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Chen Yilu, Feng Yanni, Yan Zhihui, Jia Xiaojun. Optimizing optical resonant cavity locking using fuzzy algorithm (invited)[J]. Infrared and Laser Engineering, 2022, 51(12): 20220781. doi: 10.3788/IRLA20220781
Citation: Chen Yilu, Feng Yanni, Yan Zhihui, Jia Xiaojun. Optimizing optical resonant cavity locking using fuzzy algorithm (invited)[J]. Infrared and Laser Engineering, 2022, 51(12): 20220781. doi: 10.3788/IRLA20220781

Optimizing optical resonant cavity locking using fuzzy algorithm (invited)

doi: 10.3788/IRLA20220781
Funds:  National Natural Science Foundation of China (62122044,61925503,11904218, 12147215, 11834010); Program for the Innovative Talents of Higher Education Institutions of Shanxi (2019L0794); Program for Sanjin Scholars of Shanxi Province; Fund for Shanxi “1331 Project” Key Subjects Construction
  • Received Date: 2022-10-31
  • Rev Recd Date: 2022-12-06
  • Publish Date: 2022-12-22
  • The optical resonant cavity can not only enhance the interaction between the laser and matter, but also suppress the noise of the laser, which is an important tool for research on precision measurement, quantum optics, etc. Stable locking of laser and optical resonant cavity resonance is the key to its application. However, the locking effect will be affected by factors such as mechanical vibration, temperature changes, etc in the actual environment. The fuzzy algorithm is applied to the PDH (Pound-Drever-Hall) technology, so that the three parameters of the proportional-integral-differential controller can be adjusted according to the changes of the external environment to obtain the optimal parameters in real time, which effectively improves anti-interference ability of optical resonator locking. If outside interference is still so great that the lock is lost, the system can make it re-lock automatically. The system effectively improves the practicality of the optical resonator, and provides a technical basis for the application of the optical resonator in precision measurement and quantum optics experiments.
  • [1] Abramovici A, Althouse W E, Drever R W, et al. LIGO: The laser interferometer gravitational-wave observatory [J]. Science, 1992, 256(5055): 325-333. doi:  10.1126/science.256.5055.325
    [2] Ma Lixia, Lei Xing, Yan Jieli, et al. High-performance cavity-enhanced quantum memory with warm atomic cell [J]. Nat Commun, 2022, 13(1): 2368. doi:  10.1038/s41467-022-30077-1
    [3] Zuo Xiaojie, Yan Zhihui, Feng Yanni, et al. Quantum interferometer combining squeezing and parametric amplification [J]. Physical Review Letters, 2020, 124(17): 173602. doi:  10.1103/PhysRevLett.124.173602
    [4] Yan Zhihui, Qin Jiliang, Qin Zhongzhong, et al. Generation of non-classical states of light and their application in deterministic quantum teleportation [J]. Fundamental Research, 2021, 1: 43-49. doi:  10.1016/j.fmre.2020.11.005
    [5] Abbott B P, Abbott R, Abbottet T D, et al. Observation of gravitational waves from a binary black hole merger [J]. Physical Review Letters, 2016, 116(6): 061102. doi:  10.1103/PhysRevLett.116.061102
    [6] Zhou Yaoyao, Jia Xiaojun, Li Fang, et al. Experimental generation of 8.4 dB entangled state with an optical cavity involving a wedged type-II nonlinear crystal [J]. Opt Express, 2015, 23(4): 4952-4959. doi:  10.1364/OE.23.004952
    [7] Huo Meiru, Qin Jiliang, Sun Yingrong, et al. Generation of intensity difference squeezed state of light at optical fiber communication wavelength [J]. Journal of Quantum Optics, 2018, 24(2): 134-140. (in Chinese)
    [8] Drever R W P, Hall J L, Kowalski F V, et al. Laser interferometer gravitational radiation detectors [J]. Appl Phys B, 1983, 31(5): 336-342.
    [9] Breguet J M, Henein S, Kjelberg I, et al. Tunable extended-cavity diode laser based on a novel flexure-mechanism [J]. Int J Optomechatron, 2013, 7(3): 181-192. doi:  10.1080/15599612.2013.807528
    [10] Schlager J B, Callicoatt E E, Mirin R P, et al. Passively mode-locked waveguide laser with low residual jitter [J]. IEEE Photon Technol Lett, 2002, 14(9): 1351-1353. doi:  10.1109/LPT.2002.801123
    [11] Wu Yue, Chen Guozhu, Shen Yong, et al. Optical frequency doubling cavity automatic lockingsystem for second harmonic generation [J]. Infrared and Laser Engineering, 2016, 45(6): 0606002. (in Chinese) doi:  10.3788/irla201645.0606002
    [12] Meng Xiangran. Experimental study on frequency stabilization of laser based on PID control [J]. Science and Technology Information, 2013(16): 66-67. (in Chinese) doi:  10.3969/j.issn.1001-9960.2013.16.054
    [13] Han Jong-Ho. Tracking control of moving sound source using fuzzy-gain scheduling of PID control [J]. Electronics, 2019, 9(1): 14.
    [14] Su Xinghua. Design of PID controller based on fuzzy control theory [J]. China Management Information, 2019, 22(3): 136-139. (in Chinese) doi:  10.3969/j.issn.1673-0194.2019.03.055
    [15] Yuan Xiuping, Li Heyi. MATLAB-based electro-hydraulic servo system adaptive fuzzy PID simulation [J]. Journal of Shanghai Normal University (Natural Sciences), 2006, 35(3): 43-46. (in Chinese)
    [16] Li Xin, Li Zong, Zhang Lijuan. The controllerof fuzzy auto-turning PID on line [J]. Electronics Instrumentation Customer, 2004, 11(4): 34-35. (in Chinese) doi:  10.3969/j.issn.1671-1041.2004.04.016
    [17] Canuto E, Musso F, Massotti L. Automation and control of Fabry-Perot interferometers [J]. IEEE Trans Ind Electron, 2007, 54(2): 848-857. doi:  10.1109/TIE.2007.892002
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Optimizing optical resonant cavity locking using fuzzy algorithm (invited)

