Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation
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Licai Wang
,
Chunyan Pei
Abstract
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 presented methods 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.
Funding source: The Natural Science Foundation of China
Award Identifier / Grant number: 10202006
Acknowledgments
The research described in this paper was financially supported by the Natural Science Foundation of China (10202006).
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
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- Frontmatter
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- Numerical analysis of geometrical nonlinear aeroelasticity with CFD/CSD method
- Application of moving least squares algorithm for solving systems of Volterra integral equations
- Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative
- Stochastic models with multiplicative noise for economic inequality and mobility
- Fast interaction of Cu2+ with S2O3 2− in aqueous solution
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- The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations
- Distributed consensus of multi-agent systems with increased convergence rate
- Studies on population balance equation involving aggregation and growth terms via symmetries
- Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines
- Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation
- Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical analysis of geometrical nonlinear aeroelasticity with CFD/CSD method
- Application of moving least squares algorithm for solving systems of Volterra integral equations
- Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative
- Stochastic models with multiplicative noise for economic inequality and mobility
- Fast interaction of Cu2+ with S2O3 2− in aqueous solution
- Rotorcraft fuselage/main rotor coupling dynamics modelling and analysis
- Modeling and fault identification of the gear tooth surface wear failure system
- Wavelet-optimized compact finite difference method for convection–diffusion equations
- A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint
- Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps
- The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations
- Distributed consensus of multi-agent systems with increased convergence rate
- Studies on population balance equation involving aggregation and growth terms via symmetries
- Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines
- Feedback control of a nonlinear aeroelastic system with non-semi-simple eigenvalues at the critical point of Hopf bifurcation
- Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator
