Rejection of periodic disturbance and/or tracking of periodic reference is of importance in high-precision control systems. Conventional repetitive control is often used to solve the problem, but it cannot precisely set effective frequency points and adversely amplify the non-periodic component disturbance. Therefore, it is not applicable in actual systems where external disturbances exist in the whole frequency domain. In this paper, we propose an improved discrete-time repetitive control method based on the disturbance observer to correct the undesired deviation at repetitive frequencies and mitigate the amplification of the non-components. Moreover, in the observer structure, an intuitive and flexible Q-filter design is presented to suppress low-frequency broadband and intermediate-frequency narrowband disturbances. The conditions of closed-loop stability, performance analysis, and the implementation of the proposed scheme are provided in detail. Finally, the effectiveness of the method is verified by simulation and experimentation on an optoelectronic precision positioning system under the condition of disturbances, and the disturbance suppression and tracking error attenuation are improved.

周期性干扰的抑制和/或周期性参考的跟踪在高精度控制系统中很重要。传统的重复控制经常用来解决这个问题，但它不能精确设置有效频点，不利地放大了非周期性分量扰动。因此，它不适用于整个频域存在外部干扰的实际系统。在本文中，我们提出了一种基于干扰观测器的改进的离散时间重复控制方法，以纠正重复频率处的不希望的偏差并减轻非组件的放大。此外，在观测器结构中，提出了一种直观灵活的Q滤波器设计，以抑制低频宽带和中频窄带干扰。详细提供了闭环稳定性条件、性能分析和所提出方案的实施。最后，通过在扰动条件下的光电精密定位系统上进行仿真和实验验证了该方法的有效性，提高了扰动抑制和跟踪误差衰减。