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中文摘要：
现有的重复控制设计不能同时优化低通滤波器的参数和重复控制器的参数．我们在设计重复控制系统以控制线性不确定对象时，解决了这个问题．首先，引入状态反馈以保证闭系统的鲁棒稳定性，把重复控制器设计问题转化为H∞状态反馈增益的设计问题．为获得低通滤波器最大转折频率，进一步将设计问题转化为基于线性矩阵不等式约束的凸优化问题．提出了一种迭代算法，用以计算低通滤波器的最大转折频率和H∞状态反馈增益．在保证系统鲁棒稳定性的同时，获得最高控制精度的重复控制器和低通滤波器的参数组合．该方法与已有方法比较，它的结果容易验证和求解，因而更适合于实际应用．最后，通过数值实例验证了本文所提方法的有效性．
英文摘要：
The existing methods for designing repetitive control systems cannot simultaneously optimize the parameters of the low-pass filter and the parameters of the repetitive controller. We deal with this problem in designing a repetitive control system for a class of linear uncertain plants. First, we employ the state feedback controller to robustly stabilize the closed-loop system, and treat the controller design problem as an H-infinity state-feedback design problem. Next, under the H-infinity formulation, the design is formulated as a convex optimization problem subject to linear matrix inequalities. An iterative algorithm is presented for calculating the maximum cut-off frequencies of the low-pass filter and the gain of the H-infinity state-feedback controller. It also gives the combination of parameters for the low-pass filter and the the repetitive controller, which yields the highest control precision under the requirements of robust stability of the system. The results of the proposed method can be more easily obtained and verified than by the existing methods, showing the practical value in applications. Finally, the validity of this method is verified by a numerical example.
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