基于LMI的分段线性系统共存吸引子转迁控制研究

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摘要以一类两自由度含间隙分段线性系统为研究对象，利用线性矩阵不等式(LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。首先，在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别，并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。其次，基于线性矩阵不等式(LMI)和Lyapunov理论，并利用系统的向量场信息和S-procedure，将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。最后利用数值方法验证了本文所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

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	李得洋1
	2
	吴少培2
	李国芳2
	丁旺才2
	丁杰2
	俞力洋2
	卫晓娟3

关键词 ：分段线性系统, 共存吸引子, 线性矩阵不等式, 吸引子转迁控制

Abstract：The linear matrix inequality (LMI) and linear feedback method are used to migration the attractor under the guidance of the desired target orbit in a class of a two-degree-of-freedom piecewise-linearity system with clearance. Firstly, the coexisting attractors are identified on the state plane by cell mapping method. Meanwhile, the stability and transition mechanism of the coexisting attractors are studied based on Poincaré mapping and Lyapunov exponent. Secondly, according to the linear matrix inequality and Lyapunov theory, the stability of linear feedback control and the solution for feedback gain matrix are transformed into LMI description via the vector field information and s-procedure. Finally, the linear feedback controller and its gain matrix selection method are validated by numerical simulation.

Key words： Piecewise-linearity System coexistent attractor The linear matrix inequality Attractor migration control

收稿日期: 2022-10-13 出版日期: 2023-10-15

引用本文:

李得洋1，2，吴少培2，李国芳2,丁旺才2,丁杰2，俞力洋2，卫晓娟3. 基于LMI的分段线性系统共存吸引子转迁控制研究[J]. 振动与冲击, 2023, 42(19): 30-39.
LI Deyang1,2, WU Shaopei2, LI Guofang2, DING Wangcai2, DING Jie2, YU Liyang2, WEI Xiaojuan3. LMI-based transfer control for coexisting attractors in piecewise linear system. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(19): 30-39.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I19/30

[1] V. I. Babitsky. Theory of Vibro-Impact Systems and Applications [M]. Springer. 1999.
[2] THOMSEN P G, TRUE H. Non-smooth Problems in Vehicle Systems Dynamics [M]. Springer-Verlag Berlin Heidelberg, 2010.
[3]赵武,张鸿斌,孙超凡. 三次方阻尼和间隙变化下的冷轧垂直颤振研究[J].振动与冲击, 2021, 40(24): 82-89+98.
ZHAO Wu，ZHANG Hongbin，SUN Chaofan. A study on vertical flutter of cold rolling mill with cubic damping and gap variation. Journal of vibration and shock, 2021, 40(24): 82-89.
[4] Shaw S W , Holmes P J . A periodically forced piecewise linear oscillator[J]. Journal of Sound and Vibration, 1983, 90(1):129-155.
[5] HU H. Simulation complexities in the dynamics of a continuously piecewise-linear oscillator[J]. Chaos, Solitons & Fractals, 1995, 5(11): 2201-2212.
[6] Ma Y, Ing J, Banerjee S, et al. The nature of the normal form map for soft impacting systems[J]. International Journal of Non-Linear Mechanics, 2008, 43(6): 504-513.
[7] Jiang H B, Wiercigroch M. Geometrical insight into non-smooth bifurcations of a soft impact oscillator[J]. IMA Journal of Applied Mathematics, 2016, 81(4): 662–678.
[8] MIAO P, DENGHUI L, Yue Y, et al. Generalized Hopf bifurcation of a non-smooth railway wheelset system [J]. Nonlinear Dynamics, 2020, 100:3277-3293.
[9] LEINE R I, NIJMEIJER H. Dynamics and bifurcations of non-smooth mechanical systems[M]. Springer Berlin Heidelberg, 2004.
[10] 王强, 刘永葆, 徐慧东. 外圈故障滚动轴承周期运动Neimark-Sacker分岔研究[J]. 船舶力学, 2017, 21(05): 621-632.
WANG Qiang, LIU Yong-bao, XU Hui-dong. Neimark-Sacker bifurcation of rolling bearing system with fault in outer ring[J].Journal of Ship Mechanics, 2017, 21(05): 621-632.
[11] 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. Analysis of chattering- impact motions of a two-degree-of-freedom system with clearance and soft impacts[J]. Journal of vibration and shock, 2015, 34(15): 195-200.
[12] Guofang L , Ding W , Wu S . Global Behavior of a Vibro-Impact System With Multiple Nonsmooth Mechanical Factors[J]. Journal of Computational and Nonlinear Dynamics, 2017.
[13] 林何,洪灵,刘霞,胥光申. 功率分流齿轮传动参数空间解域界及吸引域全局特性[J].振动工程学报, 2021, 34(02): 235-242.
LIN He, HONG Ling, LIU Xia.Global characteristics of basin of attraction and parameterized solution domain of power -split gear transmission[J]. Journal of Vibration Engineering,2021,34(02):235-242.
[14] 吴鑫,李高磊,乐源.单自由度碰撞振动系统的奇异非混沌动力学和多稳态共存[J].振动与冲击,2022,41(02):45-52+86.
WU Xin, LI Gaolei, YUE Yuan. Strange nonchaotic dynamics and multistable coexistence phenomena of a single-degree-of-freedom vibro-impact system[J]. Journal of vibration and shock, 2022, 41(2): 45-52.
[15] Yue X L, Xu W, Wang L. Global analysis of boundary and interior crises in an elastic impact scillator[J]. Communications in Nonlinear Science and Numerical Simulation, 2013, 18(12): 3567-3574
[16] 张惠,丁旺才,李险峰.分段光滑碰撞振动系统吸引域结构变化机理研究[J].振动与冲击,2019,38(18):141-147.
ZHANG Hui, DING Wangcai, LI Xianfeng. Structure change mechanism of the attractor basin in a piecewise-smooth vibro-impact system[J]. Journal of vibration and shock, 2019, 38(18): 141-147.
[17] Yunzhu Shen, Yongxiang Zhang, Sajad Jafari. Coexistence of strange nonchaotic attractors in a quasi-periodically forced dynamical map[J]. International Journal of Bifurcation and Chaos, 2020,30(13):2050183.
[18] Liu Y, Chávez J P. Controlling coexisting attractors of an impacting system via linear augmentation[J]. Physica D: Nonlinear Phenomena, 2017, 348: 1-11.
[19] 李得洋,丁旺才,丁杰,卫晓娟.两自由度含弹性约束碰撞振动系统共存吸引子转迁控制研究[J].振动工程学报,2021,34(01):176-184.
Li deyang ,Ding wangcai ,Ding jie .Attractor migration control of a two-degree-of-freedom vibro-impact system with soft constraints[J]. Journal of Vibration Engineering, 2021,34(01):176-184.
[20] 秦卫阳, 任兴民, 杨永锋. 含裂纹转子系统稳定性与分叉数值分析方法[J]. 振动工程学报, 2004, 17(4): 433-437.
Qin Weiyang, Ren Xingmin, Yang Yongfeng. Analysis on Stability and Bifurcation of Cracked Jeffcott Rotor[J]. Journal of Vibration Engineering, 2004, 17(4): 433-437.