粘弹性板混沌振动的输出变量反馈线性化控制

陈立群; 程昌钧

粘弹性板混沌振动的输出变量反馈线性化控制

陈立群¹,
程昌钧^1,2

1.
上海大学, 上海市应用数学和力学研究所, 上海200072;
2.
上海大学力学系, 上海200072

基金项目: 国家自然科学基金(19727027);中国博士后科学基金(98JC14032);上海市科技发展基金(98SHB1417)

详细信息

作者简介:
陈立群(1963~ ),男,教授,博士.

中图分类号: O322
计量
- 文章访问数: 2347
- HTML全文浏览量: 107
- PDF下载量: 621
- 被引次数: 0
出版历程
- 收稿日期: 1998-07-22
- 修回日期: 1999-03-30
- 刊出日期: 1999-12-15

Controlling Chaotic Oscillations of Viscoelastic Plates by the Linearization via Output Feedback

Chen Liqun¹,
Cheng Changjun^1,2

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China;
2.
Department of Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 研究了粘弹性板混沌振动的控制问题。应用非线性系统精确线性化控制理论导出了一类非仿射控制系统的非线性反馈控制律。建立了描述材料非线性的粘弹性板运动的数学模型并利用Calerkin方法进行简化。采用相空间曲线和频率谱密度函数说明了在特定参数条件下系统将出现混沌振动,并以位移为输出变量将混沌振动控制为给定的周期运动。
- 控制混沌 /
- 输出变量反馈线性化 /
- 粘弹性板 /
- 非线性
Abstract: Controlling chaotic oscillations of viscoelastic plates is investigated in this paper.Based on the exact linearization method in nonlinear system control theory,a nonlinear feedback control law is presented for a class of non-affine control systems.The mathematical model describing motion of nonlinear viscoelastic plates is established,and it is simplified by the Galerkin method.The phase space portrait and the power spectrum are employed to demonstrate chaos in the system.The deflection is treated as an output,and is controlled to given periodic goals.
- controlling chaos /
- linearization via output feedback /
- viscoelastic plate /
- nonlinearity

HTML全文

参考文献(14)

[1]	Shinbrot T, Grebogi C, Ott E, et al. Using small perturbations to control chaos[J]. Nature,1993,363(3):411～417.
[2]	Lindner J F, Ditto W L. Removal, suppression, and control of chaos by nonlinear design[J]. Rev Appl Mech,1995,45(12):795～807.
[3]	胡海岩,力学系统混沌的主动控制[J]. 力学进展,1996,26(4):453～463.
[4]	陈立群,刘延柱. 控制混沌的研究现状与展望[J]. 上海交通大学学报,1998,32(1):108～114.
[5]	Hall E K, Hanagud S V. Control of nonlinear structural dynamic systems: chaotic vibrations[J]. J Guidance Cotrol Dynamics,1993,16:470～476.
[6]	Alvarez-Gallegos J. Nonlinear regulation of a Lorenz system by feedback linearization techniques[J]. Dynam Cont,1994,4(2):277～298.
[7]	Yu X. Controlling chaos using input-output linearization approach[J]. Int J Bifur Chaos,1997,7(8):1659～1664.
[8]	陈立群,刘延柱. 用精确线性化控制Lorenz混沌[J]. 应用数学和力学,1998,19(1):63～69.
[9]	Suire G. Cederbaum G. Periodic and chaotic behavior of viscoelastic nonlinear (elastic) bars under harmonic excitations[J]. Int J Mech Sci,1995,37(7):753～772.
[10]	Ding R. The dynamic analysis of viscoelastic structure[D]. Lanzhou University: Doctoral Dissertation,1996,56～72.
[11]	Argyris J. Chaotic vibrations of a nonlinear viscoelastic beam[J]. Chaos, Solitons, Fractals,1996,7(1):151～163.
[12]	张能辉. 粘弹性板壳结构的静动力分析[D]. 博士学位论文,兰州:兰州大学,1997,39～99.
[13]	Isidori A. Nonlinear Control Systems[M]. New York: Springer-Verlag,1989,156～172.
[14]	Touati D. Cederbaum G. Dynamic stability of nonlinear viscoelastic plate[J]. Int J Solids Struct,1994,31(17):2367～2376.