Periodic Adaptive Compensating Learning Control of Nonlinear Systems with Saturated Input
-
摘要: 针对一类输入饱和不确定Brunovsky标准型非线性时滞系统,提出一种周期自适应跟踪补偿学习算法. 利用信号置换思想重组系统,基于最小公倍周期函数变换,将时滞时变项和不确定项合并为辅助参数,进而设计周期自适应学习律估计该辅助量,并利用饱和补偿器逼近和补偿超出饱和限的部分,由此构成综合控制器,以保证系统状态对有界期望值的跟踪,解决了饱和输入周期系统的重复迭代学习控制问题. 最后通过构造Lyapunov-Krasovskii复合能量函数的差分,计算证明了系统跟踪误差的收敛性和闭环信号值的有界性. 常见耦合非线性机械臂系统的力矩控制仿真,进一步验证了该算法的有效性.Abstract: A periodic adaptive tracking compensating learning algorithm is proposed for a class of Brunovsky standard nonlinear uncertain systems with time delay and input saturation. By restructuring the system according to signal replacement theory and functional transformation with the lowest common cycle, the delay and other time-varying parameters are combined into an auxiliary time-varying parameter. Then a periodic adaptive learning algorithm is designed to estimate the auxiliary parameter for approximating and compensating the section which exceeds the saturated limit by a compensator. Finally a comprehensive controller is constituted so that the system state can track the bounded expected value and the repeated iterative learning control problem based on periodic system with input saturation is solved. It is proved that the track error is convergent and all the closed-loop signals are bounded by the difference calculation of Lyapunov-Krasovskii composite energy function. The torque control simulation of common coupled nonlinear manipulator further confirms the effectiveness of the algorithm.
-
[1] Lv Ling-Ling, Duan Guang-Ren, Su Hai-Bin, Zhu An-Fu. A survey on linear discrete periodic systems. Acta Automatica Sinica, 2013, 39(7): 973-980(吕灵灵, 段广仁, 苏海滨, 朱安福. 线性离散周期系统研究综述. 自动化学报, 2013, 39(7): 973-980) [2] Liu Shi-Qian, Wang Yuan-Gang, Sheng An-Dong, Guo Zhi. Satisfactory estimation of linear discrete periodic systems. Control Theory and Applications, 2005, 22(3): 359-363(刘世前, 王远钢, 盛安冬, 郭治. 线性离散周期系统满意估计. 控制理论与应用, 2005, 22(3): 359-363) [3] Liu Shi-Qian, Guo Zhi, Qian Long-Jun, Wang Yuan-Gang. Robust state estimation with desired indices of a class of linear periodic systems. Control and Decision, 2002, 17(6): 843-846(刘世前, 郭治, 钱龙军, 王远钢. 期望指标下一类线性周期系统鲁棒状态估计. 控制与决策, 2002, 17(6): 843-846) [4] Lv Ling-Ling, Duan Guang-Ren, Zhou Bin. Parametric pole assignment for discrete-time linear periodic systems via output feedback. Acta Automatica Sinica, 2010, 36(1): 113-120(吕灵灵, 段广仁, 周彬. 线性离散周期系统输出反馈参数化极点配置. 自动化学报, 2010, 36(1): 113-120) [5] Moor K L. Iterative Learning Control for Deterministic Systems. London: Springer-Verlag, 1993. [6] Xu J X, Yan R. Linear and Nonlinear Iterative Leaning Control. New York: Springer-Verlag, 2003. [7] Longman R W. Iterative learning control and repetitive control for engineering practice. International Journal of Control, 2000, 73(10): 930-954 [8] 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 [9] Yan R, Er M J, Pan Y J. Multi-period repetitive learning control for a class of unmatched systems with unknown control direction. In: Proceedings of American Control Conference. Minneapolis, USA: IEEE, 2006. 238-243 [10] Sun Yun-Ping, Liu Yun, Li Jun-Min. Adaptive repetitive learning control for a class of second order nonlinear time-varying systems with mixed parameters. Journal of Xidian University, 2006, 33(3): 495-499(孙云平, 刘赟, 李俊民. 一类二阶时变非线性系统的混合自适应重复学习控制. 西安电子科技大学学报, 2006, 33(3): 495-499) [11] Zhu Sheng, Sun Ming-Xuan, He Xiong-Xiong. S-class function based adaptive controller design for a class of periodically time-varying nonlinear systems. Acta Automatica Sinica, 2010, 36(8): 1137-1143(朱胜, 孙明轩, 何熊熊. 基于S类函数的严格反馈非线性周期系统的自适应控制. 自动化学报, 2010, 36(8): 1137-1143) [12] Chen Wei-Sheng, Wang Yuan-Liang, Li Jun-min. Adaptive learning control for nonlinear 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) [13] Chen W S, Li R H, Li J. Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays. International Journal of Automation and Computing, 2010, 7(4): 438-446 [14] Tao Hong-Feng, Ding Bao, Yang Hui-Zhong. Forgetting learning algorithm with batches for iterative tracking control of nonlinear systems. Information and Control, 2011, 40(6): 772-776(陶洪峰, 丁保, 杨慧中. 非线性系统迭代跟踪控制的批次遗忘学习算法. 信息与控制, 2011, 40(6): 772-776) [15] Sun Yun-Ping, Li Jun-Min, Wang Yuan-Liang. Adaptive repetitive learning control for a class of nonlinearly parameterized uncertain systems. Control and Decision, 2008, 23(11): 1286-1290(孙云平, 李俊民, 王元亮. 一类高阶非线性参数化系统自适应重复学习控制. 控制与决策, 2008, 23(11): 1286-1290)
点击查看大图
计量
- 文章访问数: 2351
- HTML全文浏览量: 95
- PDF下载量: 1137
- 被引次数: 0