臺灣博碩士論文加值系統

本文主旨在於探討三度空間運動下，含繩索動態之高架式吊車(overhead crane)的非線性動態模式與抗擺動控制。在繩長固定下，本文推導出允許載重物作三度空間運動，且納入繩索動態的非線性分布參數動態模式，並以模態展開的方式將前述推導的含常微分/偏微分之運動方程組近似為有限維的常微分方程組，以供動態分析及控制之用。對於控制方面，本文提出兩種控制策略，分述如下：
針對載重物之點對點的位置控制，本文提出的控制策略為一內迴路的開路控制器加上一外迴路的閉迴路控制器。內迴路的開路控制器乃是根據吊車簡化系統，以近似最小時間控制及近似最小能量控制而設計。而外迴路的閉迴路控制器則是根據完整之非線性動態模式，且兼顧實用性質之PD控制器，用來消除載重物之擺動及增強閉迴路系統的強健性。然後以數值模擬驗證控制策略的可行性。
對於載重物的軌跡追蹤控制，本文利用輸入/輸出回授線性化之非線性控制理論，針對完整之動態模式，設計一消除載重擺動之軌跡追蹤控制器，藉由適當的選擇輸出，可使內部動態達到漸進穩定，最後由數值模擬驗證此一控制器之性能。

This thesis deals with the nonlinear modeling and anti-swing control of an overhead crane including cable dynamics. With fixed length of the rope, a set of nonlinear distributed-parameter equations of motion which allow the payload to swing in the three-dimensional space is derived. A finite-dimensional dynamic model is then obtained via eigenfunction expansion. This finite-dimensional dynamic model is subsequently used in controller design and dynamic simulation.
For the point-to-point position control of the payload, the controller design strategy is based on an inner open-loop controller which corresponds to the rigid body model of the crane and an outer closed-loop controller which deals with the unsimplied nonlinear finite-dimensional model of the crane. The inner open-loop controller can be designed using either a near minimum-time control or a near minimum-energy control . The outer closed-loop controller is an easily implementable PD controller used for the elimination of swing and vibration of the payload and for the robustness enhancement of the closed-loop system. Numerical simulation is used to demonstrate the effectiveness of this control strategy.
As for the path tracking control of the payload, a nonlinear controller is also designed using the input-output feedback linearization approach. With the properly chosen outputs, the internal dynamics are shown to be asymptotically stable. Thus the path tracking of the payload and the elimination of payload swing can be achieved simultaneously. The performance of the closed-loop system is further tested via numerical simulation.

第一章 緒論 ………….…………………..1
1.1 前言 ……………………………………1
1.2 文獻回顧 ………………………………………1
1.3 研究動機………………………………………3
1.4 本文主要貢獻…………………………3
第二章 數學模型的推導………………………..5
2.1 前言…………………………………….5
2.2 座標系統的建立……………………………6
2.3 系統的動能及位能……………………………7
2.4 系統的運動方程式………………………………11
第三章 運動路徑規劃及PD控制器的設計…… 24
3.1 前言……………………………………24
3.2 最佳控制…………………………… 24
3.3 近似最小時間控制與近似最小能量控制…………32
3.3.1 近似最小時間控制………………………… 32
3.3.2 近似最小能量控制…………………………..35
3.4 PD控制器的設計及數值模擬……………………36
3.4.1 PD控制器的設計……………………………..36
3.4.2 數值模擬……………………………37
3.5 結論………………………………………38
附錄3.A 說明為何在performance measure J中加入一常數項λ的原
因………………………………………….40
第四章 輸入 / 輸出回授線性化控制……………92
4.1 前言……………………………………..92
4.2 控制器的設計…………………………………92
4.3 內部動態之穩定性……………………………….95
4.4 數值模擬………………………………………100
4.5 結論……………………………………….101
第五章 結論與未來展望……………………..115
5.1 結論………………………………………..115
5.2 未來展望………………………………………..115
參考文獻……………………………………… 117

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