• 作者： 姚志民; 鄭文弘
• 作者服務機構： 台灣大學機械工程學系
• 中文摘要： 由於高產量、低耗能和高精度的要求，質輕具撓性之機械臂的運動和振動控制益發重要。透過尾端運動參數化，並利用反算動力學法，一單撓性旋轉臂的最佳尾端運動可以參數最佳化設計法得出，而其對應之最佳力矩可由力矩方程式的代數運算求得。此最佳尾端運動可使撓性臂的尾端在所欲時間運動至所欲位置，且使所伴生的振動能量最小。分析中先形成一反算系統，此系統以尾端加速度運動為輸入，而以振動為輸出。再用一相似轉換將此反算系統分成一因果系統和一反因果系統，利用給予在初始時之反因果系統狀態變數值的拘束條件，因果解即可由時域解得到，因果解使得力矩不須在運動開始前先作用。最佳化所得的結果可以做為開路控制策略，或是做為回饋控制系統的前饋輸入或參考輸入，來改善系統的動態反應。模擬結果顯示，所提方法對減少振動能量確實有效。
• 英文摘要： Due to the demand for high productivity, low energy consumption and high accuracy, motion andvibration control of flexible structures is needed. In this paper, after parametrilizing the motion of theend point, a parameter optimization design based on an inverse dynamics approach for a rotating flexiblelink is proposed to plan an optimal trajectory of the end point and then to synthesize the optimal torquehistory This optimal torque will drive the arm to perform a point-to-point motion with which the endpoint of the arm will move to the desired position at a specified final time with the induced vibrationenergy being minimized. The inverse system, which governs the vibration behavior under actuation ofthe specified end point acceleration, is divided into a causal system and an anticausal system due to itsunstable characteristics. A causal and bounded solution is solved in the time domain by imposing a setof constraints on the states for the part of the anticausal system at the initial time such that optimal torqueneed not be applied before the motion begins. The results can be used as an open loop control strategyor be used as a feedforward input or reference input to improve the dynamic performance of a feedbackcontrol system. From simulation results, it has been shown that this approach does effectively reducevibration energy.
• 中文關鍵字： vibration; optimization; inverse dynamics; flexible arm; trajectory planning
• 英文關鍵字： --