由Roesser模型描述的2D离散系统预见跟踪控制
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摘要
为了提高2D系统的跟踪水平和响应速度,将参考信号的可预见信息引入到2D系统中,考虑由Roesser模型描述的2D离散系统的预见跟踪控制问题。采用在状态与稳态值间取差分的方式构造了增广误差系统,基于线性矩阵不等式(Linear matrix inequity,LMI)方法给出了增广误差系统在状态反馈下渐近稳定的充分条件,并提出了具有跟踪性能的预见控制器的设计方案,从而实现了2D系统的跟踪目的。数值算例说明,增加预见信息可显著提高由Roesser模型刻画的2D系统的跟踪性能。
In order to improve the tracking level and respond speed of 2 D systems,the future information on the reference signal is first introduced into 2 D systems to deal with the preview tracking control problem for the discrete 2 D Roesser model. Firstly,the augmented error system is constructed by using the difference between the state and steady state value. Then the sufficient asymptotic stability condition for the augmented error system via state feedback is derived by applying the linear matrix inequity(LMI)technique,and the preview controller design is given to realize the tracking purpose of 2 D systems. The numerical simulation shows that the increase of previewable future information can significantly improve the tracking performance of the 2 D discrete-time system described by the Roesser model.
In order to improve the tracking level and respond speed of 2 D systems,the future information on the reference signal is first introduced into 2 D systems to deal with the preview tracking control problem for the discrete 2 D Roesser model. Firstly,the augmented error system is constructed by using the difference between the state and steady state value. Then the sufficient asymptotic stability condition for the augmented error system via state feedback is derived by applying the linear matrix inequity(LMI)technique,and the preview controller design is given to realize the tracking purpose of 2 D systems. The numerical simulation shows that the increase of previewable future information can significantly improve the tracking performance of the 2 D discrete-time system described by the Roesser model.
引文
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[12] 刘丛志,王铃燕,刘伟群,等.2-D系统H∞输出反馈迭代学习控制器设计[J].计算机应用,2016,36(s2):112-115.Liu Congzhi,Wang Lingyan,Liu Weiqun,et al.Iterative learning controller design of H∞ output feedback for 2-D systems[J].Journal of Conputer Application,2016,36(s2):112-115.
[2] Li Li,Liao Fucheng.Design of a preview controller for discrete-time systems based on LMI[J].Mathematical Problems in Engineering,2015(4):1-12.
[3] 吴江.几类线性随机系统的预见控制[D].北京:北京科技大学数理学院,2017.
[4] Li Li,Liao Fucheng.Robust preview control for a class of uncertain discrete-time systems with time-varying delay[J].ISA Transactions,2018,73:11-21.
[5] 王为群,邹云.2-D奇异系统的稳定性[J].南京理工大学学报,2002,26(6):565-569.Wang Weiqun,Zou Yun.Stability of 2-D singular system with delays[J].Jouural of Nanjing University of Science and Technology,2002,26(6):565-569.
[6] Yeganefar Nima,Yeganefar Nader,Ghamgui M,et al.Lyapunov theory for 2-D nonlinear Roesser models:application to asymptotic and exponential stability[J].IEEE Transactions on Automatic Control,2013,58(5):1299-1304.
[7] Bachelier O,Paszke W,Yeganefar N,et al.LMI stability conditions for 2D roesser models[J].IEEE Transactions on Automatic Control,2016,61(3):766-770.
[8] Nachidi M,Tadeo F,Hmamed A,et al.Static output-feedback controller design for two-dimensional Roesser models[J].Kybernetika,2001(2):205-221.
[9] Hua Dingli,Wang Weiqun,Yu Weiren,et al.Finite-region stabilization via dynamic output feedback for 2-D Roesser models[J].Mathematical Methods in the Applied Sciences,2018(1):1-12.
[10] Feng Zhiyong,Xu Li.H∞ static output feedback controller design for two-dimensional discrete systems in Roesser model[C]//IEEE International Symposium on Computer-Aided Control System Design.Yokohama,Japan:IEEE,2010:1790-1794.
[11] 张红,刘晓东.基于观测器的2D T-S模糊离散系统H∞输出跟踪控制[J].三峡大学学报(自然科学版),2014,36(3):91-97.Zhang Hong,Liu Xiaodong.H∞ output tracking control for discrete-time 2-D T-S fuzzy systems[J].Journal of China Three Gorges Unversity,2014,36(3):91-97.
[12] 刘丛志,王铃燕,刘伟群,等.2-D系统H∞输出反馈迭代学习控制器设计[J].计算机应用,2016,36(s2):112-115.Liu Congzhi,Wang Lingyan,Liu Weiqun,et al.Iterative learning controller design of H∞ output feedback for 2-D systems[J].Journal of Conputer Application,2016,36(s2):112-115.