doi: 10.3788/IRLA20220781
  • 1. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
  • 2. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Fund Project:  National Natural Science Foundation of China (62122044,61925503,11904218, 12147215, 11834010); Program for the Innovative Talents of Higher Education Institutions of Shanxi (2019L0794); Program for Sanjin Scholars of Shanxi Province; Fund for Shanxi “1331 Project” Key Subjects Construction

Abstract: The optical resonant cavity can not only enhance the interaction between the laser and matter, but also suppress the noise of the laser, which is an important tool for research on precision measurement, quantum optics, etc. Stable locking of laser and optical resonant cavity resonance is the key to its application. However, the locking effect will be affected by factors such as mechanical vibration, temperature changes, etc in the actual environment. The fuzzy algorithm is applied to the PDH (Pound-Drever-Hall) technology, so that the three parameters of the proportional-integral-differential controller can be adjusted according to the changes of the external environment to obtain the optimal parameters in real time, which effectively improves anti-interference ability of optical resonator locking. If outside interference is still so great that the lock is lost, the system can make it re-lock automatically. The system effectively improves the practicality of the optical resonator, and provides a technical basis for the application of the optical resonator in precision measurement and quantum optics experiments.

    • 光学谐振腔是一种多光束干涉器件,不仅可以使激光和物质之间的相互作用增强,而且只允许有限带宽的信号透射及反射,能够抑制激光的强度和相位噪声。因此,光学谐振腔在精密测量、量子光学等领域有着广泛的应用[1-4]。例如:利用光学谐振腔显著增强了引力波探测器的灵敏度,使其探测到了极其微弱的引力波信号[5]。光学谐振腔也是获得高质量非经典光场的重要工具[6-7]。这些光学实验常常依赖于各种锁定系统来主动稳定腔长度,以实现激光和光学谐振腔的共振。最常见和有效的一种方法是R. V. Pound,Ronald Drever和John L. Hall (PDH)技术[8]。利用相位调制技术对激光进行调制并在中心频率两侧各产生一个边频带,该信号经过光学谐振腔后的反射或透射信号再与调制信号进行混频滤波后,即得到反馈误差信号,将误差信号送入与光学谐振腔相连的由比例积分微分(Proportion Integral Differential, PID)控制器和高压放大器组成的伺服系统,实现激光和光学谐振腔共振的锁定。

      激光和光学谐振腔共振的稳定锁定是其应用的关键。然而,在实际环境中锁定效果会受机械振动、温度变化等干扰因素的影响而使系统稳定性下降[9-10]。此外,如果干扰过大甚至可能使系统直接失锁。因此,实际应用对光学谐振腔锁定的抗干扰能力及失锁后的自动恢复[11]提出了要求。

      为了提升光学谐振腔的锁腔性能,文中在PDH锁定系统中引入了模糊算法以优化PID参数,使参数能够根据外界环境变化进行自调节获得最佳参数,并且开发了自动重锁功能。PDH技术所使用的反馈伺服控制系统使用的是传统PID控制算法[12],需要预先设定比例、积分和微分三个参数,然而在不断变化的实际环境中,很难获得最佳的参数。模糊PID控制算法是一种基于规则的自适应决策方法[13],能够根据外界条件变化自动调节PID控制器的三个参数,使其实时获得最佳的参数,有效提升了光学谐振腔的锁定的抗干扰能力。如果外界干扰仍然过大以至于模糊PID无法处理导致失锁,系统也能够检测到锁定丢失,并根据失锁前记录的光学谐振腔峰值的阈值,重新开始自动锁定。模糊算法和自动重锁功能有效增强了光学谐振腔的实用性。

