臺灣博碩士論文加值系統

本篇論文主要在研究彈性旋轉樑的振動分析及定位控制與定速追蹤。於本文之分析中，非線性耦合動態方程式是由剛體運動、撓性振動以及馬達系統所組成。由動能與應變能的關係，利用漢彌爾頓原理(Hamilton''s Principle)推導出系統的統御方程式(Govern Equations)，由橫向變形、旋量變形及剛體運動方程所構成。文中提出一個新的變結構控制理論，藉由李亞波諾夫方法(Lyapunov Method)，設計出定位控制與定速追蹤的控制器，並同時滿足滑動模存在條件和系統穩定條件。並比較由選取不同的李亞波諾夫函數所設計出的線性回授定位控制器的不同點。選擇有限差分法作為其數值分析工具，在分析之前先將求得的控制輸入導入統御方程式中，接著對系統施以針對時間與空間變數的離散化以便於數值的求解。而數值分析的結果可與理論的證明相互呼應。工業機器人微適應高速及精確的需求，因此設計日趨輕量化，一繞性機器手臂連接於ㄧ剛體圓盤，且於另一端負載重物，做圓周旋轉運動時，所產生的變形將會影響到系統的動態行為及精確度。所以為了減少剛體圓盤或馬達與繞性旋轉樑耦合系統的橫向變形，以端點負載所產生的旋轉變形，將變結構控制理論應用在旋轉樑的定位振動控制和等速振動控制。應用有限差分法(Finite Difference Method, FDM)進行模擬控制分析，在分析上先將控制輸入導入統御方程式中，再將整個方程式對空間與時間離散化以求其數值解。而在方程式中所出現的積分式可運用梯形面積法求得其值。分析的過程中選取控制增益值來比較其控制結果。同時探討其物理現象。於本文之分析中，非線性耦合動態方程式是由剛體運動、撓性振動以及馬達系統所組成。 利用新的變結構控制理論，設計出定位及速度控制器，在控制理論中選擇適當的參數，則撓性系統的撓性變形量及繞性機器手臂旋轉的位置和速度即可以被控制住，達成預先設定的目標。在本文中，理論分析與數值模擬相互比較，從而了解參數值對此系統的影響。期望在機電自動化上之實際應用，能有幫助。

This paper presents the vibration control of the flexible rotating beam with a tip mass. Modeling and control of a flexible rotating beam has received a great deal of attention. When a tip mass of a flexible beam is a rigid body, not only bending vibration but also torsional vibration will occur. In this paper, the bending and torsion vibrations and rigid-body motion are governed by the nonlinear coupled partial differential equations associated with a set of nonlinear boundary conditions. The coupling provides the opportunity to suppress the flexible vibration by control torque applying to the rotating beam. A new variable structure control (VSC) law designed by Lyapunov''s direct method is proposed for vibration suppression and tracking control simultaneously. Asymptotic stability of the controlled system is proved. Simulation results are provided to show the effectiveness of the controller design.The rigid body motion and flexible vibration system can be controlled because of their coupling terms in governing equations. Due to the applying of new variable structure control method, the derived algorithm ensures that system satisfies the reaching conditions and stability conditions. By selecting a suitable sliding mode function, new variable structure control can design a controller for the propose of position regulation and speed control and sliding mode exist. The new VSC controller prevents the chattering and the control force prevents closing infinite. Although the design procedure of VSC is simple, numerical results have shown that the proposed VSC not only very effective eliminates the vibration of the flexible vibration of the rotating beam, but also keeps good tracking performance. In speed control, the sliding mode design is different from position control. The speed error is closed to zero that means rotating speed is closed to our target speed. Using the PDA controller law, no information of the flexible deformations is needed and the system is globally stable. The PDA controller is simulation results reveal that this controller is effective for regulation and vibration control.The design procedure of vibration control can also be applied to any other rigid body motion and flexible vibration coupled system.