Robust Adaptive Repetitive Control for Periodically Time-varying Systems
-
摘要: 针对周期时变系统,提出一种鲁棒自适应重复控制方法.该方法利用周期学习律估计周期时变参数,并结合鲁棒自适应方法处理非周期不确定性.与现有重复控制不同的是,在控制器设计中引入了新变量—周期数,利用周期系统的重复特性,使界的逼近误差随周期数的增加而逐渐减少,保证了系统的全局渐近稳定性.同时将该方法应用于一类非线性参数化系统,使系统在非参数化扰动的情形下,输出误差仍能收敛于0,倒立摆模型的仿真验证了此结果.该设计方法适用于消除神经网络逼近误差对重复控制系统的影响,理论证明了基于神经网络的鲁棒自适应重复控制系统中所有变量的有界性和输出误差的渐近收敛性,关于机械臂模型的仿真结果验证了受控系统具有良好的跟踪性能.Abstract: In this paper, a robust adaptive repetitive control algorithm is presented for periodically time-varying systems. The periodically time-varying parameters are estimated by periodic learning algorithms, and the non-periodic uncertainties are treated by robust adaptive approaches. Different from the existing repetitive control, a new variable periodic number is introduced to the control design. When this number increases, the convergence error will gradually decrease due to the repetition character of the periodic system, so that the global asymptotic stability is ensured. Further, this method is applied to a class of nonlinearly parameterized systems with non-parametric disturbances, and the tracking error converges asymptotically. This result is verified by a simulation of an invert pendulum model. Moreover, it is proven that the proposed design method is appropriate for the elimination of influence of approximation error of neural network. A theoretical analysis shows that the system output is convergent to the desired one and all signals in the network based robust adaptive repetitive control system are bounded. The simulation result of robotic manipulators shows a good tracking performance of the controlled system.
-
[1] Richards J A. Analysis of Periodically Time-Varying Systems. Berlin: Springer-Verlag, 1983. [2] Bittanti S, Colaneri P. Periodic Systems: Filtering and Control. London: Springer-Verlag, 2009. [3] Sinha S C, Joseph P. Control of general dynamic systems with periodically varying parameters via Liapunov-Floquet transformation. ASME Journal of Dynamic Systems, Measurement and Control, 1994, 116(4): 650-658 [4] Liuzzo S, Tomei P. Global adaptive learning control of robotic manipulators by output error feedback. International Journal of Adaptive Control and Signal Processing, 2009, 23(1): 97-109 [5] Chen W, Tian Y P. Neural network approximation for periodically disturbed functions and applications to control design. Neurocomputing, 2009, 72(16): 3891-3900 [6] 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) [7] Bodson M, Sacks A, Pradeep K. Harmonic generation in adaptive feedforward cancellation schemes. IEEE Transactions on Automatic Control, 1994, 39(9): 1939-1944 [8] Ding Z T. Asymptotic rejection of general periodic disturbances in output-feedback nonlinear systems. IEEE Transactions on Automatic Control, 2006, 51(2): 303-308 [9] Lee R C H, Smith M C. Nonlinear control for robust rejection of periodic disturbances. Systems and Control Letters, 2000, 39(2): 97-107 [10] Inoue T, Nakano M, Iwai S. High accuracy control of servomechanism for repeated contouring. In: Proceedings of the 10th Annual Symposium on Incremental Motion Control Systems and Devices. Champaign: Incremental Motion Control Society, 1981. 282-292 [11] 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 [12] Sun M X. Partial-period adaptive repetitive control by symmetry. Automatica, 2012, 48(9): 2137-2144 [13] Hu C X, Yao B, Chen Z, Wang Q F. Adaptive robust repetitive control of an industrial biaxial precision gantry for contouring tasks. IEEE Transactions on Control Systems Technology, 2011, 19(6): 1559-1568 [14] Chen W S, Zhang Z Q. Nonlinear adaptive learning control for unknown time-varying parameters and unknown time-varying delays. Asian Journal of Control, 2011, 13(6): 903-913 [15] Sun Ming-Xuan, Yu Lin-Jiang, He Hai-Gang. Discrete adaptive repetitive control: convergence analysis and implementation. Acta Automatica Sinica, 2013, 39(4): 400-406(孙明轩, 余林江, 何海港. 离散自适应重复控制: 收敛性分析与实现. 自动化学报, 2013, 39(4): 400-406) [16] Zhu Sheng, Sun Ming-Xuan, Wang Xue-Jie, Li Yan-Jun, Fang Zhi-Gang. Robust repetitive control for a class of nonlinear systems with input deadzone. Acta Automatica Sinica, 2013, 39(6): 908-912(朱胜, 孙明轩, 王雪洁, 李艳君, 方志刚. 具有输入死区的非线性系统的鲁棒重复控制. 自动化学报, 2013, 39(6): 908-912) [17] Jiang Y A, Clements D J, Hesketh T. Adaptive repetitive control of nonlinear systems. In: Proceeding of the 34th Conference on Decision and Control. New Orleans: IEEE, 1995. 1708-1713 [18] Dixon W E, Zergeroglu D M, 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 [19] 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 [20] 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 [21] Sun M X, Ge S S, Marreels I M Y. Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning. IEEE Transactions on Robotics, 2006, 29(33): 563-568 [22] Xu J X, Yan R, Chen Y Q. Repetitive learning control: existence of solution, convergence and robustification. In: Proceedings of the 2006 American Control Conference. Minneapolis, Minnesota, USA: IEEE, 2006. 958-963 [23] Polycarpou M M, Ioannou P A. A robust adaptive nonlinear control design. Automatica, 1996, 32(3): 423-427 [24] Qu Z H. Adaptive and robust controls of uncertain systems with nonlinear parameterization. IEEE Transactions on Automatic Control, 2003, 48(10): 1817-1823 [25] Peterson B B, Narendra K S. Bounded error adaptive control. IEEE Transactions on Automatic Control, 1982, 27(6): 1161-1168 [26] Ioannou P A, Kokotovic P V. Adaptive systems with reduced models. Lecture Notes in Control and Information Sciences. Vol. 47. New York: Springer-Verlag, 1983. [27] Ioannou P A, Tsakalis K S. A robust direct adaptive controller. IEEE Transactions on Automatic Control, 1986, 31(11): 1033-1043 [28] Narendra K S, Annaswamy A M. Stable Adaptive Systems. Englewood Cliffs, New Jersey: Prentice Hall, 1989. [29] Feng G. New robust model reference adaptive control algorithm. IEE Proceedings-Control Theory Applications, 1994, 141(3): 177-180 [30] Astrom K J, Whittenmark B. Adaptive Control. Reading, MA: Addison-Wesley, 1989 [31] Xu J X, Yan R. On repetitive learning control for periodic tracking tasks. IEEE Transactions on Automatic Control, 2006, 51(11): 1842-1848 [32] Zhang T, Ge S S, Hang C C. Stable adaptive control for a class of nonlinear systems using a modified Lyapunov function. IEEE Transactions on Automatic Control, 2000, 45(1): 129-132 [33] Ge S S, Hang C C, Zhang T. A direct adaptive controller for dynamic systems with a class of nonlinear parameterizations. Automatica, 1999, 35(4): 741-747
点击查看大图
计量
- 文章访问数: 1543
- HTML全文浏览量: 85
- PDF下载量: 1213
- 被引次数: 0