离散线性系统有限频域基于观测器的迭代学习控制

Observer-based iterative learning control for discrete linear systems in finite frequency domains

针对一类离散线性系统,在有限频域范围内研究基于观测器的迭代学习控制问题.首先,结合二维系统理论,构建由基于观测器的状态反馈和PID型前馈学习项组成的控制器;然后,借助于广义Kalman-YakubovichPopov (KYP)引理,将闭环系统有限频域性能规范转换为相应的线性矩阵不等式(LMI),进而得到控制器和观测器存在的充分条件,同时,该条件也确保闭环控制系统的稳定性和跟踪误差单调收敛性;最后,通过桁架机器人系统的仿真,验证所提出设计方法的有效性.

For a class of discrete linear systems,this paper deals with the problem of designing an observer-based iterative learning control scheme in the finite frequency range.First,the controller is constructed by combining an observer-based state feedback with a PID-type feedforward learning term on the basis of the two-dimensional system theory.Then,by means of the Kalman–Yakubovich–Popov(KYP)lemma,the finite frequency domain specifications of the resulting closed-loop system are transformed into corresponding linear matrix inequalities(LMI),furthermore,the sufficient conditions for the existence of the controller and the observer are also obtained.Simultaneously,these conditions guarantee the stability of the close-loop controlled system and the monotonic convergence of the tracking error.Finally,the effectiveness of the proposed method is verified by the simulation of a gantry robot.