离散自适应重复控制: 收敛性分析与实现

孙明轩; 余林江; 何海港

doi:10.3724/SP.J.1004.2013.00400

离散自适应重复控制: 收敛性分析与实现

doi: 10.3724/SP.J.1004.2013.00400 cstr: 32138.14.SP.J.1004.2013.00400

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

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- 文章访问数: 1622
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- 被引次数: 0
出版历程
- 收稿日期: 2011-11-23
- 修回日期: 2012-10-22
- 刊出日期: 2013-04-20

Discrete Adaptive Repetitive Control: Convergence Analysis and Implementation

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

摘要

摘要: 针对周期已知情形下的离散周期时变系统, 提出一种自适应重复控制方法, 参数估计采用带死区修正的重复学习投影算法. 关键技术引理在分析离散自适应控制系统时起到了关键作用, 通过推广这一引理, 文中给出重复域关键技术引理, 用于证明离散自适应重复控制系统的稳定性和收敛性. 理论分析表明, 系统的输入和输出信号均有界; 且当周期数趋于足够大时, 跟踪误差收敛于一邻域中, 其半径为干扰的界. 在直线电机实验装置上的应用结果验证了所提出重复控制方法的有效性.
- 自适应重复控制 /
- 投影算法 /
- 死区修正 /
- 离散周期系统
Abstract: This paper presents an adaptive repetitive control method for discrete periodically time-varying systems with known periodicity. When estimating unknowns, a repetitive learning projection algorithm with dead-zone is used. The result in this paper can be considered an application of the key technique lemma in repetition domain, by which stability and convergence of the discrete adaptive repetitive control system are established. It is shown that both system input and output are bounded and the tracking error would converge to the bound on the disturbance variable. A linear motor servo system is taken as an example, and experiment results are presented for demonstrating effectiveness of the proposed method.
- Adaptive repetitive control /
- projection algorithm /
- deadzone modification /
- discrete periodic systems

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参考文献(1)

[1]

Goodwin G C, Sin K S. Adaptive Filtering Prediction and Control. Englewood Cliffs, New Jersey: Prentice-Hall, 1984[2] Astrm K J, Wittenmark B. Adaptive Control. Boston: Addison-Wesley, 1989[3] Chen H F, Guo L. Identification and Stochastic Adaptive Control. Boston: Birkhauser, 1991[4] Landau Y D, Landau I D, Lozano R, M'Saad M. Adaptive Control. London: Springer-Verleg, 1998[5] Hara S, Yamamoto Y, Omata T, Nakano M. Repetitive control system: a new type servo system for periodic exogenous signals. IEEE Transactions on Automatic Control, 1988, 33(7): 659-668[6] Tomizuka M, Tsao T C, Chew K K. Analysis and synthesis of discrete-time repetitive controllers. ASME Journal of Dynamic Systems, Measurement and Control, 1989, 111(3): 353-358[7] 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 Control, 1990, 112(4): 618-629[8] Messner W, Horowitz R, Kao W W, Boals M. A new adaptive learning rule. IEEE Transactions on Automatic Control, 1991, 36(2): 188-197[9] 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[10] 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[11] Xu J X. A new periodic adaptive control approach for time-varying parameters with known periodicity. IEEE Transactions on Automatic Control, 2004, 49(4): 579-583[12] Sun M, Ge S S. Adaptive repetitive control for a class of nonlinearly parametrized systems. IEEE Transactions on Automatic Control, 2006, 51(10): 1684-1688[13] 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[14] Chi R H, Hou Z S, Xu J X. Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition. Automatica, 2008, 44(8): 2207-2213[15] Abidi K, Xu J X. A discrete-time periodic adaptive control approach for time-varying parameters with known periodicity. IEEE Transactions on Automatic Control, 2008, 53(2): 575-581[16] Li X D, Xiao T F, Zheng H X. Adaptive discrete-time iterative learning control for nonlinear multiple input multiple output systems with iteration-varying initial error and reference trajectory. IET Control Theory and Applications, 2011, 5(9): 1131-1139[17] Sun M X, He X X. Iterative learning identification and control of discrete time-varying systems. In: Proceedings of the 26th Chinese Control Conference. Hunan, China: IEEE, 2007. 520-524[18] Sun M, Liu X, He H. Adaptive iterative learning control for SISO discrete time-varying systems. In: Proceedings of the 12th International Conference on Control, Automation, Robotics and Vision, Guangzhou, China, 2012[19] Hua G F, Sun M X. Learning identification and control of a class of discrete periodic systems. In: Proceedings of the 4th IEEE Conference on Industrial Electronics and Applications. Xi'an, China: IEEE, 2009. 6-11[20] 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)[21] Chi R H, Sui S L, Hou Z S. A new discrete-time adaptive ILC for nonlinear systems with time-varying parametric uncertainties. Acta Automatica Sinica, 2008, 34(7): 805-808[22] Sun M X, Xie H Y, Wang H. Switching-function dynamics designs for uncertain variable structure systems with repetitive control. International Journal of Control, 2011, 84(7): 1196-1208[23] Sun Ming-Xuan, Fan Wei-Yun, Wang Hui. Discrete sliding mode repetitive control with novel reaching law. Acta Automatica Sinica, 2011, 37(10): 1213-1221(孙明轩, 范伟云, 王辉. 用于离散滑模重复控制的新型趋近律. 自动化学报, 2011, 37(10): 1213-1221)[24] Lee J W, Dullerud G E. Uniform stabilization of discrete-time switched and Markovian jump linear systems. Automatica, 2006, 42(2): 205-218

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