多变量非线性系统的变阶采样迭代学习控制

孙明轩; 李芝乐; 朱胜

doi:10.3724/SP.J.1004.2013.01027

多变量非线性系统的变阶采样迭代学习控制

doi: 10.3724/SP.J.1004.2013.01027

1.
浙江工业大学信息工程学院杭州 310023;
2.
浙江大学城市学院杭州 310015

基金项目:

国家自然科学基金(61174034, 60874041),浙江省自然科学基金(LQ12F03005)资助

详细信息

通讯作者:
孙明轩

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- 被引次数: 0
出版历程
- 收稿日期: 2011-11-14
- 修回日期: 2012-10-25
- 刊出日期: 2013-07-20

Varying-Order Sampled-Data Iterative Learning Control for MIMO Nonlinear Systems

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023;
2.
City College, Zhejiang University, Hangzhou 310015

Funds:

Supported by National Natural Science Foundation of China (61174034, 60874041) and Zhejiang Provincial Natural Science Foundation of China (LQ12F03005)

摘要

摘要: 针对存在初态误差的情形, 提出多变量非线性系统的变阶采样迭代学习控制方法. 相对固定阶迭代学习算法, 变阶算法可有效降低跟踪误差. 对变阶采样迭代学习算法进行了收敛性分析, 推导出收敛充分条件. 给出了变阶学习的两种实现策略-DD (Direct division)和DIP (Division in phases)策略. 数值仿真表明, 基于DIP策略的变阶采样迭代学习算法在获得较高的控制精度的同时, 具有较快的收敛速度.
- 多变量系统 /
- 采样系统 /
- 初始修正作用 /
- 变阶迭代学习控制
Abstract: In this paper, the problem of sampled-data iterative learning control is addressed for a class of nonlinear MIMO systems in the presence of perturbed initial conditions. In contrast to the fixed-order learning algorithms, a varying-order learning algorithm is proposed, for enhancing tracking performance against repositioning errors. Sufficient convergence conditions of the proposed varying-order learning algorithm are given, by which the learning gain can be chosen. The proposed learning algorithm is shown to be a unified one, because it is applicable to the systems with arbitrary but well-defined relative degree. Two implementation schemes, sampled-data direct division (DD) and division in phases (DIP) schemes, are presented, and numerical results are given to demonstrate effectiveness of the proposed schemes.
- MIMO systems /
- sampled-data systems /
- initial rectifying action /
- varying-order iterative learning control

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参考文献(23)

[1]	Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2): 123-140
[2]	Hauser J E. Learning control for a class of nonlinear systems. In: Proceedings of the 26th IEEE Conference on Decision and Control. Los Angeles, USA: IEEE, 1987. 859-860
[3]	Wu Dong-Nan, Cheng Mian, Gao Wei-Bing. Learning control under multistep modification law. Acta Automatica Sinica, 1989, 15(5): 445-449 (吴东南, 程勉, 高为炳. 多步控制修正下的学习控制. 自动化学报, 1989, 15(5): 445-449)
[4]	Sugie T, Ono T. An iterative learning control law for dynamical systems. Automatica, 1991, 27(4): 729-732
[5]	Zeng Nan, Ying Xing-Ren. Iterative learning control algorithm for linear dynamical systems. Acta Automatica Sinica, 1992, 18(2): 168-176 (曾南, 应行仁. 非线性系统迭代学习算法. 自动化学报, 1992, 18(2): 168-176)
[6]	Ahn H S, Choi C H, Kim K B. Iterative learning control for a class of nonlinear systems. Automatica, 1993, 29(6): 1575-1578
[7]	Xie S L, Tian S P, Xie Z D. New iterative learning control algorithms based on vector plots analysis. Acta Automatica Sinica, 2004, 30(2): 161-168
[8]	Hou Z S, Xu J X. A new feedback-feedforward configuration for the iterative learning control of a class of discrete-time systems. Acta Automatica Sinica, 2007, 33(3): 323-326
[9]	Tso S K, Ma Y X. Discrete learning control for robots: strategy, convergence and robustness. International Journal of Control, 1993, 57(2): 273-291
[10]	Chien C J. The sampled-data iterative learning control for nonlinear systems. In: Proceeding of the 36th IEEE Conference on Decision and Control. San Diego, California, USA: IEEE, 1997. 4306-4311
[11]	Park K H, Bien Z, Hwang D H. Design of an iterative learning controller for a class of linear dynamic systems with time delay. IEE Proceedings-Control Theory Applications, 1998, 145(6): 507-512
[12]	Sun M X, Wang D W. Sampled-data iterative learning control for nonlinear systems with arbitrary relative degree. Automatica, 2001, 37(2): 283-289
[13]	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
[14]	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
[15]	Park K H. A study on the robustness of a PID-type iterative learning controller against initial state error. International Journal of Systems Science, 1999, 30(1): 49-59
[16]	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
[17]	Sun Ming-Xuan, Huang Bao-Jian, Zhang Xue-Zhi. PD-type iterative learning control for a class of nonlinear systems. Acta Automatica Sinica, 1998, 24(5): 711-714 (孙明轩, 黄宝健, 张学智. 非线性系统的PD型迭代学习控制. 自动化学报, 1998, 24(5): 711-714)
[18]	Sun M X, Wang D W. Closed-loop iterative learning control for systems with initial shifts. International Journal of Adaptive Control and Signal Processing, 2002, 16(7): 515-538
[19]	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
[20]	Sun Ming-Xuan, Huang Bao-Jian, Zhang Xue-Zhi. PD-type iterative learning control for a class of uncertain time-delay systems with biased initial state. Control Theory and Applications, 1998, 15(6): 853-858 (孙明轩, 黄宝健, 张学智. 任意初态下不确定时滞系统的PD型迭代学习控制. 控制理论与应用, 1998, 15(6): 853-858)
[21]	Sun M X, Wang D W. Initial condition issues on iterative learning control for non-linear systems with time delay. International Journal of Systems Science, 2001, 32(11): 1365-1375
[22]	Sun M X, Wang D W, Wang Y Y. Varying-order iterative learning control against perturbed initial conditions. Journal of The Franklin Institute, 2010, 347(8): 1526-1549
[23]	Pillay P, Krishnan R. Modeling, simulation, and analysis of permanent-magnet motor drives: I. the permanent-magnet synchronous motor drive. IEEE Transactions on Industry Applications, 1989, 25(2): 265-273