摘要
针对单锁臂结构的控制器设计问题,提出了一种双层同步优化策略,在优化控制器结构的同时设计零极点取值。该方法引入延迟裕度作为后验条件,确保系统在航天器轨道周期内的稳定性,结合控制系统的绝对稳定性和相对稳定性约束,建立控制器结构优化层和参数优化层之间的反馈循环,借助非线性优化算法同步优化控制器结构及参数,在仅需20 dB增益的情况下实现了较高的激光频率噪声抑制比。结果表明,所设计的控制器可使激光频率噪声在0.01 Hz~0.1 mHz频段被抑制5到6个数量级,在0.01 Hz~1 Hz频段被抑制2到3个数量级,满足引力波探测的噪声抑制需求。
At the dawn of the 20th century,Einstein's theory of general relativity predicted the existence of Gravitational Waves(GWs).In the early 1980 s,several ground-based interferometers,such as LIGO and VIRGO,were proposed for GW detection.Due to constraints like limited arm lengths and sensitivity to ground vibrations,these detectors are restricted to detecting GWs with frequencies above 30 Hz.Consequently,the focus of GW research has shifted towards space-based detectors.Noteworthy initiatives in this domain include NASA and ESA's Laser Interferometer Space Antenna(LISA)and China's“Taiji”program,both aiming to measure GWs within the 0.1 mHz to 1 Hz frequency band.The detection of GWs,which induce extremely subtle distance changes,necessitates measurement systems with picometer(pm)precision.To achieve this sensitivity,it is crucial to reduce laser frequency noise by 10 to 12 orders of magnitude from current levels.The prevailing strategy involves a three-tiered noise suppression approach:pre-frequency stabilization,arm locking technology,and Time-Delay Interferometry(TDI).Despite pre-stabilization,laser frequency noise typically remains 2 to 3 orders of magnitude above the TDI requirements,making arm locking frequency stabilization a pivotal intermediate step in further noise reduction.Arm locking systems exploit the relative stability of the spacecraft's arm length within the target frequency band to suppress laser frequency noise.While substantial progress has been made in developing arm locking controllers,there remains a relative paucity of studies focused on the optimization of controller parameters.This paper proposes a controller design method based on a bilayer optimization strategy.The bilayer synchronized optimization strategy consists of two layers:a controller structure optimization layer and a parameter optimization layer.The two optimization layers are synchronized through feedback,with the optimized parameters from the parameter optimization layer fed back into the structure optimization layer to refine the controller design iteratively.In the structure optimization layer,the noise rejection capabilities and stability of different controller structures vary significantly.Implementing zero-pole controllers in parallel with integrators can provide enhanced noise suppression without requiring excessive gain.However,it is important to note that while increasing the number of zero-pole pairs and integrator orders can improve laser frequency noise suppression,it also increases the complexity of the controller design,thereby compromising system stability.At the same time,the different values of the controller zero-pole parameters will also affect the above performance,so the controller parameters need to be optimized by an iterative algorithm after the structure is determined.In the parameter optimization layer,accordingly,in order to compare the performance of controllers with different structures,it is necessary to update the controller structure by feeding back to the structure layer after determining the zero-pole parameter,i.e.,forming a two-layer simultaneous optimization strategy in which the controller structure layer and the parameter optimization layer are nested with each other,which can be used to adjust the controller structure through iterative calculations until convergence in a relatively perfect structural model and determine the optimal controller parameters under the structure in a simultaneous manner.In the process of optimization,the objective function for this feedback loop is a linear combination of the amplification at the zero point of the transfer function and the noise suppression ratio at other frequencies to minimize the effect of noise amplification due to the transfer function zeros.The stability and the relative stability of the close-loop system serve as constraints.To ensure absolute system stability,meaning that all poles of the system's closed-loop transfer function are located in the left half-plane of the s-domain,the padéapproximation is applied to address the issue of unsolvable characteristic equation poles caused by delay elements.With the delay margin considered as a posteriori condition due to the real-time variations in arm length,the 60th-order approximation is chosen in this paper,after comparing the effects of different order approximations.Once the absolute stability constraints are established,the relative stability of the system can be constrained by evaluating phase margins.Given that the delay time of the actual laser signal fluctuates in real time,robustness against delay fluctuations should be considered as a posteriori condition,in addition to absolute and relative stability as optimization constraints.The range of these fluctuations can be approximately determined by calculating the system's orbital parameters,which can then be used to define the delay margin.Ultimately,this method yields a controller that meets the noise rejection requirements by synchronously optimizing the structure and parameters of the controller,and meanwhile remains stably throughout the system's operational cycle.The final controller can suppress noise by up to 6 orders of magnitude,with the system maintaining a phase margin of 37°at the first zero point.Simulation analysis of the optimized controller demonstrates that it can suppress laser frequency noise by 5 to 6 orders of magnitude in the frequency band below 0.01 Hz,and by 2 to 3 orders of magnitude in the 0.01 Hz to 1 Hz range(excluding the zeros).However,the system's sensitivity to different noise input positions can lead to the amplification of technical noise.Specifically,below 1 mHz,this amplified technical noise may surpass the laser frequency noise,potentially becoming the dominant factor.While this does not significantly affect the overall noise suppression performance of the system,it does limit further improvements in the noise suppression of the single arm locking system.Finally,the accuracy of the simulated system is verified by solving the frequency domain analytical solution,while further showing that the designed controller meets the system requirements.
作者
苏士豪
马龙
赵欣怡
邵勇斌
尹绪涛
辛明
SU Shihao;MA Long;ZHAO Xinyi;SHAO Yongbin;YIN Xutao;XIN Ming(Sino-European Institute of Aviation Engineering,Civil Aviation University of China,Tianjin 300300,China;School of Electrical and Information Engineering,Tianjin University,Tianjin 300072,China)
出处
《光子学报》
北大核心
2025年第2期85-97,共13页
Acta Photonica Sinica
基金
国家重点研究发展计划(No.2021YFC2201902)。
关键词
空间引力波探测
激光频率噪声抑制
单锁臂控制
双层优化策略
延迟裕度
Space gravitational wave detection
Laser frequency noise suppression
Single arm locking control
Bilayer optimization strategy
Delay margin