    • 进入系统的稳频激光在电光位相调制器被高频信号源产生的信号进行位相调制从而产生边带,调制后的光场注入到光学谐振腔内,在激光固有频率和光学谐振腔共振频率不同的情况下,调制产生的两边带被光学谐振腔反射的强度不相等,导致与载波产生拍频后的信号位相相反且大小不等。信号从光学谐振腔出射后与经过位相延迟的高频信号源信号在混频器进行混频,再经过一个低通滤波器后,即得到误差信号并送入伺服控制系统。伺服控制系统包括模糊PID控制器和高压放大器,模糊PID控制器输出的反馈信号经高压放大后作用于腔镜上的压电陶瓷上,最终形成了一个闭环反馈控制回路,调整光学谐振腔的腔长使其与稳频激光频率完全共振。系统模型如图1所示。

      Figure 1.  Block diagram of system

    • PID控制由比例控制、积分控制和微分控制组成,比例控制可以迅速反应并减小误差,积分控制用于消除稳态误差,微分控制可以改善系统的动态性能。模糊PID控制器则由传统PID控制器和模糊控制器组成[14-15],如图2所示。

      Figure 2.  Fuzzy PID system

      模糊控制器需要两个输入参数,分别是误差值E和误差变化率${E}_{{\rm{c}}}$。在文中的系统中,误差E是指误差信号和设定点之间的差值。${E}_{{\rm{c}}}$是指误差E在短时间内的变化率,即此时的误差和上个采样时间的误差之间的差值,采样率设为与传统PID相同。${E}_{{\rm{c}}}$能够预估系统未来的变化趋势,及时调整系统参数以期有效减小误差E带来的影响。输入值首先经过模糊化和模糊推理,然后根据制定的模糊规则表查询得到模糊输出值,最后解模糊得到精确输出值。

      模糊PID控制器的三个参数${k}_{{\rm{p}}}$${k}_{{\rm{i}}}$${k}_{{\rm{d}}}$表示为公式(1):

      式中:$\Delta {k}_{{\rm{p}}}$$\Delta {k}_{{\rm{i}}}$$\Delta {k}_{{\rm{d}}}$分别为模糊控制器的输出值;${k}_{{{\rm{p}}}_{0}}$${k}_{{\rm{i}}0}$${k}_{{\rm{d}}0}$分别为传统PID控制器三个基本参数的初始值。

      模糊算法会将输入和输出数据进行量化并映射到一定的数字级别,文中:E${E}_{{\rm{c}}}$的基本论域都定义为[−0.6, 0.6];${k}_{{\rm{p}}}$的基本论域定义为[−0.0018, 0.0018]; ${k}_{{\rm{i}}}$的基本论域定义为[−12, 12];${k}_{{\rm{d}}}$的基本论域定义为[−0.18, 0.18]。选择负大[NB],负中[NM],负小[NS],零[ZO],正小[PS],正中[PM],正大[PB]七个语言变量表达模糊子集,模糊子集是用隶属度函数来描述的,NB的隶属度函数是Z型,NM、NS、ZO、PS、PM的隶属度函数是三角型,PB的隶属度函数是S型。

      模糊PID输出值由模糊控制状态表决定,根据模糊化后的误差以及误差变化率的值即可由模糊控制表得到相应的模糊输出值,再解模糊得到$\Delta {k}_{{\rm{p}}}$$\Delta {k}_{{\rm{i}}}$$\Delta {k}_{{\rm{d}}}$。与上个周期的参数相加即得到模糊PID控制器的本周期参数。三个参数的模糊控制表分别如表1表2表3所示,该表是根据反馈系统对PID参数的要求、PID控制器参数常见的调节规律以及手动经验和专家意见制定的[16]

      E
      EcNBNMNSZOPSPMPB
      NBPBPBPMPMPSZOZO
      NMPBPBPMPSPSZONS
      NSPMPMPMPSZONSNS
      ZOPMPMPSZONSNMNM
      PSPSPSZONSNSNMNM
      PMPSZONSNMNMNMNB
      PBZOZONMNMNMNBNB

      Table 1.  Fuzzy control rules table of ${k}_{{\rm{p}}}$

      E
      EcNBNMNSZOPSPMPB
      NBNBNBNMNMNSZOZO
      NMNBNBNMNSNSZOPS
      NSNBNMNSNSZOPMPM
      ZONMNMNSZOPSPMPM
      PSNMNSZOPSPSPMPB
      PMZOZOPSPSPMPBPB
      PBZOZOPSPMPMPBPB

