OPCL控制方法在准零刚度隔振系统中的应用研究
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摘要
为了降低船舶动力机械的振动噪声和线谱信号,解决常见线谱控制方法存在的小能量控制混沌化、变工况下持续混沌化和小振幅混沌化的难题,采用开环加闭环(OPCL)控制方法进行了两自由度准零刚度隔振系统的吸引子迁移控制和广义混沌同步化研究。首先,建立了两自由度准零刚度隔振系统的动力学模型,进行了全局性态分析;然后,利用OPCL控制方法将系统从大振幅吸引子迁移至小振幅吸引子,从而减小了系统振幅;最后,在单向耦合系统中,利用OPCL控制方法施加主动控制,实现了系统在大参数范围内的小振幅广义混沌同步化。结果表明,将OPCL控制方法应用于两自由度准零刚度隔振系统的吸引子迁移控制和广义混沌同步化,能够同时实现隔振系统的线谱控制和振动隔离,从而进一步扩大了OPCL控制方法的应用范围。
In order to reduce the vibration and line spectrum signals of the power machinery of the submarine and solve the problems associated with common methods of controlling line spectrum, such as chaotification with small energy, continuous chaos under varying conditions and chaos of small amplitude, a scheme applying an open-plus-closed-loop(OPCL) control method to migration of attractor and generalized chaotic synchronization using a two-degree-of-freedom vibration isolation system with quasi-zero stiffness(2 DOF-QZS-VIS) is presented. First of all, the dynamic model of a 2 DOF-QZS-VIS is established and its global characteristics in the whole phase space are analyzed. And then, the OPCL control method is used to transfer the system state from a large-amplitude attractor to a small-amplitude attractor to reduce the amplitude of the system. Finally, the OPCL control method is used to achieve the generalized synchronization of chaos in the one-way coupled system with small amplitude within a large parameter range. The results show that the requirements of reduction of line spectrum and vibration isolation of the VIS can be achieved simultaneously by applying the OPCL control method to the migration of attractor and generalized chaotic synchronization of a 2 DOF-QZS-VIS. Thereby the range of application of the OPCL control method is extended.
In order to reduce the vibration and line spectrum signals of the power machinery of the submarine and solve the problems associated with common methods of controlling line spectrum, such as chaotification with small energy, continuous chaos under varying conditions and chaos of small amplitude, a scheme applying an open-plus-closed-loop(OPCL) control method to migration of attractor and generalized chaotic synchronization using a two-degree-of-freedom vibration isolation system with quasi-zero stiffness(2 DOF-QZS-VIS) is presented. First of all, the dynamic model of a 2 DOF-QZS-VIS is established and its global characteristics in the whole phase space are analyzed. And then, the OPCL control method is used to transfer the system state from a large-amplitude attractor to a small-amplitude attractor to reduce the amplitude of the system. Finally, the OPCL control method is used to achieve the generalized synchronization of chaos in the one-way coupled system with small amplitude within a large parameter range. The results show that the requirements of reduction of line spectrum and vibration isolation of the VIS can be achieved simultaneously by applying the OPCL control method to the migration of attractor and generalized chaotic synchronization of a 2 DOF-QZS-VIS. Thereby the range of application of the OPCL control method is extended.
引文
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[2]杨庆超,柴凯,楼京俊,等.柔性基础准零刚度隔振系统动力学特性分析[J].应用力学学报,2018,35(1):70-74.(YANG Qingchao,CHAI Kai,LOU Jingjun,et al.Dynamic characteristic analysis of quasi-zero stiffness vibration isolation system with flexible foundation[J].Chinese journal of applied mechanics,2018,35(1):70-74(in Chinese)).
[3]朱石坚,姜荣俊,何琳.线谱激励的混沌隔振研究[J].海军工程大学学报,2003,15(1):19-22.(ZHU Shijian,JIANG Rongjun,HE Lin.Research on the chaos vibration isolation of line spectra excitation[J].Journal of naval university of engineering,2003,15(1):19-22(in Chinese)).
[4]JACKSON E A,GROSU I.An Open-Plus-Closed-Loop(OPCL)control of complex dynamic systems[J].Physica D:nonlinear phenomena,1995,85(1/2):1-9.
[5]JACKSON E A.The entrainment and migration control of multiple attractor systems[J].Physics letters A,1990,151(9):478-484.
[6]JACKSON E A,HUBLER A.Periodic entrainment of chaotic logistic map dynamics[J].Physica,1990,44(3):407-420.
[7]HTIBLER A,LIISCHER E.Resonant stimulation and control of nonlinear oscillators[J].Naturwissenschaften,1989,76(2):67-69.
[8]SONG Yunzhong.The Open-Plus-Closed Loop(OPCL)method for chaotic systems with multiple strange attractors[J].Chinese physics,2007,16(7):1918-1922.
[9]SHEN Jianhe,CHEN Shuhui.An Open-Plus-Closed-Loop control for chaotic Mathieu-Duffing oscillator[J].Applied mathematics and mechanics,2009,30(1):19-27.
[10]YANG Lixin,JIANG Jun,LIU Xiaojun.Synchronization of fractional-order colored dynamical networks via Open-Plus-Closed-Loop control[J].Physica A:statistical mechanics and its applications,2016,443:200-211.
[11]WU Zhaoyan,LENG Hui.Complex hybrid projective synchronization of complex-variable dynamical networks via Open-Plus-Closed-Loop control[J].Journal of the Franklin institute,2017,354(2):689-701.
[12]CARRELLA A,BRENMAN M J,WATERS T P.Static analysis of a passive vibration isolator with quasi-zero-stiffness characteristic[J].Journal of sound and vibration,2007,301(3/5):678-689.
[13]朱石坚,徐道临.舰船机械隔振系统线谱混沌化控制[M].北京:国防工业出版社,2014.(ZHU Shijian,XU Daolin.Line spectra chaotification for vibration isolation system of onboard machinery[M].Beijing:National Defense Industry Press,2014(in Chinese)).
[14]GROSU I,PADMANABAN E,ROY P K,et al.Designing coupling for synchronization and amplification of chaos[J].Physical review letters,2008,100(23):234102.