史都沃特平台銑切工具機之複合適應控制研究

本文針對以史都沃特平台為基礎之銑切工具機，推導系統數學模式並含括慣性力、銑切力等之物理量，另結合濾波動力技巧，推導出鑑別銑切力切削參數之線性迴歸公式，建立含有參數估測新權重之複合適應控制，並以沿X軸平面端銑為例進行數值模擬，分析驗證其效益。平台數模上，涵蓋可動平台、六腳致動連桿等整體之運動學、動態力學，腳部連桿分成固定部、延伸部二項，並以適當之座標系組來描述其姿態轉動時各質心平移、連桿轉動之運動公式，在六腳致動連桿符合所提出假定物性條件下，平台數模得以簡化，且各慣性項係數公式內不需含有連桿轉動角度與角速度項，利用Euler-Lagrange method推導出之系統動態數模方便於參數估測及控制器設計。透過以主軸週轉時間來平均切削力，再結合濾波動力迴歸技巧推導出鑑別銑切力切削參數之線性迴歸公式，嵌入於複合適應控制內，免除加速度訊號之擷取需求，及避免力量量測回授高頻雜訊處理之困擾。複合適應控制之控制法則含入PID項，以提高切削加工之精度，而參數估測更新法則包含命令追蹤誤差及參數估測誤差資訊，而形成複合適應機制。分別對不同之控制增益及不同之材料予以進行模擬驗證。由非適應控制及多種情況之複合適應控制的模擬結果，驗證銑切工具機用史都沃特平台之複合適應控制架構無論在追蹤控制及參數估測收斂性能都良好，並暸解參數估測增益與權重及工件材料之影響關係，作為控制設計之重要參考。

關鍵字

銑切工具機；史都沃特平台；複合適應控制

並列摘要

This study presents a composite adaptive control of a Gough-Stewart platform-type milling machine. Kinematics and dynamic modeling of the platform, modeling of the cutting force, derivation of the linear regressive equation for estimating the cutting parameters, and design of a composite control with an appropriate estimator factor are included in this study. Several cases with different materials and estimation gain sets are simulated and analyzed. The modeling of the platform contains both movable platform and six actuator legs. Each leg is decomposed into two parts: the fixed part and the extensible part. Using suitable coordinates and assumed matching conditions, both the translating and rotating motions are well defined, so that the dynamic model is simplified without including items of the angle and angular velocity of leg’s local rotation. Euler-Lagrange method is used to derive the dynamic modeling and design the adaptive control law. Averaging the cutting forces of end-milling and using filtering dynamics regression technique, the linear regressive equation to identify (important or selected) parameters of the cutting forces is derived, and embedded in composite adaptive control without need of acceleration measurement. The control law includes PID terms to improve the accuracy of machining. The parameter adaptation law consists of the law of the estimator extracts information from both the tracking errors and prediction errors to construct a composite adaptation feature. By adding an appropriate factor in the side of prediction errors, we can adjust its weight. Various estimation gains and materials under the same cutting conditions are investigated with simulation to verify the performance of composite adaptive control. The simulation results indicate that the proposed composite adaptive control can achieve good tracking performance and parameter estimation.

並列關鍵字

composite adaptive control ； milling machine ； Gough-Stewart platform

參考文獻

[23] Tlusty, J. and MacNeil, P., “Dynamics of cutting forces in end milling”, CIRP Annals, pp 21-25, 1975.

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[2] Nanua, P., Waldron, K. J. and Murthy, V., “Direct Kinematic Solution of a Stewart Platform”, IEEE Trans. on Robotics and Automation, v 6, n 4, pp 438-444, Aug 1990.

[4] Nguyen, C. C., Antrazi, S. S. and Zhou, Z.-L., “Adaptive Control of a Stewart Platform-Based Manipulator”, Journal of Robotic Systems, v 10, n 5, pp 657-687, July 1993.

[6] Lebret, G., Liu, K. and Lewis, F. L., “Dynamic Analysis and Control of a Stewart Platform Manipulator”, Journal of Robotic Systems, v 10, n 5, pp 629-655, July 1993.

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史都沃特平台銑切工具機之複合適應控制研究

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