優異性。

In this thesis, a single-link flexible manipulator having a tip payload is investigated using a linear distributed parameter model. With the joint torque as the input and the joint angle plus a weighted value of tip deflection as the measured output, an exact transfer function involving transcendental functions is derived. A necessary and sufficient condition independent of the parameters of the system is obtained such that the irrational transfer function is marginal minimum phase. The effect of the mass of tip payload on the marginal minimum phase condition is also examined. As for the irrational marginal minimum phase transfer function, the connection between the passivity and the interlacing of the poles and zeros is established. Necessary and sufficient conditions for the irrational marginal minimum phase transfer function to be passive are found. Passivation using the feedback of either the root strain or the joint angular acceleration is also discussed. For the passive irrational transfer function, it is shown that a passivity-based PD controller suffices to stabilize the overall system.
The force control problem of a constrained one-single flexible arm is also considered in this thesis based on a linear distributed parameter model. To overcome the inherent limitations caused by the non-minimum phase nature of the noncollocation of the joint torque input and the tip contact force output, a passive transfer function is obtained by using the methods of feedback and output redefinition. A passivity-based PD controller is then designed to accomplish the regulation of the contact force.
Since the controller designs of the above approaches are based on infinite dimensional models, the resulting closed loop systems do not suffer from the control and observation spillover problems. Moreover, so long as the infinite dimensional subsystem controlled by a passivity-based PD controller remains passive, the closed loop system has stability robustness with respect to the parameter uncertainties. In order to preserve the exact poles and zeros of the infinite dimensional closed loop system, the infinite product formulation is employed throughout the thesis. Numerical examples are given to show the efficacy of the proposed approaches.

第一章 緒論********.*************************** 1
1-1 單桿撓性機械臂控制問題之文獻回顧**.******** 1
1-1-1 有限維動態模式與無限維動態模式******* 1
1-1-2 共點控制與非共點控*********..****** 3
1-1-3 非最小相位系統與最小相位系統********* 5
1-1-4 非被動式系統與被動式系統************ 6
1-1-5 模態展開法與無窮乘積表示法********** 7
1-2 研究目標**.**************************** 8
1-2-1 無拘束單桿撓性機械臂之非共點被動式控制** 8
1-2-2 受拘束單桿撓性機械臂之非共點被動式控制** 9
1-3 本文之架構*.*************************** 10
第二章 單桿撓性機械臂之最小相位轉移函數*********** 12
2-1 前言*.********************************* 12
2-2 動力學模式的推導********************************13
2-3 無限維系統之開路轉移函數的推導************ 15
2-4 轉移函數為最小相位且與系統參數無關之充要條件** 19
2-4-1 特例1： (即 )********* 20
2-4-2 特例2： (即 , )* 22
2-4-3 特例3： (即 , ** 23
2-4-4 特例4：
*************** 25
2-5 轉移函數為最小相位但與端點質量相關的特殊條件** 28
2-6 結論與未來研究方向的建議***************** 30
2-6-1 結論*************************** 30
2-6-2 未來研究方向之建議**************** 30
第三章 單桿撓性機械臂之被動式系統的非共點PD控制**** 41
3-1 前言*.****************************** 41
3-2 無端點負載之動態模式******************** 42
3-3 非共點輸入與輸出轉移函數為被動式之條件****** 46
3-3-1 無理數的轉移函數為被動式之條件******* 46
3-3-2 邊界最小相位轉移函數為被動式之條件**** 46
3-4 被動式轉移函數利用PD控制的穩定性分析******* 48
3-5 利用回授使邊界最小相位轉移函數
轉換成被動式轉移函數******************** 51
3-5-1 撓性臂根部應變回授法*************** 51
3-5-2 關節角加速度回授法***************** 53
3-6 端點質量負載的影響********************* 55
3-7 實例數值模擬************************** 59
3-7-1 截短被動式轉移函數之控制************ 60
3-7-2 非截短被動式轉移函數之控制********** 61
3-8 結論與未來研究方向的建議***************** 61
3-8-1 結論*************************** 61
3-8-2 未來研究方向之建議**************** 62
第四章 受拘束單桿撓性臂之分佈參數模式的接觸力控制**** 80
4-1 前言*.******************************* 80
4-2 動態模式***************************** 81
4-2-1 運動方程式的推導****************** 81
4-2-2 穩定平衡狀態的解****************** 83
4-2-3 非最小相位轉移函數的推導************ 84
4-3 控制器的設計************************** 86
4-3-1 利用回授及重新定義輸出建構一被動式
轉移函數************************ 86
4-3-2 被動式系統之PD控制**************** 89
4-4 數值模擬***************************** 92
4-5 結論與未來研究方向的建議***************** 93
4-5-1 結論*************************** 93
4-5-2 未來研究方向之建議**************** 94
第五章 結論與未來研究方向的建議***************** 104
5-1 結論*.****************************** 104
5-2 未來研究方向的建議********************* 105
參考文獻******..******..******..************* 106
附錄 超越函數之無窮乘積展開式**..******..******** 117

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