迭代学习控制系统的误差跟踪设计方法

孙明轩; 严求真

doi:10.3724/SP.J.1004.2013.00251

迭代学习控制系统的误差跟踪设计方法

doi: 10.3724/SP.J.1004.2013.00251

1.
浙江工业大学信息工程学院杭州 310023

详细信息

通讯作者:
孙明轩

计量
- 文章访问数: 1894
- HTML全文浏览量: 71
- PDF下载量: 781
- 被引次数: 0
出版历程
- 收稿日期: 2011-06-10
- 修回日期: 2012-07-25
- 刊出日期: 2013-03-20

Error Tracking of Iterative Learning Control Systems

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023

摘要

摘要: 提出能够实现期望误差轨迹完全跟踪的迭代学习控制系统设计方法, 旨在放宽常规迭代学习控制方法的初始定位条件, 在每次迭代时允许初值定位在任意位置. 这种方法对于预先给定的期望误差轨迹, 经迭代学习, 使得实际跟踪误差收敛于预定的误差轨迹, 这样, 预设的误差轨迹即最终形成的误差轨迹. 针对常参数、时变参数以及复合参数三种情形, 分别采用类Lyapunov方法设计迭代学习控制系统. 所设计的未含/含限幅作用的参数学习律, 能够使得跟踪误差轨迹在整个作业区间上与预定轨迹完全吻合, 并保证系统中所有信号的有界性. 给出的仿真结果表明所提方法的有效性.
- 初值问题 /
- 收敛性 /
- 迭代学习控制 /
- 类Lyapunov方法
Abstract: This paper presents an iterative learning control method with which the error trajectory can be pre-specified. The method dose not require that the initial condition remains to be a fixed value for each iteration, whereas this requirement is usually assumed in conventional methods. The proposed strategy is to make the tracking error trajectory converge to the pre-specified one over the entire interval. The constant parametrization, time-varying parametrization, and a combined situation are respectively examined. By the Lyapunov-like approach, accordingly, learning laws are given and the learning systems are analyzed in details. With the help of unsaturated/saturated learning law, the system error coincides with the pre-specified error trajectory over the entire interval, and all the signals in close-loop system are guaranteed to be bounded. Numerical results are presented to demonstrate the effectiveness of the proposed learning control method.
- Initial condition problem /
- convergence /
- iterative learning control /
- Lyapunov-like approach

HTML全文

参考文献(1)

[1]

Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2): 123-140[2] Heinzinger G, Fenwick D, Paden B, Miyazaki F. Robust learning control. In: Proceedings of the 28th IEEE Conference on Decision and Control. Tampa, Florida, USA: IEEE, 1989. 436-440[3] Lee H S, Bien Z. Study on robustness of iterative learning control with non-zero initial error. International Journal of Control, 1996, 64(3): 345-359[4] Park K H. An average operator-based PD-type iterative learning control for variable initial state error. IEEE Transactions on Automatic Control, 2005, 50(6): 865-869[5] Porter B, Mohamed S S. Iterative learning control of partially irregular multivariable plants with initial impulsive action. International Journal of Systems Science, 1991, 22(3): 447-454[6] Sun Ming-Xuan, Huang Bao-Jian. Iterative Learning Control. Beijing: National Defence Industry Press, 1999(孙明轩, 黄宝健. 迭代学习控制. 北京: 国防工业出版社, 1999)[7] Dawson D M, Qu Z, Dorsey J F, Lewis F L. On the learning control of a robot manipulator. Journal of Intelligent and Robotic Systems, 1991, 4(1): 43-53[8] Qu Z H, Dorsey J, Dawson D M, Johnson R W. Linear learning control of robot motion. Journal of Robotic Systems, 1993, 10(1): 123-140[9] Arimoto S, Naniwa T, Suzuki H. Robustness of P-type learning control with a forgetting factor for robotic motions. In: Proceedings of the 29th IEEE Conference on Decision and Control. Honolulu, Hawaii, USA: IEEE, 1990. 2640-2645[10] Sadegh N, Horowitz R, Kao W W, Tomizuka M. A unified approach to the design of adaptive and repetitive controllers for robotic manipulators. ASME Journal of Dynamic Systems, Measurement, and Control, 1990, 112(4): 618-629[11] Kuc T, Lee J S. An adaptive learning control of uncertain robotic systems. In: Proceedings of the 30th IEEE Conference on Decision and Control. Brighton, England: IEEE, 1991. 1206-1211[12] Park B H, Kuc T Y, Lee J S. Adaptive learning control of uncertain robotic systems. International Journal of Control, 1996, 65(5): 725-744[13] Dixon W E, Zergeroglu E, Dawson D M, Costic B T. Repetitive learning control: a Lyapunov-based approach. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics , 2002, 32(4): 538-545[14] Xu J X, Tan Y. A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties. IEEE Transactions on Automatic Control, 2002, 47(11): 1940-1945[15] Qu Z H, Xu J X. Asymptotic learning control for a class of cascaded nonlinear uncertain systems. IEEE Transactions on Automatic Control, 2002, 47(8): 1369-1376[16] Tayebi A, Chien C J. A unified adaptive iterative learning control framework for uncertain nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(10): 1907-1913[17] Marino R, Tomei P. An iterative learning control for a class of partially feedback linearizable systems. IEEE Transactions on Automatic Control, 2009, 54(8): 1991-1996[18] Chien C J, Hsu C T, Yao C Y. Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors. IEEE Transactions on Fuzzy Systems, 2004, 12(5): 724-732[19] Sun Ming-Xuan. Finite-time iterative learning control. Journal of Systems Science and Mathematical Sciences, 2010, 30(6): 733-741(孙明轩. 有限时间迭代学习控制. 系统科学与数学, 2010, 30(6): 733-741)[20] Xu J X, Yan R. On initial conditions in iterative learning control. IEEE Transactions on Automatic Control, 2005, 50(9): 1349-1354[21] Sun Ming-Xuan, Wang Dan-Wei, Chen Peng-Nian. Repetitive learning control of nonlinear systems over finite intervals. Science China Information Sciences, 2010, 40(3): 433-444(孙明轩, 王郸维, 陈彭年. 有限区间非线性系统的重复学习控制. 中国科学: 信息科学, 2010, 40(3): 433-444) 　[22] Saab S S, Vogt W G, Mickle M H. Learning control algorithms for tracking “slowly” varying trajectories. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics , 1997, 27(4): 657-670[23] Xu J X, Xu J. On iterative learning from different tracking tasks in the presence of time-varying uncertainties. IEEE Transactions on System, Man, and Cybernetics-Part B: Cybernetics, 2004, 34(1): 589-597[24] Yin C K, Xu J X, Hou Z S. A high-order internal model based learning control scheme for nonlinear systems with time-iteration-varying parameters. IEEE Transactions on Automatic Control, 2010, 55(11): 2665-2670[25] Chen Wei-Sheng, Wang Yuan-Liang, Li Jun-Min. Adaptive learning control for nonlinearly parameterized systems with periodically time-varying delays. Acta Automatica Sinica, 2008, 34(12): 1556-1560(陈为胜, 王元亮, 李俊民. 周期时变时滞非线性参数化系统的自适应学习控制. 自动化学报, 2008, 34(12): 1556-1560) 　[26] Zhang Yu-Dong, Fang Yong-Chun. Learning control for systems with saturated output. Acta Automatica Sinica, 2011, 37(1): 92-98(张玉东, 方勇纯. 一类输出饱和系统的学习控制算法研究. 自动化学报, 2011, 37(1): 92-98) 　[27] Tian Hui-Hui, Su Yu-Xin. Nonlinear decentralized repetitive control for global asymptotic tracking of robot manipulators. Acta Automatica Sinica, 2011, 37(10): 1264-1271(田慧慧, 苏玉鑫. 机器人系统非线性分散重复学习轨迹跟踪控制. 自动化学报, 2011, 37(10): 1264-1271) 　

施引文献

资源附件(0)

访问统计