两自由度非线性隔振系统的吸引子迁移控制
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摘要
针对非线性隔振系统存在多个不同拓扑特性的吸引子,提出了实现不同吸引子之间迁移控制的方法。对两自由度非线性隔振系统进行全局分岔分析,证明系统存在多个吸引子;利用控制方法实现系统不同吸引子之间的迁移。仿真结果表明:开环加非线性闭环控制方法相比开环、闭环和开环加线性闭环控制方法,传递域是全局的,且不受目标函数的影响,为降低潜艇辐射水声中的低频线谱特征提供了新的思路。
A migration control strategy for a nonlinear vibration isolation system with multiple coexistent attractors was investigated. First,a global bifurcation analysis was carried out and the multiple coexistent attractors were obtained.Then,several control methods were adopted to accomplish the migration of different attractors. The umerical simulations show that the open-plus-nonlinear-closed-loop( OPNCL) control has the global controlling basin property,compared with the open loop,linear feedback and open-plus-closed-loop( OPCL) controls. The results providea novel approach for the line spectrum reduction in the low frequency band of submarine radiated underwater noises.
A migration control strategy for a nonlinear vibration isolation system with multiple coexistent attractors was investigated. First,a global bifurcation analysis was carried out and the multiple coexistent attractors were obtained.Then,several control methods were adopted to accomplish the migration of different attractors. The umerical simulations show that the open-plus-nonlinear-closed-loop( OPNCL) control has the global controlling basin property,compared with the open loop,linear feedback and open-plus-closed-loop( OPCL) controls. The results providea novel approach for the line spectrum reduction in the low frequency band of submarine radiated underwater noises.
引文
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[14]俞翔,朱石坚,刘树勇.PMUCR方法在高维非线性动力学系统中的应用[J].应用力学学报,2006,23(2):232-236.YU Xiang,ZHU Shijan,LIU Shuyong.PMUCR method with applications to high-dimensional nonlinear system[J].Chinese Journal of Applied Mechanics,2006,23(2):232-236.
[2]FENSTERMACHER P R,SWINNEY H L,GOLLUB J P.Dynamical instabilities and transition to chaotic Taylor vortex flow[J].Journal of Fluid Mechanics,1979,94:103-128.
[3]JACKSON E A.The OPCL control method for entrainment,model-resonance,and migration actions on multiple-attractor systems[J].American Institute of Physics,1997,7(4):550-559.
[4]CHEN L Q,LIU Y Z.An open plus closed loop control approach to synchronization of chaotic and hyper-chaotic maps[J].International Journal of Bifurcation and Chaos,2002,12(5):1219-1225.
[5]ATLEE JACKSON E,GROSU I.An open-plus-closed-loop(OPCL)control of complex dynamic systems[J].Physica D,1995,85(1):1-9.
[6]SONG Yunzhong.The open-plus-closed-loop(OPCL)method for chaotic systems with multiple strange attractors[J].Chinese Physics,2007,16(7):1918-2005.
[7]SHEN Jianhe,CHEN Shuhui.An open-plus-closed-loop control for chaotic Mathieu-Duffing oscillator[J].Applied Mathematics and Mechanics(English Edition),2009,30(1):19-21.
[8]HU Tongchun,WU Yongqing,LI Shixing.Lag synchronization between two coupled networks via open-plusclosed-loop and adaptive controls[J].Communications in Theoretical Physics,2016,65(1):33-38.
[9]WANG Jie,WANG Xiaohong.A global control of polynomial chaotic system[J].International Journal of Control,1999,72(10):911-918.
[10]王杰,田沛,陈陈.连续多项式混沌系统的全局控制[J].控制与决策,2000,15(3):309-313.WANG Jie,TIAN Pei,CHEN Chen.Global control of continuous polynomial chaotic system[J].Journal of Control and Decision,2000,15(3):309-313.
[11]CHEN L Q.An open plus nonlinear closed loop control of chaotic oscillators[J].Chinese Physics,2002,11(9):900-904.
[12]TIAN Yuchu,TADM O,TANG Jinyu.Nonlinear openplus-closed-loop(NOPCL)control of dynamic systems[J].Chaos,Solitons and Fractals,2000,11:1029-1035.
[13]徐伟,孙春艳,孙建桥,等.胞映射方法的研究和进展[J].力学进展,2013,43(1):91-100.XU Wei,SUN Chunyan,SUN Jianqiao,et al.Development and study on cell mapping methods[J].Advances in Mechanics,2013,43(1):91-100.
[14]俞翔,朱石坚,刘树勇.PMUCR方法在高维非线性动力学系统中的应用[J].应用力学学报,2006,23(2):232-236.YU Xiang,ZHU Shijan,LIU Shuyong.PMUCR method with applications to high-dimensional nonlinear system[J].Chinese Journal of Applied Mechanics,2006,23(2):232-236.