Iterative Learning Control of a Class of Nonlinear Systems with Input Backlash
-
摘要: 针对一类具有输入齿隙特性的非线性系统, 提出一种实现有限作业区间轨迹跟踪的迭代学习控制方法. 在系统不确定项可参数化的情形下, 基于类Lyapunov方法设计迭代学习控制器, 回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求. 对未知时变参数进行泰勒级数展开, 参数估计采用微分学习律, 并在控制器设计中, 采用双曲函数处理级数展开后的余项以及齿隙特性里的有界误差项, 以保证控制器可导, 且可抑制颤振. 引入一级数收敛序列确保系统输出完全跟踪期望轨迹, 且闭环系统所有信号有界.Abstract: In this paper, an iterative learning control method is presented for a class of time-varying nonlinear systems with input backlash. In the circumstance of parameterized nonlinear uncertainties, unknown time-varying parameters are expanded into Taylor series and differential learning mechanisms are used to handle non-global Lipschitz nonlinearities in system dynamics. In the controller design, hyperbolic tangent function is introduced to eliminate the influence of the remaining term and the bounded error term due to input backlash, and simultaneously to guarantee the differentiability of the controller and suppress the chattering. Through Lyapunov-like synthesis and with the aid of a convergent series, the complete tracking over a pre-specified time interval is achieved and boundedness of all the signals in the closed-loop system is ensured.
-
Key words:
- Iterative learning control /
- backlash /
- time-varying nonlinear systems /
- finite interval
-
[1] Tao G, Kokotovic P V. Adaptive control of plants with unknown dead-zone. IEEE Transactions on Automatic Control, 1994, 39(1): 59-68[2] Pachter M, Miller R B. Manual flight control with saturating actuators. IEEE Control Systems Magzine, 1998, 18(1): 10-20[3] Tao G, Kokotovic P V, Adaptive control of systems with backlash. Automatica, 1993, 29(2): 323-335[4] Tao G, Kokotovic P V, Adaptive control of plants with unknown hysteresis. IEEE Transactions on Automatic Control, 1995, 40(2): 200-212[5] Tustin A. The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems. Journal of the Institution of Electrical Engineers---Part IIA: Automatic Regulators and Servo Mechanisms, 1947, 94(1): 143-151[6] Grundelisu M, Angeli D. Adaptive control of systems with backlash acting on the input. In: Proceedings of the 35th IEEE Conference on Decision and Control. Kobe, Japan: IEEE, 1996, 4689-4694%[7] Tao G, Ma X, Ling Y. Optimal and nonlinear decoupling control of systems with sandwiched backlash. Automatica, 2001, 37(2): 165-176[8] Mata-Jimenez M T, Brogliato B, Goswami A. On the control of mechanical systems with dynamic backlash. In: Proceedings of the 36th Conference on Decision and Control. Washington D.C., USA: IEEE, 1997, 1990-1995[9] Gerdes J C, Kumar V. An impact model of mechanical backlash for control system analysis. In: Proceedings of American Control Conference. Seattle, USA: IEEE, 1995. 3311-3315[10] Tao G, Kokotovic P V. Continuous-time adaptive control of systems with unknown backlash. IEEE Transactions on Automatic Control, 1995, 40(6): 1083-1087.[11] Jang J O, Lee P G, Park S B, Ahn I S. Backlash compensation of systems using fuzzy logic. In: Proceedings of the American Control Conference. Washington D.C., USA: IEEE, 2001. 4788-4789[12] Selmic R R, Lewis F L. Neural net backlash compensation with Hebbian tuning using dynamic inversion. Automatica, 2001, 37(8): 1269-1277[13] Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robotics by learning. Journal of Robotic Systems, 1984, 1(2): 123-140[14] Sun Ming-Xuan, Huang Bao-Jian. Iterative Learning Control. Beijing: National Defence Press, 1999 (孙明轩,黄宝健. 迭代学习控制. 北京: 国防工业出版社,1999)[15] French M, Rogers E. Nonlinear iterative learning by an adaptive Lyapunov technique. International Journal of Control, 2000, 73(10): 840-850[16] Zhu Sheng, Sun Ming-Xuan. Iterative learning control of a class of nonlinear systems with unknown input dead-zone. Control and Decision, 2009, 24(1): 96-100 (朱胜, 孙明轩. 具有未知死区输入非线性系统的迭代学习控制. 控制与决策, 2009, 24(1): 96-100)[17] Tan Y, Xu J X. A note on iterative learning control for nonlinear systems with input uncertainties. In: Proceedings of the 17th World Congress of The International Federation of Automatic Control. Seoul, Korea: IFAC, 2008. 12474-12479[18] Pagilla P R, Zhu Y. Adaptive control of mechanical systems with time-varying parameters and disturbances. Journal of Dynamic Systems, Measurement, and Control, 2004, 126(3): 520-530[19] Zhu Sheng, Sun Ming-Xuan, He Xiong-Xiong. S-class functions 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)[20] Zhu Sheng, Sun Ming-Xuan, He Xiong-Xiong. Iterative learning control strict-feedback nonlinear time-varying systems. Acta Automatica Sinica, 2010, 36(3): 454-458 (朱胜, 孙明轩, 何熊熊. 严格反馈非线性时变系统的迭代学习控制. 自动化学报, 2010, 36(3): 454-458)
点击查看大图
计量
- 文章访问数: 2142
- HTML全文浏览量: 32
- PDF下载量: 961
- 被引次数: 0