An Intermittent Chaos Control Method for a Class of Symmetric Impact Systems
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摘要: 研究了对称碰撞系统的间歇混沌控制方法,将Hopf分岔控制思想应用于该系统上,对该类系统的混沌控制提供一个新的控制方法.这里以两自由度弹性双碰系统为探究对象,首先,建立两自由度弹性双碰系统的力学模型,并根据其运动特点将其分成4个阶段,建立了合适的Poincaré映射;然后,取定一个合适的定相位面,施加间歇线性控制律,并构建施加控制后的映射,根据映射的稳定性判据得到该系统混沌控制的显式条件;最后,分别对原系统和控制系统进行了数值模拟.计算结果表明,该控制方法能够很好地控制原系统的混沌运动,实现了预期目的,验证了该控制方法在弹性系统上的有效应用.该控制方法有利于提高系统的运行稳定性和使用寿命,具有一定的实际意义.
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关键词:
- 混沌控制 /
- Poincaré映射 /
- 间歇线性控制 /
- 显式条件
Abstract: An intermittent chaos control method for symmetric impact systems was studied. The Hopf bifurcation control was applied to make a new control method for chaos control of such systems. The 2DOF elastic doubleimpact system was considered. Firstly, the mechanical model for the 2DOF system was built and its motion was divided into 4 stages according to the dynamic characteristics. Then, an appropriate Poincaré mapping was established; a suitable fixed phase plane was chosen, a linear controller was applied to the section to get the mapping with control, and the chaotic control explicit condition was obtained according to the stability criterion. Finally, numerical analyses of the original system and the controlled system were carried out respectively. The numerical results show that, the proposed method controls the chaos movement of the original system well, to achieve the desired goal and verify the correctness of the method. The method, with practical significance, is helpful to improve the stability, working efficiency and service life of the system.-
Key words:
- chaos control /
- Poincaré mapping /
- intermittent linear control /
- explicit condition
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[1] OTT E, GREBOGI C, YORKE J. Controlling chaos[J]. Physical Review Letters,1990,64(11): 1196-1199. [2] 杨凌, 刘曾荣. OGY方法的改进及证明[J]. 应用数学和力学, 1998,19(1): 1-7.(YANG Ling, LIU Zengrong. An improvement and proof of OGY method[J]. Applied Mathematics and Mechanics,1998,19(1): 1-7.(in Chinese)) [3] 张晓明, 彭建华, 张入元. 利用线性可逆变换增强延迟反馈方法控制混沌的有效性[J]. 物理学报, 2005,54(7): 3019-3026.(ZHANG Xiaoming, PENG Jianhua, ZHANG Ruyuan. Improving the efficiency of time-delayed feedback control of chaos through linear invertible transform[J]. Acta Physica Sinica,2005,54(7): 3019-3026.(in Chinese)) [4] 马莉. 一类双自由度含间隙振动系统的混沌碰撞运动及控制[J]. 兰州交通大学学报(自然科学版), 2007,26(6): 136-139.(MA Li. Controlling chaotic motions for a two-degree-of-freedom vibratory system with a clearance[J]. Journal of Lanzhou Jiaotong University(Natural Sciences),2007,〖STHZ〗 26(6):136-139.(in Chinese)) [5] 李彬, 郝鹏, 孟增, 等. 基于改进自适应混沌控制的逆可靠度分析方法[J]. 应用数学和力学, 2017,38(9): 979-987.(LI Bin, HAO Peng, MENG Zeng, et al. An improved adaptive chaos control method for inverse reliability analysis[J]. Applied Mathematics and Mechanics,2017,38(9):979-987.(in Chinese)) [6] 吕小红. 外加正弦力抑制小型打桩机的分岔与混沌[J]. 兰州交通大学学报, 2015,34(4): 146-150.(L Xiaohong. Bifurcations and chaos of small pile driver controlled by external sine force[J]. Journal of Lanzhou Jiaotong University,2015,34(4): 146-150.(in Chinese)) [7] 吕小红, 朱喜锋, 罗冠炜. 含双侧约束碰撞振动系统的OGY混沌控制[J]. 机械科学与技术, 2016,35(4):531-534.(Lü Xiaohong, ZHU Xifeng, LUO Guanwei. Chaos control of a vibro-impact system with two-sided constraints based on OGY method[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(4): 531-534.(in Chinese)) [8] 朱喜锋, 罗冠炜. 两自由度含间隙弹性碰撞系统的颤碰运动分析[J]. 振动与冲击, 2015,34(15): 195-200.(ZHU Xifeng, LUO Guanwei. Chattering-impact motion of a 2-DOF system with clearance and soft impacts[J]. Journal of Vibration and Shock,2015,34(15): 195-200.(in Chinese)) [9] 张惠, 丁旺才, 李飞. 两自由度含间隙和预紧弹簧碰撞振动系统动力学分析[J]. 工程力学, 2011,28(3): 209-217.(ZHANG Hui, DING Wangcai, LI Fei. Dynamics of a two-degree-of-freedom impact system with clearance and pre-compressed spring[J]. Engineering Mechanics, 2011,28(3): 209-217.(in Chinese)) [10] LIU Yang, CHAVEZ J P. Controlling coexisting attractors of an impacting system via linear augmentation[J]. Physica D: Nonlinear Phenomena,2017,348: 1-11. [11] 张文娟, 俞建宁, 张建刚, 等. 利用非线性反馈控制一类振动系统的振动[J]. 重庆理工大学学报(自然科学), 2013,27(1): 27-31.(ZHANG Wenjuan, YU Jianning, ZHANG Jiangang, et al. Using nonlinear feedback control for the vibration of a nonlinear vibration system[J]. Journal of Chongqing University of Technology(Natural Science),2013,27(1): 27-31.(in Chinese)) [12] WEN G L, CHEN S J, JIN Q T. A new criterion of period-doubling bifurcation in maps and its application to an inertial impact shaker[J]. Journal of Sound and Vibration,2008,311(1): 212-223. [13] 吴少培, 李国芳, 丁旺才. 含间隙运动副模型的机械动力学分析[J]. 兰州交通大学学报, 2016,35(4): 111-116.(WU Shaopei, LI Guofang, DING Wangcai. Dynamics analysis of mechanisms with joint clearance[J]. Journal of Lanzhou Jiaotong University, 2016,35(4): 111-116.(in Chinese)) [14] 郭树卓, 靳玲. 轮轨碰撞系统的分岔与混沌研究[J]. 兰州交通大学学报, 2012,31(1): 153-157.(GUO Shuzhuo, JIN Ling. Research on bifurcation and chaos of wheel-rail collision system[J]. Journal of Lanzhou Jiaotong University,2012,31(1): 153-157.(in Chinese)) [15] 张晨旭, 杨晓东, 张伟. 含间隙齿轮传动系统的非线性动力学特性的研究[J]. 动力学与控制学报, 2016,14(2): 117-121.(ZHANG Chenxu, YANG Xiaodong, ZHANG Wei. Study on non-linear dynamics of gear transmission system with clearance[J]. Journal of Dynamics and Control,2016,14(2): 117-121.(in Chinese)) [16] 周鹏. 非光滑系统的动力学及其在车辆工程中的应用[D]. 硕士学位论文. 兰州: 兰州交通大学, 2014.(ZHOU Peng. The dynamics of nonsmooth system and its application in vehicle engineering[D]. Master Thesis. Lanzhou: Lanzhou Jiaotong University, 2014.(in Chinese)) [17] LASALLE J P.The Stability and Control of Discrete Processes[M]. New York: Springer-Verlag, 1986.
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