离散重复控制系统设计的二维模型方法

Discrete-time repetitive control systems design method based on two-dimensional model

针对一类线性不确定系统,提出了一种基于离散二维模型的重复控制系统设计方法.通过独立考虑重复控制系统的控制与学习行为,建立了离散重复控制系统的二维模型,构造二维状态反馈控制器,将离散重复控制系统设计问题转化为一类离散二维系统的设计问题.然后应用二维系统理论和线性矩阵不等式方法,分别获得了标称和不确定重复控制系统的稳定性条件.根据稳定性条件,通过求解线性矩阵不等式,求得重复控制器参数.最后数值仿真实例验证了本研究所提方法的有效性.

A novel design method for discrete-time repetitive control systems（RCS） was presented based on two-dimensional（2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in an RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and line- ar matrix inequality（LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI in the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.