單連桿撓性機械手臂之非線性遞回步階控制

Nonlinear Backstepping Control of a Single-Link Flexible Robotic Manipulator

黃志偉(Jhih-Wei Huang)

指導教授 ： 林容杉

國立暨南國際大學/科技學院/電機工程學系/碩士(2007年)

https://doi.org/10.6837/NCNU.2007.00163

摘要

近年來，撓性機械手臂已被廣泛應用在現代工業裡，高生產力需具備能高速移動、高精確度、低功率消耗和能承受不同負載的機械手臂。所以，機械手臂之結構逐漸朝向具有彈性及輕量化發展。本論文中將利用非線性遞回步階設計法則設計單連桿撓性機械手臂末端位置軌跡追蹤的控制器。並且，一無限維度的撓性臂數學模型將透過設模法(Assumed modes method)和拉格朗日方程式(Lagrange formulation)被得到。在設計過程中，由於分析非線性系統是複雜及困難的，所以一開始我們先分析線性化模型以便了解非線性系統的動態行為與特性。然而，我們將透過數學分析證明零動態的穩定性。也就是說，設計的控制器不僅能使系統達到穩定，並能夠使手臂之軌跡追蹤誤差及末端因振動產生的偏移量收歛到零。經初步分析，遞回式步階設計法則已成功用於線性系統，因此，此設計概念將被拓展到非線性系統。最後由模擬證明我們的設計法則在撓性機械手臂上擁有出色的效能。

關鍵字

單連桿撓性機械手臂 ； 遞回式步階控制設計 ； 設模法

並列摘要

At present, lots of flexible manipulators are commonly utilized in modern industry. In the manufacturing industry, higher productivity needs to have manipulators that can operate with higher speed, more precision, less power consumption, lower cost and improved payload handing capabilities. These requirements translate into manipulators that must have structural flexibility and be lightweight. In this thesis, the backstepping design scheme is developed for the tip-position trajectory tracking control of single-link flexible robotic manipulator systems. An infinite dimensional dynamic model of a single-link flexible manipulator is derived through the assumed modes method (AMM) associated with Lagrange approach. In the procedure of backstepping design, the analysis of this nonlinear system is complex and difficult for control design. Therefore, in the first instance a linearized system model will be investigated so that the behavior of this nonlinear system can be further understood. In the procedure of analysis, the zero dynamics will be utilized to prove the stability of closed-loop system by Routh stability criterion. That is to say, the proposed backstepping controller is not only to stabilize the flexible robotic manipulator, but also to drive the trajectory tracking errors and tip-deflection to converge to zero asymptotically. In preliminary analysis, the feasibility of backstepping control scheme is verified in linear system. Therefore, the concept of linear backstepping will be expanded to nonlinear system. Furthermore, some simulation results are given to illustrate the excellent performance of the backstepping control design applied to a single-link flexible robot arm.

並列關鍵字

A single-link flexible robotic manipulator ； Backstepping control design ； Assumed modes method

參考文獻

[1] B. Paden, D. Chen, R. Ledesma, and E. Bayo, “Exponentially Stable Tracking Control for Multijoint Flexible-Link Manipulators,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 53-59, Mar. 1992.

[2] T. C. Yang, C. S. Jackson and P. Kudva, “Adaptive control of a single-link flexible manipulator with unknown load,” IEE Proceedings-Control Theory and Applications, Vol. 138, pp. 153 -159, Mar, 1991.

[3] S. S. Ge, T. H. Lee and G. Zhu, “Tip Tracking Control of a Flexible Manipulator Using PD Type Controller,”Proceedings of IEEE International Conference on Control Applications, pp. 309-313, 1996.

[4] H. Geniele, R. V. Patel and K. Khorasani, “End-Point Control of a Flexible-Link Manipulator: Theory and Experiments,” IEEE Transactions on Control System Technology, Vol. 5, No. 6, pp. 556-570, 1997.

[5] S. Thomas and B. Bandyopadhyay, “Position Control of Single Link Flexible Manipulator by Variable Structure Model Follow-ing Control,” ASME Journal of Dynamic System, Measurement, and Control, Vol. 119, pp. 330-335, 1997. [6] D. Karandikar and B. Bandyopadhyay, “Sliding Mode Control of Single Link Flexible Manipulator,” Proceedings of IEEE International Conference on Industrial Technology, Vol. 1, pp. 712-717, Jan. 2000.