Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation

doi:10.1515/ijnsns-2019-0020

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	Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation
	L. C. Wang; Y. D. Chen; C. Y. Pei; L. N. Liu and S. H. Chen
刊名	International Journal of Nonlinear Sciences and Numerical Simulation
	2021
卷号	22 期号:3-4 页码:461-478
ISSN号	1565-1339
DOI	10.1515/ijnsns-2019-0020
英文摘要	The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presentedmethods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.
URL标识	查看原文
内容类型	期刊论文
源URL	[http://ir.ciomp.ac.cn/handle/181722/65246]
专题	中国科学院长春光学精密机械与物理研究所
推荐引用方式 GB/T 7714	L. C. Wang,Y. D. Chen,C. Y. Pei,et al. Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2021,22(3-4):461-478.
APA	L. C. Wang,Y. D. Chen,C. Y. Pei,&L. N. Liu and S. H. Chen.(2021).Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation.International Journal of Nonlinear Sciences and Numerical Simulation,22(3-4),461-478.
MLA	L. C. Wang,et al."Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation".International Journal of Nonlinear Sciences and Numerical Simulation 22.3-4(2021):461-478.