      Table 2.  Fuzzy control rules table of ${k}_{{\rm{i}}}$

      E
      EcNBNMNSZOPSPMPB
      NBPSNSNBNBNBNMPS
      NMPSNSNBNMNMNSZO
      NSZONSNMNMNSNSZO
      ZOZONSNSNSNSNSZO
      PSZOZOZOZOZOZOZO
      PMPBPMPMPMPSPSPB
      PBPBPMPMPMPSPSPB

      Table 3.  Fuzzy control rules table of ${k}_{{\rm{d}}}$

      模糊算法对三个参数的自整定规则如下:

      (1) 系统响应初期,误差E的值较大,需要较大的${k}_{{\rm{p}}}$和较小的${k}_{{\rm{d}}}$来跟踪设定点。同时,为了防止积分饱和现象的发生,避免系统响应出现过大的超调,需要将${k}_{{\rm{i}}}$设为0,即此阶段无需积分控制。

      (2) 当系统处于超调阶段,即误差E和误差变化率${E}_{{\rm{c}}}$的值都为中等大小时,需要逐步减小${k}_{{\rm{p}}}$${k}_{{\rm{d}}}$的值以期实现更小的超调量。此时也需取适中的${k}_{{\rm{i}}}$值为系统引入积分作用,才能保证良好的响应能力。

      (3) 当系统逐渐趋于稳定时,误差E的值较小。此时需要适度增大${k}_{{\rm{p}}}$${k}_{{\rm{i}}}$的值以提高系统的稳定性,且如果误差变化率${E}_{{\rm{c}}}$较大即系统响应出现振荡,则也需取较大的${k}_{{\rm{d}}}$

    • 光学谐振腔的重锁机制是通过系统在扫描模式和锁定模式之间切换来实现的,程序流程如图3所示。在光学谐振腔的共振频率和激光的固有频率相同时,系统处于锁定模式。此时以与光电探测器相连的FPGA模拟数据输入口采集到的直流探测信号[17]幅值的绝对值作为高阈值,再定义一个绝对值稍大于零点的直流探测信号幅值作为低阈值,将信号是否处于该透射区域内作为判断条件。如果条件判断为是,将误差信号送入模糊PID控制器,使其输出控制信号保持系统的锁定模式;如果条件判断为否,则认为系统此时已失锁,将模糊PID控制器关闭,退出锁定模式进入扫描模式,打开信号发生器输出三角波信号重新扫描腔长,直到满足共振条件即直流探测信号大于等于高阈值为止。此时将系统切换回锁定模式,这样就完成了一次失锁后重新锁定的流程。

      Figure 3.  Flowchart of relocking cavity

    • 在保证激光器稳定的前提下,分别对使用传统PID控制算法和模糊PID控制算法进行锁定的稳频系统进行了监测。图4图5分别为使用传统PID控制算法时的误差信号和直流监视信号,图6图7分别为使用模糊PID控制算法时的误差信号和直流监视信号。

      Figure 4.  Error signal of conventional PID algorithm

      Figure 5.  DC signal of conventional PID algorithm

      Figure 6.  Error signal of fuzzy PID algorithm

      Figure 7.  DC signal of fuzzy PID algorithm

      可以看出,在700 s的时间内,使用模糊PID控制算法时的光学谐振腔误差信号偏离设定点的幅度只有使用传统PID控制算法时的60%左右。在实验过程中,通过人为敲击实验平台向系统加入扰动,可以观察到使用模糊PID控制算法时的抖动峰数量不到使用传统PID控制算法时的一半,且抖动幅度也在50%以内,小于使用传统PID控制算法时70%~90%的抖动幅度。光学谐振腔的抗干扰性能有了较大的提升。

    • 将得到的误差信号送入模糊PID控制器后就可以对光学谐振腔进行锁定。在最佳的锁定状态下,误差信号斜率最大处对应于光学谐振腔的共振峰,系统就是要实现腔在共振峰处的锁定。在锁定状态下通过手动遮挡入射光束使系统失锁,探测器采集到的直流监视信号从原本的锁定点掉到了地线。图8为系统从锁定到失锁再到重新锁定的过程,通过挡住注入信号光场的实际测试,系统自动实现了从失锁到重新锁定,无需人工操作,且时间一般不超过3 s,满足一般实验时的基本需求。

      Figure 8.  Reflected DC monitor signal when relocking

    • 文中利用模糊PID控制算法,实时获得了光学谐振腔锁定系统中PID的最佳参数,并实现了光学谐振腔失锁后的自动重锁。实验结果表明,相比传统PID控制算法,模糊PID控制算法使光学谐振腔锁定效果有了更好的抗干扰能力,而且光学谐振腔失锁后能够自动重新锁定,不需要人工操作。这些技术有效增强了光学谐振腔的实用性,为光学谐振腔在量子光学实验中的应用提供了技术基础。

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