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首页> 外文期刊>International Journal of Innovative Computing Information and Control >LINEAR MATRIX INEQUALITY-BASED REPETITIVE CONTROLLER DESIGN FOR LINEAR SYSTEMS WITH TIME-VARYING UNCERTAINTIES TO REJECT POSITION-DEPENDENT DISTURBANCES
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LINEAR MATRIX INEQUALITY-BASED REPETITIVE CONTROLLER DESIGN FOR LINEAR SYSTEMS WITH TIME-VARYING UNCERTAINTIES TO REJECT POSITION-DEPENDENT DISTURBANCES

机译：具有时变不确定性的线性系统基于线性矩阵不等式的重复控制器设计，用以拒绝位置相关的干扰

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摘要

This paper addresses the problem of designing an optimal modified repetitive controller for a strictly proper plant with time-varying uncertainties to reject position-dependent disturbances. A modified repetitive controller with time-varying delay structure, inserted by a low-pass filter and an adjustable parameter, is developed for this class of system. Two linear matrix inequalities (LMIs)-based robust stability conditions of the closed-loop system with time-varying state delay are derived for fixed parameters. One is a delay-dependent robust stability condition that is derived based on the free-weight matrix. The other robust stability condition is obtained based on the H_∞, control problem by introducing a linear unitary operator. To obtain the desired controller, the design problems are converted to two LMI-constrained optimization problems by reformulating the LMIs given in the robust stability conditions. The validity of the proposed method is verified through a numerical example.
机译：本文解决了为具有时变不确定性的严格正确工厂设计最优的修改型重复控制器的问题，以消除与位置有关的干扰。针对此类系统，开发了一种具有时变延迟结构的改进型重复控制器，该控制器具有低通滤波器和可调参数。针对固定参数，推导了基于两个线性矩阵不等式（LMI）的具有时变状态时滞的闭环系统的鲁棒稳定性条件。一种是基于延迟的鲁棒稳定性条件，该条件基于自由权重矩阵得出。通过引入线性unit算子，基于H_∞控制问题获得其他鲁棒稳定性条件。为了获得所需的控制器，通过重新构造鲁棒稳定性条件下给出的LMI，将设计问题转换为两个LMI约束的优化问题。通过数值算例验证了所提方法的有效性。

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