A Method for Identifying and Controlling Hammerstein Model with Hysteresis
-
摘要: 迟滞特性具有非光滑、多值映射等复杂特性,如果迟滞环节的末端还存在一个线性子系统,导致其输出信号不可测,常规的方法难以进行有效的辨识和控制。提出一种基于退化激励信号的分步辨识法。设计一个退化激励信号将迟滞退化为一条光滑的、一一映射的曲线,并由广义递推最小二乘法(RGIA)辨识线性环节;根据已辨识的线性子模型,采用"扩展输入空间法"辨识迟滞环节;根据辨识所得的Hammerstein模型设计一个PID前馈控制器,实现对PEA的精确运动控制。
-
关键词:
- Hammerstein迟滞系统 /
- 退化激励信号 /
- 扩展输入空间法 /
- 前馈补偿器
Abstract: Due to its non-smoothness and multi-value mapping,it is difficult to apply the conventional identification methods to identifying the hysteresis model. Moreover,if the hysteresis subsystem follows with a linear subsystem,it is more challenging to identify the Hammerstein model because the output of the hysteresis model cannot be measured directly. This paper proposes a two-stage method. Firstly,the degeneration input,which is a special exciting signal,is designed to degenerate the hysteresis into a static smooth curve with one-to-one mapping. Thus, the non-smoothness and multi-value mapping of hysteresis are avoided so that the parameters of the linear subsystem can be estimated by the recursive general identification algorithm(RGIA). Secondly,with the identified linear submodel,the hysteresis subsystem is modeled with the expanded input space method. Finally,a PID feedforward controller for controlling the motion of the PEA is proposed. The experimental results on the PEA are presented to show the effects of the identification and control method. -
[1] Ping Ge,Jouaneh M. Modeling hysteresis in piezoceramic actuators[J]. Precision Engineering,1995,17(2): 211-221 [2] Hong H. Compensation of hysteresis in piezoceramic actuators and control of nanopositioning system [D].Toronto: University of Toronto,2003 [3] Mayergoyz I D. Mathematical models of hysteresis[M].New York: Springer-Verlag,1991 [4] Macki J W,Nistri P,Zecca P. Mathematical models for hysteresis[J]. SIAM Review,1993,35(1): 94-123 [5] Zhao X L,Tan Y H. Modeling hysteresis and its inverse model using neural networks based on expanded input space method[J]. IEEE Transaction on Control Systems Technology,2008,16(3): 484-490 [6] Cerone V,Regruto D. Bounding the parameters of linear systems with input backlash [J]. IEEE Transaction on Automatic Control,2007,52 (3): 531-536 [7] Giri F,Rochdi Y,Chaoui F Z. Identification of hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities [J].Automatica,2008,44(5): 767-775 [8] Zhang X L,Tan Y H,Su M Y,et al. Neural networks based identification and compensation of rate-dependent hysteresis in piezoelectric actuators [J]. Physica B,2010,405(12): 2687-2693 [9] Chen X K,Su C Y,Fukuda T S. Adaptive control for systems preceded by hysteresis [J]. IEEE Transaction on Automatic Control,2008,53(4): 1019-1025 [10] Tao G,Kolotovic P V. Adaptive control of plants with unknown hysteresis[J]. IEEE Transaction on Automatic Control,1995,40(2): 200-212 [11] Ge P. Modelling and control of hysteresis in piezoceramic actuator[ D]. Kingston:University of Rhode Island,1996 [12] Billing S A. Nonlinear system design [M]. London:Peter Peregrinus Ltd.,1984 [13] Xie Y Q,Tan Y H,Dong R L. Nonlinear modeling and decoupling control of XY micropositioning stages with piezoelectric actuators[J]. IEEE/ASME Transaction on Mechatronics,2013,18(3): 821-832 [14] 方崇智,萧德云.过程辨识[M].北京: 清华大学出版社,2004 Fang C Z,Xiao D Y. Process Identification [M].Beijing: Tsinghua University Press,2004 (in Chinese) [15] Jozef Vrs. Parameter identification of Wiener systems with discontinuous nonlinearities [J]. System and Control Letters,2001,44(3): 363-372 [16] Hagan M T,Menhaj M B. Training feedforward networks with the marquardt algorithm[J]. IEEE Transaction on Neural Networks,1994,5(6): 889-993 [17] Dorsey J. Continuous and discrete control systems[M].New York: McGraw-Hill,2001 [18] 谢扬球,谭永红.基于退化激励信号的含有迟滞的三明治系统辨识[J].控制理论与应用,2012,29(5): 555-563 Xie Y Q,Tan Y H. Identification of sandwich systems with hysteresis based on degeneration inputs [J].Control Theory and Applications,2012,29(5): 555-563 (in Chinese)
点击查看大图
计量
- 文章访问数: 98
- HTML全文浏览量: 18
- PDF下载量: 2
- 被引次数: 0