Model Reduction and Active Control of a Flexible Beam Using Internal Balance Technique

XIE Yong; ZHAO Tong; CAI Guo-ping

doi:10.3879/j.issn.1000-0887.2011.08.005

Volume 32 Issue 8

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(8): 946-955

XIE Yong, ZHAO Tong, CAI Guo-ping. Model Reduction and Active Control of a Flexible Beam Using Internal Balance Technique[J]. Applied Mathematics and Mechanics, 2011, 32(8): 946-955. doi: 10.3879/j.issn.1000-0887.2011.08.005

Citation:

PDF( 1627 KB)

Model Reduction and Active Control of a Flexible Beam Using Internal Balance Technique

doi: 10.3879/j.issn.1000-0887.2011.08.005

Department of Engineering Mechanics, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

Received Date: 2011-01-14
Rev Recd Date: 2011-06-17
Publish Date: 2011-08-15

Abstract

Abstract

The internal balance technique was effective for model reduction in flexible structures,especially ones with dense frequencies.However,due to the difficulty in extracting internal balance modal coordinates from physical sensor readings,research so far on this topic has been mostly theo retic and little on experiment or engineering applications.The internal balance method theo retically as well as experimentally was studied,and further an active controller based on the reduction model was designed.The research works on a DSP TMS320F2812-based experiment system with a flexible beam and brings forward an approximating approach to access internal balance modal coordinates.Simulation and test results have proven the proposed approximating approach feasible and effective,and the designed controller successful in restraining the beam vibration.
- flexible beam,
- internal balance model reduction,
- active control,
- experiment

FullText(HTML)

References(16)

References

[1]	缪炳祺, 曲广吉, 程道生. 柔性航天器的动力学建模问题[J]. 中国空间科学技术, 1999, 19(5): 35-40. (MIAO Bing-qi, QU Guang-ji, CHENG Dao-sheng. A study on dynamics modeling of flexible spacecraft[J]. Chinese Space Science and Technology, 1999, 19(5): 35-40. (in Chinese))
[2]	Hughes P C. Modal identities for elastic bodies with application to vehicle dynamics and control[J]. Journal of Applied Mechanics, 1980, 47(1): 177-184. doi: 10.1115/1.3153599
[3]	Skelton R E, Yousuff A. Component cost analysis of large scale systems[J]. International Journal of Control, 1983, 37(2): 285-304. doi: 10.1080/00207178308932973
[4]	Skelton R E, Gregory C Z. Measurement feedback and model reduction by modal cost analysis[C]Proceedings of the Joint Automatic Control Conference. USA: Denver, 1979: 211-218.
[5]	Moore B C. Principal component analysis in linear system: controllability, observability and model reduction[J]. IEEE Transaction on Automatic Control, 1981, 26(1): 17-31. doi: 10.1109/TAC.1981.1102568
[6]	Gregory C Z. Reduction of large flexible model using internal balancing theory[J]. Journal of Guidance, 1984, 7(6): 725-732. doi: 10.2514/3.19919
[7]	Jonckheere E A, Opdencker Ph. Singular value analysis balancing and model reduction of large space structures[C]American Control Conference. San Diego, CA, USA, 1984: 141-149.
[8]	Jonckheere E A. Principal component analysis of flexible system—open-loop case[J]. IEEE Transaction on Automatic Control, 1984, 29(12): 1059-1097.
[9]	Gawronski W, Williams T. Model reduction for flexible space structures[J]. Journal of Guidance, 1991, 14(1): 68-76. doi: 10.2514/3.20606
[10]	Williams T. Closed-form grammians and model reduction for flexible space structures[J]. IEEE Transaction on Automatic Control, 1990, 35(3): 379-382. doi: 10.1109/9.50365
[11]	Zhou K, Salomon G, Wu E. Balanced realization and model reduction for unstable system[J]. International Journal Robust Nonlinear Control, 1999, 9(3): 183-198. doi: 10.1002/(SICI)1099-1239(199903)9:3<183::AID-RNC399>3.0.CO;2-E
[12]	Laub A J. Computation of balancing transformations[C]Proceedings of the Joint Automatic Control Conference. San Francisco, CA, USA, FA8-E, 1980.
[13]	Bartels R H, Stewart G W. Solution of the matrix equation AX+XB=C [J]. Communications of the ACM, 1972, 15(9): 820-826. doi: 10.1145/361573.361582
[14]	陈龙祥. 柔性结构振动的时滞反馈控制及其实验研究[D]. 博士学位论文. 上海: 上海交通大学, 2008. (CHEN Long-xiang. Delayed feedback control and experiment study of flexible structures[D]. PhD Dissertation. Shanghai: Shanghai Jiao Tong University, 2008. (in Chinese))
[15]	韩京清, 袁露林. 跟踪微分器的离散形式[J]. 系统科学与数学, 1999, 19(3): 268-273. (HAN Jing-qing, YUAN Lu-lin. The discrete form of tracking-differentiator[J]. Journal of Systems Science and Mathematical Sciences, 1999, 19(3): 268-273. (in Chinese))
[16]	CHEN Long-xiang, CAI Guo-ping, PAN Ji. Experimental study of delayed feedback control for a flexible plate[J]. Journal of Sound and Vibration, 2009, 322(4/5): 629-651. doi: 10.1016/j.jsv.2008.11.045