基于数学建模验证的三维振镜激光扫描仪
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摘要
为了提高三维振镜激光扫描系统的稳定性和鲁棒性,进行三维振镜激光扫描系统的数学优化建模,提出一种基于时滞二自由度微分系统的三维振镜激光扫描系统建模方法。采用时滞二自由度微分方程进行三维振镜激光扫描的能量波动系统建模,在激光能量分裂波束的超临界条件下进行激光扫描系统的半正定性分析,求得三维振镜激光扫描系统的幅值裕度和相位裕度,考虑振荡特性对系统的稳定性影响,构建等效的开环传递函数进行激光扫描的稳定性调节,构造Lyapunove泛函,使得三维振镜激光扫描系统处于临界稳定状态,保证了系统的稳定性。数据实证分析表明,该三维振镜激光扫描系统的数学模型是渐进稳定的,系统的收敛性较好。
In order to improve the stability and robustness of the three-dimensional galvanometer laser scanning system,the mathematical optimization modeling of the three-dimensional galvanometer laser scanning system is carried out,and a three-dimensional galvanometer laser scanning system modeling method based on time-delay two-degreeof-freedom differential system is proposed. The energy fluctuation system of three-dimensional galvanometer laser scanning is modeled by two-degree-of-freedom differential equations with time-delay. The semi-positive definite analysis of the laser scanning system is carried out under the super-critical condition of laser energy splitting beam,and the magnitude amplitude and phase margin of three-dimensional galvanometer laser scanning system are obtained. Considering the influence of oscillation characteristics on the stability of the system,construct an equivalent open-loop transfer function to adjust the stability of laser scanning,and construct a Lyapunove functional to make the three-dimensional galvanometer laser scanning system in super-critical stability. The empirical analysis of the data shows that the mathematical model of the three-dimensional galvanometer laser scanning system is asymptotically stable,and the convergence of the system is better.
In order to improve the stability and robustness of the three-dimensional galvanometer laser scanning system,the mathematical optimization modeling of the three-dimensional galvanometer laser scanning system is carried out,and a three-dimensional galvanometer laser scanning system modeling method based on time-delay two-degreeof-freedom differential system is proposed. The energy fluctuation system of three-dimensional galvanometer laser scanning is modeled by two-degree-of-freedom differential equations with time-delay. The semi-positive definite analysis of the laser scanning system is carried out under the super-critical condition of laser energy splitting beam,and the magnitude amplitude and phase margin of three-dimensional galvanometer laser scanning system are obtained. Considering the influence of oscillation characteristics on the stability of the system,construct an equivalent open-loop transfer function to adjust the stability of laser scanning,and construct a Lyapunove functional to make the three-dimensional galvanometer laser scanning system in super-critical stability. The empirical analysis of the data shows that the mathematical model of the three-dimensional galvanometer laser scanning system is asymptotically stable,and the convergence of the system is better.
引文
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[3]杜文博，王小林，朱家健，等．光纤放大器受激布里渊散射效应抑制[J]．强激光与粒子束，2013,25(3):598-602.
[4]王满，文有为，陈智斌．全变差噪声消除问题的半光滑牛顿法[J]．激光技术，2017,41(2):289-295.
[5]赵建君，闫石，陈红叶．利用光栅探测激光信息的迭代算法研究[J]．激光与红外，2015,45(7):770-774.
[6] WANG C,QU Y,PANG Y,et al. A study of relationship between laser intensity and scanning frequency in MEMS scanning system[J]. Infrared Physics&Technology,2015,69:179-183.
[7] PANG Y,ZHANG Y,YANG H,et al. Angle extended linear MEMS scanning system for 3D laser vision sensor[J].Infrared Physics&Technology,2016,78:129-132.
[8]许党朋，张锐，田小程，等．高功率激光驱动器中幅频效应及其抑制技术研究进展[J]．激光与光电子进展，2017,54(2):51-62.
[9]张明，任建文，陈文，等．光折变长周期波导光栅耦合器的设计和分析[J]．光学学报，2015,35(3):313002.
[10]闫广拓，张爱玲，何培栋，等．晶片与光刻胶温度差对波导损耗的影响[J]．光通信技术，2015,12(3):8-11.
[11] YANG P M,LO Y L,CHANG Y H. Laser galvanometric scanning system for improved average power uniformity and larger scanning area[J]. Applied Optics,2016,55(19):5001.
[12] JONSSON M,CEBERG S,NORDSTRM F,et al. Technical evaluation of a laser-based optical surface scanning system for prospective and retrospective breathing adapted computed tomography[J]. Acta Oncologica,2015,54(2):1-5.
[13] ZHANG Haibin,HE Qingbo,KONG Fanrang. Stochastic resonance in an underdamped system with pinning potential for weak signal detection[J]. Sensors,2015,15(9):21169-21195.
[14]赵维谦，任利利，盛忠，等．激光共焦显微光束的偏转扫描[J]．光学精密工程，2016,24(6):1257-1263.
[15]闫伟，陈志华，杜太焦，等．基于相关波前探测算法校正热晕的数值模拟[J]．红外与激光工程，2016,45(10):1032001-1032001(5).
[16] GUAN H,LI J,YU Y,et al. Automated Road Information Extraction From Mobile Laser Scanning Data[J]. IEEE Transactions on Intelligent Transportation Systems,2015,16(1):194-205.
[17] WEN C,LI J,LUO H,et al. Spatial-Related Traffic Sign Inspection for Inventory Purposes Using Mobile Laser Scanning Data[J]. IEEE Transactions on Intelligent Transportation Systems,2015,17(1):27-37.
[18]段良君，祝连庆，娄小平，等．激光扫描测头视觉系统结构参数优化[J]．应用光学，2016,37(2):308-314.
[19] VITO G D,CANTA A,MARMIROLI P,et al. A largefield polarisation-resolved laser scanning microscope:applications to CARS imaging[J]. Journal of Microscopy,2015,260(2):194-9.
[20]寇计萍，邓家先，陈益刚．基于Laplacian塔式分解的自适应图像模糊增强[J]．激光杂志，2015(1):21-26.
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