基于二维模型理论的离散观测器重复控制系统

摘要

To implement less conservative than those that ignore the difference between the control and learning actions, an observer using discrete-time repetitive control ( RC) design schema was presented, based on the two-dimensional (2D) system theory for linear systems with uncertainty. First, to describe both the learning process occurring between two cycles and the control behavior during a repetitive cycle, a two dimensional discrete-time model was established accordingly. Furthermore, by rebuilding the state variables, the repetitive controller designing was transformed to the feedback gain design problem. Thus, through linear matrix inequality ( LMI ) , the stability conditions that also gained quotient of repetitive system were obtained. By comparison, the applicability of the proposal is stronger, significantly improving the robustness and tracking speed. Test numerical simulation results show that the method can achieve high control accuracy within only a few learning cycles, and the two-dimensional system theory has broad application prospects in repetitive control design and analysis.%为了克服传统设计方法在一维时域中忽视控制和学习这2种行为的差异所带来的保守性，提出了一种应用离散的观测器重复控制(RC)的设计方案，基于二维(2D)系统的理论，研究某些带有不确定性的线性系统。首先，建立了一种二维离散模型，既考虑用来描述在一个重复周期之内的控制行为，也考虑用来描述在周期之间发生的学习过程。然后，通过重建状态变量，将重复控制器的设计转化为反馈增益的设计问题。最后，通过线性矩阵不等式( LMI)获得其稳定性的条件，以及重复系统的增益系数。对比分析表明：该方案算法的适用性强，对鲁棒性与跟踪速度的改善显著。经过数据仿真，检测结果显示出仅需几个学习周期就可达到很高的控制精度，说明二维系统理论在重复控制设计与分析中具有广泛的应用前景。