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Frequency control of atomic clock is a key technology in time keeping operation. At present, the open-loop control algorithm is mainly used for the frequency control of foreign microwave clock, but the working principle and performance of domestic optically pumped small cesium clock (hereinafter referred to as domestic clock) are different from those of foreign atomic clock of the same type, so the algorithm cannot be well adapted to domestic clock. In order to improve the autonomy and security of the national standard time, based on the noise characteristics of domestic clock, in this work, the linear quadratic Gaussian control algorithm is studied in the framework of optimal control theory. This algorithm belongs to closed-loop control algorithm. The performance of domestic clock is studied from the aspects of synchronization time, frequency control accuracy and frequency control stability. Finally, the influence of different control intervals on the performance of domestic clock is analyzed. The results show that with the increase of the constraint matrix
$ {{{W}}_{\text{R}}} $ in the quadratic loss function, the synchronization time increases, the control accuracy decreases, and the control short-term stability increases. When$ {{{W}}_{\text{R}}} $ is the same, with the increase of control interval, the synchronization time increases, the control accuracy decreases, and the control short-term stability increases. When$ {W_{\text{R}}} = 1 $ , the synchronization time with control interval of 1 h is 5 h, the control accuracy is 1.83 ns, and the Allan deviation of 1 hour is 1.81×10–13. When the control interval is 8 h, the synchronization time is 28 h, the control accuracy is 4.48 ns, and the Allan deviation of 1 h is 1.48×10–13. The medium-term stability and long-term stability of domestic optically pumped small cesium clock are both improved.-
Keywords:
- atomic clock state model /
- linear quadratic Gaussian control /
- Kalman filter /
- atomic clock noise
[1] Godel M, Schmidt T D, Furthner J 2019 Metrologia 56 3
Google Scholar
[2] Schmidt T D, Trainotti C, Furthner J 2019 Proceedings of the Precise Time and Time Interval Meeting ( ION PTTI 2019), Reston, Virginia, January 28–31, 2019 p290
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Google Scholar
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Google Scholar
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[11] Panfilo G, Harmegnies A, Tisserand L 2012 Metrologia 49 49
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[12] 宋会杰, 董绍武, 屈俐俐, 王翔, 广伟 2017 仪器仪表学报 38 1809
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Song H J, Dong S W, Qu L L, Wang X, Guang W 2017 Chin. J. Sci. Instrum. 38 1809
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Google Scholar
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Liu Y, Wang W H, He D J, Zhou Y Z, Shen Y, Zou H X 2023 Acta Phys. Sin. 72 184202
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[19] 梁悦, 谢勇辉, 陈鹏飞, 帅涛, 裴雨贤, 徐昊天, 赵阳, 夏天, 潘晓燕, 张朋军, 林传富 2023 72 013702
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Google Scholar
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Google Scholar
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图 1 铯原子钟与氢原子钟的Allan偏差曲线
Figure 1. Allan deviation curves of cesium atomic clock and hydrogen atomic clock.
图 2 国产钟的控制结构图
Figure 2. Control structure diagram of domestic clock.
图 3 不同$ {{{W}}_{\text{R}}} $值的控制同步时间比较
Figure 3. Comparison of control synchronization time with different $ {{{W}}_{\text{R}}} $ values.
图 4 同步后不同$ {{{W}}_{\text{R}}} $值的控制测量值
Figure 4. Control measurements of different $ {{{W}}_{\text{R}}} $ values after synchronization
图 5 约束矩阵$ {{{W}}_{\text{R}}} $取不同值时的控制国产钟的稳定度
Figure 5. Stability of the controlled domestic clock with different values of the constrained matrix $ {{{W}}_{\text{R}}} $.
图 6 约束矩阵$ {{{W}}_{\text{R}}} $取不同值时控制测量值的稳定度
Figure 6. Stability of control measurement with different values of the constrained matrix $ {{{W}}_{\text{R}}} $.
图 7 不同控制间隔的同步时间比较
Figure 7. Comparison of synchronization time with different control interval.
图 8 同步后不同控制间隔的测量值
Figure 8. Measurements at different control intervals after synchronization.
图 9 基于不同控制间隔的国产钟的稳定度
Figure 9. Stability of the domestic clock based on different control intervals.
图 10 基于不同控制间隔的控制测量值的稳定度
Figure 10. Stability of control measurements based on different control intervals.
图 11 控制后Cs3050与UTCr的相位偏差
Figure 11. Phase deviation of the controlled Cs3050 from the UTCr.
图 12 自由运行Cs3050与驾驭后Cs3050相对于UTCr的频率稳定度
Figure 12. Frequency stability of free running Cs3050 and controlled Cs3050 relatived to UTCr.
表 1 同步后不同$ {{{W}}_{\text{R}}} $值的3倍标准差($ 3\sigma $)
Table 1. Three times standard deviation of different $ {{{W}}_{\text{R}}} $values after synchronization.
$ {{{W}}_{\text{R}}} $ 1/2 1 102 104 $ 3\sigma $的值/ns 1.76 1.83 3.03 6.26 
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表 2 同步后不同控制间隔测量值的3倍标准差($ 3\sigma $)
Table 2. Three times standard deviation of different control intervals after synchronization.
控制间隔/h 1 2 4 8 $ 3\sigma $的值/ns 1.83 2.29 3.10 4.48
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表 3 自由运行Cs3050与驾驭后Cs3050相对于UTCr的频率稳定度
Table 3. Frequency stability of free running Cs3050 and controlled Cs3050 relative to UTCr.
