基于等价输入干扰的不确定离散时间系统预见重复控制  

Equivalent Input Disturbance Based Preview and Repetitive Control for Uncertain Discrete-time Systems

作　　者：兰永红[1] 邓云强 LAN Yonghong;DENG Yunqiang(School of Automation and Electronic Information,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学自动化与电子信息学院,湖南湘潭411105

出　　处：《控制工程》2024年第5期815-824,共10页Control Engineering of China

基　　金：国家自然科学基金资助项目(61573298);湖南省自然科学基金资助项目(2020JJ6037)。

摘　　要：针对一类具有外部干扰的不确定线性离散系统,提出一种基于等价输入干扰(equi-valent input disturbance,EID)补偿的预见重复控制设计方法。首先,为了在提高系统跟踪精度的同时对外部干扰进行主动抑制,提出一种前向通道包含预见和重复控制器、反馈通道包含EID补偿的多自由度系统结构。然后,利用T阶差分算子,获得包含目标信号预见信息、重复控制器输出以及重构干扰的增广离散系统。于是,设计控制器的问题,变成了离散系统在二次性能指标下的稳定性问题。进一步,利用Lyapunov稳定性理论和线性矩阵不等式(linear matrix inequality,LMI)处理技巧,得到系统稳定性条件,进而获得控制器参数化方法。最后,数值仿真验证了所提方法的有效性。For a class of uncertain linear discrete-time systems with external disturbances,an equivalent input disturbance(EID)based preview repetitive controller design method is proposed.Firstly,in order to improve the tracking accuracy of the system and suppress the external interference actively,a multi degree of freedom system structure,which contains with preview and repetitive controller in forward channel and EID compensator in feedback channel is constructed.Then,by using T-order difference operator,the augmented discrete-time system with preview information of target signal,repetitive control output and reconstructed disturbance are obtained.Therefore,the problem of designing controller becomes the stability problem of discrete system under quadratic performance index.Furthermore,by applying Lyapunov stability theory and linear matrix inequality(LMI),the stability condition of the augmented discrete-time system as well as the parameterization methods of the proposed controller are obtained.Finally,the numerical simulation verifies the effectiveness of the proposed method.

关 键 词：离散时间不确定系统 预见重复控制 等价输入干扰 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]