Repetitive-control-based high-frequency disturbance suppression method in tip-tilt correction

Feng Nian; Tang Tao; Hu Long

doi:10.12086/oee.2025.240294

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Feng N, Tang T, Hu L. Repetitive-control-based high-frequency disturbance suppression method in tip-tilt correction[J]. Opto-Electron Eng, 2025, 52(4): 240294. doi: 10.12086/oee.2025.240294

Citation:

Feng N, Tang T, Hu L. Repetitive-control-based high-frequency disturbance suppression method in tip-tilt correction[J]. Opto-Electron Eng, 2025, 52(4): 240294. doi: 10.12086/oee.2025.240294

Repetitive-control-based high-frequency disturbance suppression method in tip-tilt correction

1.
National Key Laboratory of Optical Field Manipulation Science and Technology, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
2.
Key Laboratory of Optical Engineering, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
3.
Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China
4.
School of Electronics, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Fund Project: General Program of National Natural Science Foundation of China (62375267)

More Information

^*Corresponding author: taotang@ioe.ac.cn
CSTR: 32245.14.oee.2025.240294

Received Date 16 December 2024

Revised Date 03 March 2025

Accepted Date 03 March 2025

Published Date 25 April 2025

Abstract

Abstract

Disturbance suppression, especially high-frequency disturbance suppression beyond the closed-loop bandwidth, is the core of realizing high-precision stability control for tip-tilt correction systems. Repetitive control has good performance of periodic trajectory tracking and disturbance suppression, which is applied to the stability control of high-precision systems. The high-frequency disturbance suppression problem of the tip-tilt correction system is analyzed in this paper, and the performance of high-frequency disturbance suppression based on repetitive control is summarized. To solve the problems of natural frequency drift and waterbed amplification in traditional repetitive controllers, a comb-like repetitive controller based on Youla parameterization is designed to suppress high-frequency disturbances beyond the closed-loop bandwidth. In order to solve the problem that the integer-order repetitive control is only effective for specific frequency points, especially in most high frequency regions, the controller will fail due to disturbance fluctuations and uncertainty, an all-pass frit-order delay filter is optimized to suppress the high frequency disturbance at any frequency point up to Nyquist frequency in the tip-tilt correction system. Finally, a parallel repetitive control scheme is designed to suppress the vibration of aperiodic structures which is difficult to suppress, and its robust stability and effectiveness are discussed.
- disturbance suppression /
- tip-tilt correction /
- repetitive control /
- high-frequency disturbance

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References

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Overview

Overview

In optical telescope systems, the control accuracy with tip-tilt correction systems as a fine tracking link is improved to the level of micro radian or even sub-micro radian. Disturbance suppression, especially high-frequency disturbance suppression outside the closed-loop bandwidth, is the key to achieving high precision stability control of tip-tilt correction systems, so as to approach the diffraction limit of the telescope system. Repetitive control has good performance of periodic trajectory tracking and disturbance suppression and is widely applied to improve the control performance of high-precision control systems, such as nanopositioning stages, power inventers, and hard disk drive systems. Therefore, repetitive control is a promising algorithm for high-frequency disturbance suppression. Firstly, this paper analyzes the problem of high-frequency disturbance suppression of tip-tilt correction systems and summarizes the performance of high-frequency interference suppression based on repetitive control. To solve the problem of natural frequency drift and waterbed amplification of traditional repetitive controllers, a comb-like repetitive controller based on Youla parameterization is designed to suppress high-frequency interference outside the closed-loop bandwidth. In the optimal design of the controller, time delays are compensated by the delay characteristic of the repetitive controller to improve the stability of the closed-loop system in suppressing high-frequency disturbance. In addition, in order to solve the problem that the integer-order repetitive controller is only effective for certain frequency points, especially in most high frequency regions, the controller fails due to interference fluctuations and uncertainties, an all-pass fractional delay filter is optimized, which can suppress high-frequency disturbance at any frequency point up to the Nyquist frequency in the tip-tilt correction system. An additional delay compensation factor is designed to preserve the notch characteristic of the repetitive controller in high-frequency domains and improve the system's stability. Finally, a parallel repetitive control scheme is designed for the non-periodic structure vibration which is difficult to suppress, and its robust stability and effectiveness are discussed. A series of experiments were designed to suppress a single peak disturbance, and the results show that repetitive control suppresses any frequency disturbance up to the Nyquist frequency. Furthermore, the experimental results of multiple periodic and aperiodic disturbance suppression prove that the repetitive controller is superior in dealing with multiple high-frequency disturbances beyond the closed-loop bandwidth. In general, these proposed repetitive controllers have good performance in improving the high-frequency disturbance suppression ability of the tip-tilt correction system, and these algorithms are also suitable for other high-precision control systems in the future.