取样间隔/d 10 20 30 40 Allan偏差
(Cs3050)1.85×10–14 2.16×10–14 2.10×10–14 2.50×10–14 Allan偏差
(控制Cs3050)1.24×10–15 9.17×10–16 8.86×10–16 6.73×10–16
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表 4 自由运行 Cs3050相对于UTCr的频率漂移
Table 4. Frequency drift of free-running Cs3050 with respect to UTCr.
估计周期 (MJD) 59978—60007 60008—60037 60038—60067 60068—60097 60098—60127 频率漂移/(ns·d–1) 0.1938 –0.0236 0.0446 –0.2062 0.1859 估计周期 (MJD) 60128—60157 60158—60187 60188—60217 60218—60247 60248—60277 频率漂移/(ns·d–1) –0.0374 –0.1158 0.3041 0.0457 0.1263
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表 5 控制Cs3050相对于UTCr的频率漂移
Table 5. Frequency drift of controlled Cs3050 relative to UTCr.
估计周期(MJD) 59978—60007 60008—60037 60038—60067 60068—60097 60098—60127 频率漂移/(ns·d–1) 0.0050 0.0010 –0.0131 0.0031 0.0016 估计周期(MJD) 60128—60157 60158—60187 60188—60217 60218—60247 60248—60277 频率漂移/(ns·d–1) –0.0088 0.0082 0.0143 –0.0029 –0.0003
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[1] Godel M, Schmidt T D, Furthner J 2019 Metrologia 56 3
Google Scholar
[2] Schmidt T D, Trainotti C, Furthner J 2019 Proceedings of the Precise Time and Time Interval Meeting ( ION PTTI 2019), Reston, Virginia, January 28–31, 2019 p290
[3] Galleani L, Signorile G, Formichella V, Sesia I 2020 Metrologia 57 3
Google Scholar
[4] Arias E, Panfilo G, Petit G 2011 Metrologia 48 S145
Google Scholar
[5] McCarthy D 2011 Metrologia 48 S132
Google Scholar
[6] Koppang P A 2016 Metrologia 53 R60
Google Scholar
[7] 陈法喜, 赵侃, 李立波, 郭宝龙 2022 71 230702
Google Scholar
Chen F X, Zhao K, Li L B, Guo B L 2022 Acta Phys. Sin. 71 230702
Google Scholar
[8] Song H J, Dong S W, Wu W J, Jiang M, Wang W X 2018 Metrologia 55 350
Google Scholar
[9] 韩孟纳, 童明雷 2023 72 079701
Google Scholar
Han M N, Tong M L 2023 Acta Phys. Sin. 72 079701
Google Scholar
[10] Kaczmarek J, Miczulski W, Koziol M, Czubla A 2013 IEEE Trans. Instrum. Meas 65 2828
Google Scholar
[11] Panfilo G, Harmegnies A, Tisserand L 2012 Metrologia 49 49
Google Scholar
[12] 宋会杰, 董绍武, 屈俐俐, 王翔, 广伟 2017 仪器仪表学报 38 1809
Google Scholar
Song H J, Dong S W, Qu L L, Wang X, Guang W 2017 Chin. J. Sci. Instrum. 38 1809
Google Scholar
[13] Panfilo G, Harmegnies A, Tisserand L 2014 Metrologia 51 285
Google Scholar
[14] 宋会杰, 董绍武, 王翔, 章宇, 王燕平 2020 69 170201
Google Scholar
Song H J, Dong S W, Wang X, Zhang Y, Wang Y P 2020 Acta Phys. Sin. 69 170201
Google Scholar
[15] 宋会杰, 董绍武, 王燕平, 安卫, 侯娟 2019 武汉大学学报(信息科学版) 44 1205
Google Scholar
Song H J, Dong S W, Wang Y P, An W, Hou J 2019 Geomat. Inf. Sci. Wuhan Univ. 44 1205
Google Scholar
[16] Panfilo G, Arias E F 2010 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 140
Google Scholar
[17] Tavella P, Thomas C 1991 Metrologia 28 2
Google Scholar
[18] 刘云, 王文海, 贺德晶, 周勇壮, 沈咏, 邹宏新 2023 72 184202
Google Scholar
Liu Y, Wang W H, He D J, Zhou Y Z, Shen Y, Zou H X 2023 Acta Phys. Sin. 72 184202
Google Scholar
[19] 梁悦, 谢勇辉, 陈鹏飞, 帅涛, 裴雨贤, 徐昊天, 赵阳, 夏天, 潘晓燕, 张朋军, 林传富 2023 72 013702
Google Scholar
Liang Y, Xie Y H, Chen P F, Shuai T, Pei Y X, Xu H T, Zhao Y, Xia T, Pan X Y, Zhang P J, Lin C F 2023 Acta Phys. Sin. 72 013702
Google Scholar
[20] 邵晓东, 韩海年, 魏志义 2021 70 134204
Google Scholar
Shao X D, Han H N, Wei Z Y 2021 Acta Phys. Sin. 70 134204
Google Scholar
[21] Galleani L 2008 Metrologia 45 S175
Google Scholar
[22] Tavella P 2008 Metrologia 45 S183
Google Scholar
[23] Yao J, Parker T E, Ashby N, Levine J 2018 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 65 127
Google Scholar
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